0321_1032
Counting sequence:
1, 1, 2, 6, 22, 89, 381, 1696, 7781, 36572, 175277, 853410, 4209376, 20988122, 105611537, 535638107, 2735303546, 14052318081, 72576606964, 376616279797, 1962646712114, 10267016702607, 53895142688122, 283807158368210, 1498814755776705, 7936344718181112, 42126008006042152, 224107780692072667, 1194727534919520715, 6381491115295466765, 34147539809674959051, 183032793143464260058, 982616083490440149184, 5283015487751599026270, 28443586396635718275494, 153340211415040987386363, 827684383873305999315780, 4472814607156698124909148, 24197877589473740641311162, 131047527967041143291732804, 710415487340274404130193623, 3854842259859593204491614768, 20935895118297109855038307220, 113801693708552958584926065319, 619100283073677586145586922079, 3370639793619142838758248697188, 18364867053635351493198268875970, 100132105010369981284602913597540, 546331084709183792155611409438031, 2982793537106174605376607710774808, 16295348349815214138786686342645103, 89077172384856173767081316201763168, 487215721429608735330476910622825553, 2666359028244640150695105857388293743, 14599881495993745183130163964303045587, 79984311982165625120087302076410582256, 438406465556000009070524667032607361607, 2404130564166785834625721730151135619712, 13189879312881735090352204706269500459731, 72396630207050558211832173949329416470149, 397542967348089315951547292392578121588062, 2183894994041059915175987113553259874162482, 12002050554084516116966799647490008474323520, 65985653791240643463075981407847701538565219, 362918067466629583013198126157006623893015717, 1996767590190158393756462112331881086669224955, 10990094287514771742179326190774845175683521452, 60509785779853871477773677060148777540777077328, 333269558224862374477003577692960443473791291610, 1836146128371920350494379692136256882578614367768, 10119436236675113553217791917883221941207393477599, 55787765578044268896384454021418899568821793245347, 307646120979237594947764148658307876199628995135430, 1697032491117414542044324457220996903749083983860688, 9363790011483067005420205189409817401368646093620142, 51681209055482287783875629020780525861732941558547866, 285318533542305760727343900670887236876191494512992198, 1575580409501868531852776092597622066921537055742498425, 8702850094413415999079549099395945379902565096734995437, 48082823044038029469169860432921834316457747753051751587, 265719377963952146712552172789649152577423146752355129463, 1468786596041221898929834958590410003069679639250165892369, 8120707450830872376756191550788358119254709201587095511272, 44908267373363930590751997156269760352323615613452654753802, 248401188437134467754627542124649905782276108322904545928414, 1374275242807331688425231420014324419239992603718982482559661, 7604738557552716156580386424231742733114905755171433445549224, 42090420857263381192531874532216384034537636743943430610191814, 233006823103906644200422880459226361845439242282843171642669023, 1290144761215931080911710396066664958430549907023572193651477537, 7144811770968667481378014545656873893259384913409655144496012778, 39575267311948353143765940720152956383039278193579416928245990030, 219248116518653719463970863675403515896542627397438621423247676150, 1214856899184842110869818154421260253518695343807743774412141659924, 6732710824119213048804962757939819797158387602018712615957143394929, 37318895363880911059341062056247102009426734591812596507859219303078, 206890251871266564392965813834320082452099327112961556537078851602575, 1147155263872001466637467068758034565047657963495811554659031657665516, 6361709661594123891322707742514525826881467071012100180838455919140343, 35285277943880850411448155851666068051580373694247142796564645617354951, 195740154230696177131521702567160635847499234135843856951110163064946553
Implicit equation for the generating function in Maple syntax:
x*(x-1)*(16*x^8-92*x^7+228*x^6-343*x^5+345*x^4-222*x^3+100*x^2-27*x+3)*(2*x-1)^2*F(x)^8-(32*x^12-320*x^11+1432*x^10-3852*x^9+7040*x^8-9269*x^7+8950*x^6-6305*x^5+3206*x^4-1111*x^3+197*x^2-x-3)*(2*x-1)^2*F(x)^7+(2*x-1)*(32*x^15-432*x^14+2768*x^13-11136*x^12+31286*x^11-64773*x^10+101885*x^9-123424*x^8+115026*x^7-81514*x^6+42660*x^5-14927*x^4+2235*x^3+556*x^2-288*x+34)*F(x)^6-(2*x-1)*(64*x^15-880*x^14+5584*x^13-21768*x^12+58508*x^11-115027*x^10+170159*x^9-190187*x^8+157491*x^7-90705*x^6+27461*x^5+7657*x^4-14059*x^3+7275*x^2-1748*x+162)*F(x)^5+(16*x^17-176*x^16+728*x^15-816*x^14-4623*x^13+24411*x^12-57292*x^11+71304*x^10-12983*x^9-134003*x^8+305614*x^7-403001*x^6+374932*x^5-251513*x^4+116646*x^3-34673*x^2+5843*x-420)*F(x)^4+(-80*x^15+1128*x^14-7732*x^13+34582*x^12-113186*x^11+284672*x^10-560167*x^9+869521*x^8-1074044*x^7+1061462*x^6-829369*x^5+492560*x^4-208617*x^3+57889*x^2-9257*x+639)*F(x)^3+(x-1)*(8*x^15-88*x^14+382*x^13-216*x^12-6245*x^11+37395*x^10-120348*x^9+260401*x^8-411296*x^7+494948*x^6-457144*x^5+313396*x^4-149465*x^3+45555*x^2-7826*x+570)*F(x)^2-(x-1)*(44*x^13-384*x^12+1001*x^11+1486*x^10-17219*x^9+57506*x^8-119599*x^7+176555*x^6-188454*x^5+141157*x^4-70504*x^3+21931*x^2-3792*x+276)*F(x)+(x^13-3*x^12-17*x^11+99*x^10-163*x^9-195*x^8+2101*x^7-7043*x^6+13253*x^5-14693*x^4+9594*x^3-3586*x^2+704*x-56)*(x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
x \left(x -1\right) \left(16 x^{8}-92 x^{7}+228 x^{6}-343 x^{5}+345 x^{4}-222 x^{3}+100 x^{2}-27 x +3\right) \left(2 x -1\right)^{2} F \! \left(x \right)^{8}-\left(32 x^{12}-320 x^{11}+1432 x^{10}-3852 x^{9}+7040 x^{8}-9269 x^{7}+8950 x^{6}-6305 x^{5}+3206 x^{4}-1111 x^{3}+197 x^{2}-x -3\right) \left(2 x -1\right)^{2} F \! \left(x \right)^{7}+\left(2 x -1\right) \left(32 x^{15}-432 x^{14}+2768 x^{13}-11136 x^{12}+31286 x^{11}-64773 x^{10}+101885 x^{9}-123424 x^{8}+115026 x^{7}-81514 x^{6}+42660 x^{5}-14927 x^{4}+2235 x^{3}+556 x^{2}-288 x +34\right) F \! \left(x \right)^{6}-\left(2 x -1\right) \left(64 x^{15}-880 x^{14}+5584 x^{13}-21768 x^{12}+58508 x^{11}-115027 x^{10}+170159 x^{9}-190187 x^{8}+157491 x^{7}-90705 x^{6}+27461 x^{5}+7657 x^{4}-14059 x^{3}+7275 x^{2}-1748 x +162\right) F \! \left(x \right)^{5}+\left(16 x^{17}-176 x^{16}+728 x^{15}-816 x^{14}-4623 x^{13}+24411 x^{12}-57292 x^{11}+71304 x^{10}-12983 x^{9}-134003 x^{8}+305614 x^{7}-403001 x^{6}+374932 x^{5}-251513 x^{4}+116646 x^{3}-34673 x^{2}+5843 x -420\right) F \! \left(x \right)^{4}+\left(-80 x^{15}+1128 x^{14}-7732 x^{13}+34582 x^{12}-113186 x^{11}+284672 x^{10}-560167 x^{9}+869521 x^{8}-1074044 x^{7}+1061462 x^{6}-829369 x^{5}+492560 x^{4}-208617 x^{3}+57889 x^{2}-9257 x +639\right) F \! \left(x \right)^{3}+\left(x -1\right) \left(8 x^{15}-88 x^{14}+382 x^{13}-216 x^{12}-6245 x^{11}+37395 x^{10}-120348 x^{9}+260401 x^{8}-411296 x^{7}+494948 x^{6}-457144 x^{5}+313396 x^{4}-149465 x^{3}+45555 x^{2}-7826 x +570\right) F \! \left(x \right)^{2}-\left(x -1\right) \left(44 x^{13}-384 x^{12}+1001 x^{11}+1486 x^{10}-17219 x^{9}+57506 x^{8}-119599 x^{7}+176555 x^{6}-188454 x^{5}+141157 x^{4}-70504 x^{3}+21931 x^{2}-3792 x +276\right) F \! \left(x \right)+\left(x^{13}-3 x^{12}-17 x^{11}+99 x^{10}-163 x^{9}-195 x^{8}+2101 x^{7}-7043 x^{6}+13253 x^{5}-14693 x^{4}+9594 x^{3}-3586 x^{2}+704 x -56\right) \left(x -1\right)^{2} = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 22
a(5) = 89
a(6) = 381
a(7) = 1696
a(8) = 7781
a(9) = 36572
a(10) = 175277
a(11) = 853410
a(12) = 4209376
a(13) = 20988122
a(14) = 105611537
a(15) = 535638107
a(16) = 2735303546
a(17) = 14052318081
a(18) = 72576606964
a(19) = 376616279797
a(20) = 1962646712114
a(21) = 10267016702607
a(22) = 53895142688122
a(23) = 283807158368210
a(24) = 1498814755776705
a(25) = 7936344718181112
a(26) = 42126008006042152
a(27) = 224107780692072667
a(28) = 1194727534919520715
a(29) = 6381491115295466765
a(30) = 34147539809674959051
a(31) = 183032793143464260058
a(32) = 982616083490440149184
a(33) = 5283015487751599026270
a(34) = 28443586396635718275494
a(35) = 153340211415040987386363
a(36) = 827684383873305999315780
a(37) = 4472814607156698124909148
a(38) = 24197877589473740641311162
a(39) = 131047527967041143291732804
a(40) = 710415487340274404130193623
a(41) = 3854842259859593204491614768
a(42) = 20935895118297109855038307220
a(43) = 113801693708552958584926065319
a(44) = 619100283073677586145586922079
a(45) = 3370639793619142838758248697188
a(46) = 18364867053635351493198268875970
a(47) = 100132105010369981284602913597540
a(48) = 546331084709183792155611409438031
a(49) = 2982793537106174605376607710774808
a(50) = 16295348349815214138786686342645103
a(51) = 89077172384856173767081316201763168
a(52) = 487215721429608735330476910622825553
a(53) = 2666359028244640150695105857388293743
a(54) = 14599881495993745183130163964303045587
a(55) = 79984311982165625120087302076410582256
a(56) = 438406465556000009070524667032607361607
a(57) = 2404130564166785834625721730151135619712
a(58) = 13189879312881735090352204706269500459731
a(59) = 72396630207050558211832173949329416470149
a(60) = 397542967348089315951547292392578121588062
a(61) = 2183894994041059915175987113553259874162482
a(62) = 12002050554084516116966799647490008474323520
a(63) = 65985653791240643463075981407847701538565219
a(64) = 362918067466629583013198126157006623893015717
a(65) = 1996767590190158393756462112331881086669224955
a(66) = 10990094287514771742179326190774845175683521452
a(67) = 60509785779853871477773677060148777540777077328
a(68) = 333269558224862374477003577692960443473791291610
a(69) = 1836146128371920350494379692136256882578614367768
a(70) = 10119436236675113553217791917883221941207393477599
a(71) = 55787765578044268896384454021418899568821793245347
a(72) = 307646120979237594947764148658307876199628995135430
a(73) = 1697032491117414542044324457220996903749083983860688
a(74) = 9363790011483067005420205189409817401368646093620142
a(75) = 51681209055482287783875629020780525861732941558547866
a(76) = 285318533542305760727343900670887236876191494512992198
a(77) = 1575580409501868531852776092597622066921537055742498425
a(78) = 8702850094413415999079549099395945379902565096734995437
a(79) = 48082823044038029469169860432921834316457747753051751587
a(80) = 265719377963952146712552172789649152577423146752355129463
a(81) = 1468786596041221898929834958590410003069679639250165892369
a(82) = 8120707450830872376756191550788358119254709201587095511272
a(83) = 44908267373363930590751997156269760352323615613452654753802
a(84) = 248401188437134467754627542124649905782276108322904545928414
a(85) = 1374275242807331688425231420014324419239992603718982482559661
a(86) = 7604738557552716156580386424231742733114905755171433445549224
a(87) = 42090420857263381192531874532216384034537636743943430610191814
a(88) = 233006823103906644200422880459226361845439242282843171642669023
a(89) = 1290144761215931080911710396066664958430549907023572193651477537
a(90) = 7144811770968667481378014545656873893259384913409655144496012778
a(91) = 39575267311948353143765940720152956383039278193579416928245990030
a(92) = 219248116518653719463970863675403515896542627397438621423247676150
a(93) = 1214856899184842110869818154421260253518695343807743774412141659924
a(94) = 6732710824119213048804962757939819797158387602018712615957143394929
a(95) = 37318895363880911059341062056247102009426734591812596507859219303078
a(96) = 206890251871266564392965813834320082452099327112961556537078851602575
a(97) = 1147155263872001466637467068758034565047657963495811554659031657665516
a(98) = 6361709661594123891322707742514525826881467071012100180838455919140343
a(99) = 35285277943880850411448155851666068051580373694247142796564645617354951
a(100) = 195740154230696177131521702567160635847499234135843856951110163064946553
a(101) = 1086004602452197031766496315055195255739423382904725050816006732107437542
a(102) = 6026254539927397710876889540349534659377957014082703206645607781428292920
a(103) = 33444606595778477923661328202122649514186933679068860811874939116272515697
a(104) = 185637756158580363376931227547585262125239212875670550798078988061866677434
a(105) = 1030544967204484480053157098934603074993420981899397824335782181625882700380
a(106) = 5721723325654802340937834126672966051608620389569118423133134003192206885382
a(107) = 31772026520980077776251454260288376866497468059991184550330366578808668683008
a(108) = 176449345333473913476095864182102820753709279105933343149823461827035366603540
a(109) = 980056706656382785258588573502216824589033603590747570762502413451423599638567
a(110) = 5444241132838660120038836666730879719193718474282484003830044314163719842951165
a(111) = 30246665051918541010293783185489423469275634132317905609799260295584262769297211
a(112) = 168062441618914035120909132690830354100328803481897630550093553615523914310881691
a(113) = 933933434797555015316040931506278351692789526980516965743449138076620454699199453
a(114) = 5190537608097484430642409330446482045368682008392854653202108918307747617534679982
a(115) = 28850877696267022668285262892133793024136504892644798318365583191248959670486512608
a(116) = 160381811565295775248624296455866421716714346991289154493397789121750374393404105246
a(117) = 891660950878262235347802315382425648152892813662053079298412292144629709770632807591
a(118) = 4957835368294306580691330860719269629203499036444258059905858256163645404952691963068
a(119) = 27569657383634636490158975010289460553771314109690952688533114282176131344827591452931
a(120) = 153326338468757919026339581008993374955014479963889496434629975009435436180210357058053
a(121) = 852800647242884070383122314412913804739947580709846904289007507382442166589338378015366
a(122) = 4743761996490637323784959981968575655680727079967536196841572595001377583777770027718877
a(123) = 26390167450809626861998288496507198823002020347384895653610609571240704149361658077326520
a(124) = 146826542763862942947104914842278231586905721283224782950160046863373175363406298202590942
a(125) = 816976337212691360153524715237575047130836978370349729524712302055405417813559674915795194
a(126) = 4546280034414061215933315778920318830713899608114165172836174785597604586382199482880974708
a(127) = 25301369381484079421369786935826121343988269578112395716912549269463944544173284409145267510
a(128) = 140822601601823333865392381928362104632672614861501079465347882168354019519217244891280557010
a(129) = 783863714270810312908727021652100595963451035647138647097301549963081967106707056346312257158
a(130) = 4363630852759252407841550460249638288376855087262413611308424362407537880015959549708477385609
a(131) = 24293723779627851753942222039231093608685075534786585515576697435029136114856314048222914714247
a(132) = 135262755092688034312927407679306138611025951789209200577455341026161385089251279061199268995441
a(133) = 753181853863432947690685973774243677253584658377125009657141417578825101333703803370121386054840
a(134) = 4194289317568913091492621598303931371001786841778941073800242267107915669957964422096673382864762
a(135) = 23358948433891641893113761480249731920552344330698625226739905031097953944109802114250466040259645
a(136) = 130102014604224477853558788658710870484639046296257670053455881404072582155074325008793938082575127
a(137) = 724686314112097189888106547082032257856520755334928905740609461422812287262147936039373544508413883
a(138) = 4036926924440565990740883979138256258834610867158674805104800339310681742753803395235098561429772609
a(139) = 22489821249099404969649848944966276512804301439609492080996639844023788842824926464457416234950342464
a(140) = 125301108903009833648529090020199353788840777325426923229792595258634924119978581959895025727522986413
a(141) = 698163497922934316719570578608388819916246441571685095088570508418135496445621157437588139375609855493
a(142) = 3890381625617281340589809081419341310506830523546592649590703889385413582804014963998912572033230543708
a(143) = 21680018705709481934561602114917125773607272962192415331603381382197384416323868708350020928052980317485
a(144) = 120825618972981865945585967342182936424042290550526403191891650315379238426661969725285199267676974015565
a(145) = 673426017537967091880265278241845684526711952450705818965332318485994674589531623428737203442064447315288
a(146) = 3753632985336680949780047506191595380342107513923957114138590238644315511548946935957954664332044188895231
a(147) = 20923982652446800019398110482738336180891514309056658187696153887287642849394064219415446135300123168716772
a(148) = 116645263559330382937195619801420744192472042303318229641837242171521943219398445271457599684431276975666333
a(149) = 650308861236893562623911955376075658118095207148033849764719726600489178074029067062333824512339574198420587
a(150) = 3625781605901786488930297528719290281565544820439820659804195432582727382384458460828932624208424305729508435
a(151) = 20216809845719427851242884579291091708919751052266993570473895574438442069318065740092326897632605389906621459
a(152) = 112733305914311212977516956923650251412204072472594052728492014145046059700286210313699424368008152086913131376
a(153) = 628666206090642456075371864977475100028182109529722534102275124611119690922930808307430311985449429487587958732
a(154) = 3506031998766276652645998119888422118363249917382891130575026895775569031807121090320737419649617604907291947977
a(155) = 19554159866191737922814909739149772464108283797284935326609653401040670739629961459750570315732045192835090752940
a(156) = 109066058610951559600706739434172785093458905289109906419897478303580523461518754964555407464421004562171724774736
a(157) = 608368754236220007387891819328337931237795994504518059102849292105462661312871380296095659063958411895793326658388
a(158) = 3393678251371727658628058520381670239982826208523798477412538828920766989621798673749066073861901042220599712661378
a(159) = 18932177970781413427938988412853060515612388211082574987616680410953687383427533700594546440300842853979149598217994
a(160) = 105622468172571739041278014348155666727241903746060539461134952544746614882166037274126454886561887603383933556685408
a(161) = 589301495839912502144527152058477031085385583849231403974814118732124467768939710288490189065194852558667870866284764
a(162) = 3288091975802904877764457538841887204697480726250454227589596601929135652446689308131575021850492241186007645438951468
a(163) = 18347430151338393826159100475098884676321298620734587054773494327082218145060159272152438696708289951365270785561195983
a(164) = 102383765024189137091592136242897536047448812070542928976275705529635234641246087901555391172575698779801320745951505282
a(165) = 571361821733636417111944530650059310951463194341325026653830234204594612936215336317685870923213149077223847300599381067
a(166) = 3188712129877107881568395738652651622188967877034115774755380200850192034071413785494792922537535835438792311148038826707
a(167) = 17796848223061987981545173887688525318788181116894878853053271873945928157483434149998073345587131143999948793978943247766
a(168) = 99333167185408583883944637657209363812153779285952459316746511483069461295264435525627729556297227115579525770014732648967
a(169) = 554457924099377992146163166619478435145662543617870017315894738869301383583938512999063013110473901672283383183568242098887
a(170) = 3095036382612332215800973866709490769642459399638200854677748827547737839555746742256841664692585694221567710640045221185872
a(171) = 17277683195666686899414398775436951083624184566096345869560277689488465943220115750242838953181245313213546087405292753937206
a(172) = 96455628398322253671244029266221858647446750208838416046429202993754593554793048569182973647220217918084291504154809901721433
a(173) = 538507435607613772186142918239743248678607349357347876053221538100539146783913053360199287171551719210654551557086321503782975
a(174) = 3006613759697814703889674260444861961187020502263501191731453543352008000930174429648715779609937149184102894117628485417910074
a(175) = 16787465517484055267193303611068473212400403792634393651328496429238032241247795040119561790156528151648024153447044386116973435
a(176) = 93737623169962239450375334362460106663975979779834337084994949367985945561328452324359972167590272959831357763096577054118313749
a(177) = 523436266879686825613766973007990243557227029701807927615076568541736361009320264638437349727151467974631396337788926884461872992
a(178) = 2923038354759171567431235365787547983309639785426184415499560799314184712591855867112103390284816352844983264778203737966969917775
a(179) = 16323971048727331777788733120548627496321937174685125729131787305772584164632510237851092745198943149473572003597351505582386319557
a(180) = 91166962620140266196380652327963800298748593031072191421829663637920557231380041302281613331941229703078223040215805833983480294499
a(181) = 509177609633448477837306828705609800362836740354048597137859683574934641556448620051568432588276967385053690183418116323280645137278
a(182) = 2843943931968253419735010479238980295033109133668823986994415540150428193464944905169776250658480490631606796850260963777340351994618
a(183) = 15885191831278212189857354016234389223083175302277668716503103108664761400577864874751512750646588095309014912783163951052405205240595
a(184) = 88732636147109070846890790754516014393899600901834415781086374677548086912443286146739455717046443682568003155896865687861723188669609
a(185) = 495671078831780313304851726400122621336617810500320344604569875322039239064880842824204384000618772663067659498030026594975009908747293
a(186) = 2768999277232233545714454481827760889946432960123776835955534165217519738345767218834910041332306895352183747412920004084758161108320993
a(187) = 15469310890842522960599915746210719682945678758630817795286982915584431369488124379706895110767852757450251663297223355104267228740085772
a(188) = 86424674819735039896799118861310661928864912413163518203563613249092646397578813532694226276085304999311713805290257319525893816454703829
a(189) = 482861971922723712462447349906719331633162427531250728763701875008431601814611128038672674766571227753712801614671401865314826612911160525
a(190) = 2697904180581797937148280581543296551798708945370665582865245964381716687828326176106685592655591793011515799246698061666345711883762091012
a(191) = 15074680442487308589014136753849400037083968218506312413016156167129850552808978686421969887297698349297390008904048162812419702673015032050
a(192) = 84234033124796287360994715143092397740022246931098538944313056151266637729003755006757838788186155422200131485926083742677685374268223312096
a(193) = 470700627095621359035043763953369459963625925289833974046395242804598266455740488198197394434074866751699417255622517818642335428027296919398
a(194) = 2630385952820637970914201682565772871021718533735777876742124673692267099734727008439699267226272021996388616577853511790702068530140269125164
a(195) = 14699802979552831874232764228182415461486761001079851068034594966995795034819319471713163394975999759222751576442527985351943982146733065521765
a(196) = 82152486279187832921256564856896710959591297131767272755903263052018383446722231871235229991094142350361533658436382974433313191711385560569324
a(197) = 459141865577811629864464723080839529767224393761592554178295858028222665885938866476740496261577486512550890406949077299223622618257259365578414
a(198) = 2566196396040437930308448925384608625203221944806746030150168521813221544939929998366383224972135431841204354611612429599357152842302936484884188
a(199) = 14343314814224876758823185160086176786474515954256795099147137717782196074013983887687462343977473494605369894613643743993253790694165144695262384
a(200) = 80172540788203522350461148875475983469714450244904615838562877676793108502193480905452084173691145111099268038150992460412926031426483798219677784
a(201) = 448144505513858895568196468889840234275336222947452048665769923808602850111892661771184819620309194197199508530254608089672537472469541247946343107
a(202) = 2505109161053696139375001364908344336943871698321061375015949349461874601023065247691680946255573621304401290308002230973178232876114335350144972361
a(203) = 14003971709912543591325655292639897461121148862806626993881701490617285221096284143406102597883866088998301973756385544377417158537651661034677863353
a(204) = 78287356315150712421345570599291459236151221630895951265869061887608419927458971093081059364670096829178249046870162310052143476639411849664880416540
a(205) = 437670937022779842842943234134206616799253799749581951012742688740352015559569518297583255569541442833797892441352766142258530818667109896948485754084
a(n+206) = 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199899162697451309*n^5+1840734507636689476585249997361438104626874286417970519175898795994268559146850*n^4+260228750829534491814499665387043300510872037343044870253758816993028922333165463*n^3+22074011024120785915559608995993282079563853181972698462293402634639450661929697610*n^2+1040268314776968534024652225858415758115796157275451528341959350520127635413810935156*n+21010838283625724034759056055087082622565198249690451104797391209648070974580777877500)/(n+207)/(n+206)/(n+205)/(n+204)/(n+203)/(n+202)/(n+201)*a(n+142)-1/218506529232*(673526453391028117877013446546980300537738796511409800899213922596932414*n^7+647145073696872615755012449260565438342252793207269581796667459196059832096*n^6+266493574589349811005274602247862426773489949096319494675241899091370382951560*n^5+60969735136422832030228349504777540924157506900886786878375149760571886147511625*n^4+8369667280072947688991823858642868807047648849805437535049117806712561931571884286*n^3+689395567913454157801531937429433934901935710031814235408196357217551313010215883459*n^2+31547977262150733793901951578707678737604210672511547196682205334414928601318534526300*n+618746983365533808394282012611487443532789591877200212577488304663901747727545325079380)/(n+207)/(n+206)/(n+205)/(n+204)/(n+203)/(n+202)/(n+201)*a(n+138)+1/437013058464*(562489706945430723445082001887171692367157577762899161485394575072287056*n^7+544556869072883251174298854244841429854163209088962231508561816564068754416*n^6+225948328269474981582586215682999867237621061168969605202909682947665509299975*n^5+52085472441608113930989936435502788669351447440697864252143426567812937890548800*n^4+7204261904688967293200316879718398509612307750862088957510904967032221402475857309*n^3+597899040589055924665728264407314141735910822840382426704788146567966650054025726704*n^2+27568174593269834484649048972824266018782833521507174015390315971599037929301635795420*n+544785751129792461789087824534809686330113419003060031872134227738983739703541584741360)/(n+207)/(n+206)/(n+205)/(n+204)/(n+203)/(n+202)/(n+201)*a(n+139)-1/437013058464*(231424262183343368508118986329468040990417521945586489474296201664583904*n^7+225716254788293257798081194078711309259825017513840342072603701901865462688*n^6+94352391583777935767381003400138053267724147605935013945642980706997015481358*n^5+21912072552875488885001169100991006762932491714685545540427660377042241253060225*n^4+3053361885802521846108425940583903720552091328661203226462311572133521568212506676*n^3+255292135302040445855948709700798924677620446037437035733408773301073117198119198967*n^2+11858703801089444243977124851292335678088504866097238848085273592565498803899626174502*n+236087725737362541987790384097746989604712016315682215743087169473098154644148595986880)/(n+207)/(n+206)/(n+205)/(n+204)/(n+203)/(n+202)/(n+201)*a(n+140)+1/437013058464*(3182667344644018335885936856390564809899582475954068439472079138209022072*n^7+3034625611000835334401318442838849433737702116551646257639564920660907424616*n^6+1240102552344184661069908772781801521065241635849421176664551754007175636779137*n^5+281548418304218547176410955437816311969765436164867000960444515365465195793442115*n^4+38354423542837324333214022272171612455747484432589422440252683396030885754155938513*n^3+3135052493832644285851888670085538128068031950349842586067711794624046790769082603729*n^2+142369683145938975424106033505735229879887411953505053214250617537914700276098929391298*n+2770954482352189700339252473698050099024689760626612264519446613862489555986625684840400)/(n+207)/(n+206)/(n+205)/(n+204)/(n+203)/(n+202)/(n+201)*a(n+137), n >= 206
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 22
a \! \left(5\right) = 89
a \! \left(6\right) = 381
a \! \left(7\right) = 1696
a \! \left(8\right) = 7781
a \! \left(9\right) = 36572
a \! \left(10\right) = 175277
a \! \left(11\right) = 853410
a \! \left(12\right) = 4209376
a \! \left(13\right) = 20988122
a \! \left(14\right) = 105611537
a \! \left(15\right) = 535638107
a \! \left(16\right) = 2735303546
a \! \left(17\right) = 14052318081
a \! \left(18\right) = 72576606964
a \! \left(19\right) = 376616279797
a \! \left(20\right) = 1962646712114
a \! \left(21\right) = 10267016702607
a \! \left(22\right) = 53895142688122
a \! \left(23\right) = 283807158368210
a \! \left(24\right) = 1498814755776705
a \! \left(25\right) = 7936344718181112
a \! \left(26\right) = 42126008006042152
a \! \left(27\right) = 224107780692072667
a \! \left(28\right) = 1194727534919520715
a \! \left(29\right) = 6381491115295466765
a \! \left(30\right) = 34147539809674959051
a \! \left(31\right) = 183032793143464260058
a \! \left(32\right) = 982616083490440149184
a \! \left(33\right) = 5283015487751599026270
a \! \left(34\right) = 28443586396635718275494
a \! \left(35\right) = 153340211415040987386363
a \! \left(36\right) = 827684383873305999315780
a \! \left(37\right) = 4472814607156698124909148
a \! \left(38\right) = 24197877589473740641311162
a \! \left(39\right) = 131047527967041143291732804
a \! \left(40\right) = 710415487340274404130193623
a \! \left(41\right) = 3854842259859593204491614768
a \! \left(42\right) = 20935895118297109855038307220
a \! \left(43\right) = 113801693708552958584926065319
a \! \left(44\right) = 619100283073677586145586922079
a \! \left(45\right) = 3370639793619142838758248697188
a \! \left(46\right) = 18364867053635351493198268875970
a \! \left(47\right) = 100132105010369981284602913597540
a \! \left(48\right) = 546331084709183792155611409438031
a \! \left(49\right) = 2982793537106174605376607710774808
a \! \left(50\right) = 16295348349815214138786686342645103
a \! \left(51\right) = 89077172384856173767081316201763168
a \! \left(52\right) = 487215721429608735330476910622825553
a \! \left(53\right) = 2666359028244640150695105857388293743
a \! \left(54\right) = 14599881495993745183130163964303045587
a \! \left(55\right) = 79984311982165625120087302076410582256
a \! \left(56\right) = 438406465556000009070524667032607361607
a \! \left(57\right) = 2404130564166785834625721730151135619712
a \! \left(58\right) = 13189879312881735090352204706269500459731
a \! \left(59\right) = 72396630207050558211832173949329416470149
a \! \left(60\right) = 397542967348089315951547292392578121588062
a \! \left(61\right) = 2183894994041059915175987113553259874162482
a \! \left(62\right) = 12002050554084516116966799647490008474323520
a \! \left(63\right) = 65985653791240643463075981407847701538565219
a \! \left(64\right) = 362918067466629583013198126157006623893015717
a \! \left(65\right) = 1996767590190158393756462112331881086669224955
a \! \left(66\right) = 10990094287514771742179326190774845175683521452
a \! \left(67\right) = 60509785779853871477773677060148777540777077328
a \! \left(68\right) = 333269558224862374477003577692960443473791291610
a \! \left(69\right) = 1836146128371920350494379692136256882578614367768
a \! \left(70\right) = 10119436236675113553217791917883221941207393477599
a \! \left(71\right) = 55787765578044268896384454021418899568821793245347
a \! \left(72\right) = 307646120979237594947764148658307876199628995135430
a \! \left(73\right) = 1697032491117414542044324457220996903749083983860688
a \! \left(74\right) = 9363790011483067005420205189409817401368646093620142
a \! \left(75\right) = 51681209055482287783875629020780525861732941558547866
a \! \left(76\right) = 285318533542305760727343900670887236876191494512992198
a \! \left(77\right) = 1575580409501868531852776092597622066921537055742498425
a \! \left(78\right) = 8702850094413415999079549099395945379902565096734995437
a \! \left(79\right) = 48082823044038029469169860432921834316457747753051751587
a \! \left(80\right) = 265719377963952146712552172789649152577423146752355129463
a \! \left(81\right) = 1468786596041221898929834958590410003069679639250165892369
a \! \left(82\right) = 8120707450830872376756191550788358119254709201587095511272
a \! \left(83\right) = 44908267373363930590751997156269760352323615613452654753802
a \! \left(84\right) = 248401188437134467754627542124649905782276108322904545928414
a \! \left(85\right) = 1374275242807331688425231420014324419239992603718982482559661
a \! \left(86\right) = 7604738557552716156580386424231742733114905755171433445549224
a \! \left(87\right) = 42090420857263381192531874532216384034537636743943430610191814
a \! \left(88\right) = 233006823103906644200422880459226361845439242282843171642669023
a \! \left(89\right) = 1290144761215931080911710396066664958430549907023572193651477537
a \! \left(90\right) = 7144811770968667481378014545656873893259384913409655144496012778
a \! \left(91\right) = 39575267311948353143765940720152956383039278193579416928245990030
a \! \left(92\right) = 219248116518653719463970863675403515896542627397438621423247676150
a \! \left(93\right) = 1214856899184842110869818154421260253518695343807743774412141659924
a \! \left(94\right) = 6732710824119213048804962757939819797158387602018712615957143394929
a \! \left(95\right) = 37318895363880911059341062056247102009426734591812596507859219303078
a \! \left(96\right) = 206890251871266564392965813834320082452099327112961556537078851602575
a \! \left(97\right) = 1147155263872001466637467068758034565047657963495811554659031657665516
a \! \left(98\right) = 6361709661594123891322707742514525826881467071012100180838455919140343
a \! \left(99\right) = 35285277943880850411448155851666068051580373694247142796564645617354951
a \! \left(100\right) = 195740154230696177131521702567160635847499234135843856951110163064946553
a \! \left(101\right) = 1086004602452197031766496315055195255739423382904725050816006732107437542
a \! \left(102\right) = 6026254539927397710876889540349534659377957014082703206645607781428292920
a \! \left(103\right) = 33444606595778477923661328202122649514186933679068860811874939116272515697
a \! \left(104\right) = 185637756158580363376931227547585262125239212875670550798078988061866677434
a \! \left(105\right) = 1030544967204484480053157098934603074993420981899397824335782181625882700380
a \! \left(106\right) = 5721723325654802340937834126672966051608620389569118423133134003192206885382
a \! \left(107\right) = 31772026520980077776251454260288376866497468059991184550330366578808668683008
a \! \left(108\right) = 176449345333473913476095864182102820753709279105933343149823461827035366603540
a \! \left(109\right) = 980056706656382785258588573502216824589033603590747570762502413451423599638567
a \! \left(110\right) = 5444241132838660120038836666730879719193718474282484003830044314163719842951165
a \! \left(111\right) = 30246665051918541010293783185489423469275634132317905609799260295584262769297211
a \! \left(112\right) = 168062441618914035120909132690830354100328803481897630550093553615523914310881691
a \! \left(113\right) = 933933434797555015316040931506278351692789526980516965743449138076620454699199453
a \! \left(114\right) = 5190537608097484430642409330446482045368682008392854653202108918307747617534679982
a \! \left(115\right) = 28850877696267022668285262892133793024136504892644798318365583191248959670486512608
a \! \left(116\right) = 160381811565295775248624296455866421716714346991289154493397789121750374393404105246
a \! \left(117\right) = 891660950878262235347802315382425648152892813662053079298412292144629709770632807591
a \! \left(118\right) = 4957835368294306580691330860719269629203499036444258059905858256163645404952691963068
a \! \left(119\right) = 27569657383634636490158975010289460553771314109690952688533114282176131344827591452931
a \! \left(120\right) = 153326338468757919026339581008993374955014479963889496434629975009435436180210357058053
a \! \left(121\right) = 852800647242884070383122314412913804739947580709846904289007507382442166589338378015366
a \! \left(122\right) = 4743761996490637323784959981968575655680727079967536196841572595001377583777770027718877
a \! \left(123\right) = 26390167450809626861998288496507198823002020347384895653610609571240704149361658077326520
a \! \left(124\right) = 146826542763862942947104914842278231586905721283224782950160046863373175363406298202590942
a \! \left(125\right) = 816976337212691360153524715237575047130836978370349729524712302055405417813559674915795194
a \! \left(126\right) = 4546280034414061215933315778920318830713899608114165172836174785597604586382199482880974708
a \! \left(127\right) = 25301369381484079421369786935826121343988269578112395716912549269463944544173284409145267510
a \! \left(128\right) = 140822601601823333865392381928362104632672614861501079465347882168354019519217244891280557010
a \! \left(129\right) = 783863714270810312908727021652100595963451035647138647097301549963081967106707056346312257158
a \! \left(130\right) = 4363630852759252407841550460249638288376855087262413611308424362407537880015959549708477385609
a \! \left(131\right) = 24293723779627851753942222039231093608685075534786585515576697435029136114856314048222914714247
a \! \left(132\right) = 135262755092688034312927407679306138611025951789209200577455341026161385089251279061199268995441
a \! \left(133\right) = 753181853863432947690685973774243677253584658377125009657141417578825101333703803370121386054840
a \! \left(134\right) = 4194289317568913091492621598303931371001786841778941073800242267107915669957964422096673382864762
a \! \left(135\right) = 23358948433891641893113761480249731920552344330698625226739905031097953944109802114250466040259645
a \! \left(136\right) = 130102014604224477853558788658710870484639046296257670053455881404072582155074325008793938082575127
a \! \left(137\right) = 724686314112097189888106547082032257856520755334928905740609461422812287262147936039373544508413883
a \! \left(138\right) = 4036926924440565990740883979138256258834610867158674805104800339310681742753803395235098561429772609
a \! \left(139\right) = 22489821249099404969649848944966276512804301439609492080996639844023788842824926464457416234950342464
a \! \left(140\right) = 125301108903009833648529090020199353788840777325426923229792595258634924119978581959895025727522986413
a \! \left(141\right) = 698163497922934316719570578608388819916246441571685095088570508418135496445621157437588139375609855493
a \! \left(142\right) = 3890381625617281340589809081419341310506830523546592649590703889385413582804014963998912572033230543708
a \! \left(143\right) = 21680018705709481934561602114917125773607272962192415331603381382197384416323868708350020928052980317485
a \! \left(144\right) = 120825618972981865945585967342182936424042290550526403191891650315379238426661969725285199267676974015565
a \! \left(145\right) = 673426017537967091880265278241845684526711952450705818965332318485994674589531623428737203442064447315288
a \! \left(146\right) = 3753632985336680949780047506191595380342107513923957114138590238644315511548946935957954664332044188895231
a \! \left(147\right) = 20923982652446800019398110482738336180891514309056658187696153887287642849394064219415446135300123168716772
a \! \left(148\right) = 116645263559330382937195619801420744192472042303318229641837242171521943219398445271457599684431276975666333
a \! \left(149\right) = 650308861236893562623911955376075658118095207148033849764719726600489178074029067062333824512339574198420587
a \! \left(150\right) = 3625781605901786488930297528719290281565544820439820659804195432582727382384458460828932624208424305729508435
a \! \left(151\right) = 20216809845719427851242884579291091708919751052266993570473895574438442069318065740092326897632605389906621459
a \! \left(152\right) = 112733305914311212977516956923650251412204072472594052728492014145046059700286210313699424368008152086913131376
a \! \left(153\right) = 628666206090642456075371864977475100028182109529722534102275124611119690922930808307430311985449429487587958732
a \! \left(154\right) = 3506031998766276652645998119888422118363249917382891130575026895775569031807121090320737419649617604907291947977
a \! \left(155\right) = 19554159866191737922814909739149772464108283797284935326609653401040670739629961459750570315732045192835090752940
a \! \left(156\right) = 109066058610951559600706739434172785093458905289109906419897478303580523461518754964555407464421004562171724774736
a \! \left(157\right) = 608368754236220007387891819328337931237795994504518059102849292105462661312871380296095659063958411895793326658388
a \! \left(158\right) = 3393678251371727658628058520381670239982826208523798477412538828920766989621798673749066073861901042220599712661378
a \! \left(159\right) = 18932177970781413427938988412853060515612388211082574987616680410953687383427533700594546440300842853979149598217994
a \! \left(160\right) = 105622468172571739041278014348155666727241903746060539461134952544746614882166037274126454886561887603383933556685408
a \! \left(161\right) = 589301495839912502144527152058477031085385583849231403974814118732124467768939710288490189065194852558667870866284764
a \! \left(162\right) = 3288091975802904877764457538841887204697480726250454227589596601929135652446689308131575021850492241186007645438951468
a \! \left(163\right) = 18347430151338393826159100475098884676321298620734587054773494327082218145060159272152438696708289951365270785561195983
a \! \left(164\right) = 102383765024189137091592136242897536047448812070542928976275705529635234641246087901555391172575698779801320745951505282
a \! \left(165\right) = 571361821733636417111944530650059310951463194341325026653830234204594612936215336317685870923213149077223847300599381067
a \! \left(166\right) = 3188712129877107881568395738652651622188967877034115774755380200850192034071413785494792922537535835438792311148038826707
a \! \left(167\right) = 17796848223061987981545173887688525318788181116894878853053271873945928157483434149998073345587131143999948793978943247766
a \! \left(168\right) = 99333167185408583883944637657209363812153779285952459316746511483069461295264435525627729556297227115579525770014732648967
a \! \left(169\right) = 554457924099377992146163166619478435145662543617870017315894738869301383583938512999063013110473901672283383183568242098887
a \! \left(170\right) = 3095036382612332215800973866709490769642459399638200854677748827547737839555746742256841664692585694221567710640045221185872
a \! \left(171\right) = 17277683195666686899414398775436951083624184566096345869560277689488465943220115750242838953181245313213546087405292753937206
a \! \left(172\right) = 96455628398322253671244029266221858647446750208838416046429202993754593554793048569182973647220217918084291504154809901721433
a \! \left(173\right) = 538507435607613772186142918239743248678607349357347876053221538100539146783913053360199287171551719210654551557086321503782975
a \! \left(174\right) = 3006613759697814703889674260444861961187020502263501191731453543352008000930174429648715779609937149184102894117628485417910074
a \! \left(175\right) = 16787465517484055267193303611068473212400403792634393651328496429238032241247795040119561790156528151648024153447044386116973435
a \! \left(176\right) = 93737623169962239450375334362460106663975979779834337084994949367985945561328452324359972167590272959831357763096577054118313749
a \! \left(177\right) = 523436266879686825613766973007990243557227029701807927615076568541736361009320264638437349727151467974631396337788926884461872992
a \! \left(178\right) = 2923038354759171567431235365787547983309639785426184415499560799314184712591855867112103390284816352844983264778203737966969917775
a \! \left(179\right) = 16323971048727331777788733120548627496321937174685125729131787305772584164632510237851092745198943149473572003597351505582386319557
a \! \left(180\right) = 91166962620140266196380652327963800298748593031072191421829663637920557231380041302281613331941229703078223040215805833983480294499
a \! \left(181\right) = 509177609633448477837306828705609800362836740354048597137859683574934641556448620051568432588276967385053690183418116323280645137278
a \! \left(182\right) = 2843943931968253419735010479238980295033109133668823986994415540150428193464944905169776250658480490631606796850260963777340351994618
a \! \left(183\right) = 15885191831278212189857354016234389223083175302277668716503103108664761400577864874751512750646588095309014912783163951052405205240595
a \! \left(184\right) = 88732636147109070846890790754516014393899600901834415781086374677548086912443286146739455717046443682568003155896865687861723188669609
a \! \left(185\right) = 495671078831780313304851726400122621336617810500320344604569875322039239064880842824204384000618772663067659498030026594975009908747293
a \! \left(186\right) = 2768999277232233545714454481827760889946432960123776835955534165217519738345767218834910041332306895352183747412920004084758161108320993
a \! \left(187\right) = 15469310890842522960599915746210719682945678758630817795286982915584431369488124379706895110767852757450251663297223355104267228740085772
a \! \left(188\right) = 86424674819735039896799118861310661928864912413163518203563613249092646397578813532694226276085304999311713805290257319525893816454703829
a \! \left(189\right) = 482861971922723712462447349906719331633162427531250728763701875008431601814611128038672674766571227753712801614671401865314826612911160525
a \! \left(190\right) = 2697904180581797937148280581543296551798708945370665582865245964381716687828326176106685592655591793011515799246698061666345711883762091012
a \! \left(191\right) = 15074680442487308589014136753849400037083968218506312413016156167129850552808978686421969887297698349297390008904048162812419702673015032050
a \! \left(192\right) = 84234033124796287360994715143092397740022246931098538944313056151266637729003755006757838788186155422200131485926083742677685374268223312096
a \! \left(193\right) = 470700627095621359035043763953369459963625925289833974046395242804598266455740488198197394434074866751699417255622517818642335428027296919398
a \! \left(194\right) = 2630385952820637970914201682565772871021718533735777876742124673692267099734727008439699267226272021996388616577853511790702068530140269125164
a \! \left(195\right) = 14699802979552831874232764228182415461486761001079851068034594966995795034819319471713163394975999759222751576442527985351943982146733065521765
a \! \left(196\right) = 82152486279187832921256564856896710959591297131767272755903263052018383446722231871235229991094142350361533658436382974433313191711385560569324
a \! \left(197\right) = 459141865577811629864464723080839529767224393761592554178295858028222665885938866476740496261577486512550890406949077299223622618257259365578414
a \! \left(198\right) = 2566196396040437930308448925384608625203221944806746030150168521813221544939929998366383224972135431841204354611612429599357152842302936484884188
a \! \left(199\right) = 14343314814224876758823185160086176786474515954256795099147137717782196074013983887687462343977473494605369894613643743993253790694165144695262384
a \! \left(200\right) = 80172540788203522350461148875475983469714450244904615838562877676793108502193480905452084173691145111099268038150992460412926031426483798219677784
a \! \left(201\right) = 448144505513858895568196468889840234275336222947452048665769923808602850111892661771184819620309194197199508530254608089672537472469541247946343107
a \! \left(202\right) = 2505109161053696139375001364908344336943871698321061375015949349461874601023065247691680946255573621304401290308002230973178232876114335350144972361
a \! \left(203\right) = 14003971709912543591325655292639897461121148862806626993881701490617285221096284143406102597883866088998301973756385544377417158537651661034677863353
a \! \left(204\right) = 78287356315150712421345570599291459236151221630895951265869061887608419927458971093081059364670096829178249046870162310052143476639411849664880416540
a \! \left(205\right) = 437670937022779842842943234134206616799253799749581951012742688740352015559569518297583255569541442833797892441352766142258530818667109896948485754084
a \! \left(n +206\right) = \frac{524288 \left(308100594085461799471252811929015395268676981815146993478897765626368 n^{7}+118257238845329534104166647459207205826160815534702066927201691345265088 n^{6}+19452382884104988692303022435475135901842909178290152010319499964414470992 n^{5}+1777586435645022546351259041138820323602003786267861298885267380026031803740 n^{4}+97459452721184294360421516929908757666354958852802805051265008541617435502212 n^{3}+3205909734821573376664306285269678308833771565004941858959788300378219143414967 n^{2}+58585175155759444283503073167103938801944011798643915253626834733273868772094623 n +458804687018609308592231375916505063933880270638902326033434479266392594410358290\right) a \! \left(n +55\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{524288 \left(670219198584436658134511583493843674473168911704512135702288739046784 n^{7}+261914505584810481754576989192015400494064325427594620246977462294264512 n^{6}+43864032922057380255228052544143915624055960003207564030466298935704134316 n^{5}+4081004449579274195021500565336162463499685844165356528602487055422209966860 n^{4}+227802123501128745112329565509289977286069822998862348894945819148020578652691 n^{3}+7629210916265562201857267259843330272595401200394272773033524218107441506301738 n^{2}+141941001980889811764888862655603038465783600901660354099555935305512116003212999 n +1131715456581836609748494072063783587895532677940050206428269104670902624904784600\right) a \! \left(n +56\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{262144 \left(2844876665924896085327464959338483488314515883308536241952218163006928 n^{7}+1131454160523455286737419809968419964410764653402659196595998045895438384 n^{6}+192847552000893491176216090742437962477778337963504641738659366529951268704 n^{5}+18259896598875558597412152111343863479824766229073139731932910450418032704540 n^{4}+1037319128009165248289617355588927830064348518952498660124610597453879653624457 n^{3}+35355378359502257429213431005751444002941610067211724880110300833639822372568501 n^{2}+669426706673281378868982866891447533523636569336574592064259874238652318638380606 n +5431877088578836126842372394908436583653416807568628227589865065077974341502831390\right) a \! \left(n +57\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(193246323075514832514366463632134462526005208529097744285610636632375618689607776 n^{7}+117992368696395758431188144637523018572275988337838804103670995650239754823771022856 n^{6}+30872644666024613600710797948525297430837412265323936172438267123533789905047968150158 n^{5}+4487191860903440114755083707015977979068584657062037381087773912226563927593211836095075 n^{4}+391272609525210788736102525607028338390096700326858313355068181978536053434334177554255394 n^{3}+20468574340676827185221338286310858090910527386848090533439696656382405199592444589775767509 n^{2}+594805046886268894910413190079767062392232393905564081061863341102416699418066448624371418252 n +7406885212649298273474748580275654711980404928858089288039395926991923024383901552922797699180\right) a \! \left(n +89\right)}{109253264616 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(22449018171892670362741993799146767858673093361752547092254737810235898321149664 n^{7}+12540532194620477308053437603147296104470902016289539421500298419235187774830552864 n^{6}+3002130787471641397377384623621258995604021752318526729526250825763130372696209645056 n^{5}+399247566845474296340180699700042025860544829303961562179397040684022876417888585852720 n^{4}+31854988272568626915351657986156805383552156235417026590021197570781984274290442778230926 n^{3}+1524877067976975234438161871629574294936938113688084169890912399042547412744707932512127151 n^{2}+40549955103024810066433502651390566535054022958127844143651137798910632623367654670472262989 n +462103757086493465142328066397349523429774310354068072336192037163837409511366862559732862340\right) a \! \left(n +81\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(46773762727471688456 n^{5}+46352743924342950713128 n^{4}+18374058849450245042620015 n^{3}+3641675926440583003797828509 n^{2}+360881013266475945164403692412 n +14304850185116048426862157694880\right) a \! \left(n +201\right)}{5395222944 \left(n +203\right) \left(n +204\right) \left(n +205\right) \left(n +206\right) \left(n +207\right)}+\frac{33849922949209616891772928 \left(2 n +3\right) \left(395412976 n^{6}+7345066704 n^{5}+55340929120 n^{4}+215143330800 n^{3}+450919294369 n^{2}+475583621391 n +191328405450\right) a \! \left(n +3\right)}{4552219359 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(8302319913582670993133101243414294184573813235162085934639293923292157621308880 n^{7}+4692053466313362107904476008575839549327725155910319890611644532676843837893820992 n^{6}+1136368653536745723566598863559552949674947764194718897029158558238103587978248735560 n^{5}+152887612228324925820850529971306032887817675679679615012111282026241036588246648983910 n^{4}+12340863034891159738389255504396444898458361656485321151613717199616050305878870913818675 n^{3}+597638554331139649421394841966559363257983892485707262795103173245579253619596041900321803 n^{2}+16077829352835368478579561315576591750022137849409553697387073770398287479681810811086083430 n +185356285649802765253064635619550292509948495859677551448445954365010470708527815348553071500\right) a \! \left(n +82\right)}{4552219359 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{32768 \left(186940332326195494116573231170245315501219421359422931839994326696854432 n^{7}+78200469343931512940222957702902880439266412296672594261466271327868865664 n^{6}+14018952626532865983313270374256828316169938123281720096826128962433520288312 n^{5}+1396128582383408549971431338492468598835265674044651813428804040310295294710900 n^{4}+83418462502901184634027902200422512841496906089600367961556851540931703630104208 n^{3}+2990373153661338710128380473940475664016883075990817550639940183514131110928459471 n^{2}+59551241140840484954718992355592405542818476349586934705095137274007063210514470023 n +508222341590034161040675306305013554246811626924670352684709845306016744940213870840\right) a \! \left(n +60\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{131072 \left(11776548047501742730688235152413553009059548168161771164967009481354640 n^{7}+4764924408714862799884830963705913930045071102243158368220937630935829760 n^{6}+826220142185478403822350737943439576396776988786022203065562516573051911712 n^{5}+79586760981318114723056715159019260804386075797659474008986137647734367377960 n^{4}+4599537880988848614541595367383188050538447909048909253146606766925571394411485 n^{3}+159483288542229402005031370633839186483935730921454021857199261393135893249345505 n^{2}+3071986739325179560402519340774831994072173790668974856357459481539139636564629388 n +25358392470195156384482544603222469092315133062665619448862822691708792348774343950\right) a \! \left(n +58\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(4908518728277 n^{2}+1960503496427497 n +195760089794517354\right) a \! \left(n +204\right)}{149867304 \left(n +206\right) \left(n +207\right)}+\frac{7 \left(31335280058198664755805455315193116874916111139616349386563004635935402407559404 n^{7}+20000597226049451227092801296798921426872662344208905781027926550936230937701161064 n^{6}+5470961802801999822520741758519377667212036693033307856947234867318409720113871037139 n^{5}+831382053844640621584510699293001679030171413210405383044138103816773669146920135293315 n^{4}+75801580248248157239597504976544081800494052345507014612643373574168776501100552623729911 n^{3}+4146648260066900120636275769257196120099632305567421016758144629465149925087454251215271041 n^{2}+126018527795117868013931835764788850324868251773514561110324651305590688662833160469853814286 n +1641293733469373853509843301698578294660992629677762708406318088839845546531454214022947405480\right) a \! \left(n +93\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(91974779388246525169232904493809510883170234514952239535462991264418976724946906 n^{7}+59423108299806837208593393903113152565773076256393109845131242876923083269631799692 n^{6}+16454176577907202587048998890764176369846427083533036556470203839463456458451265155739 n^{5}+2531258816251867381149521010292120051432783238200963241180941227439530247605585684839330 n^{4}+233647692880784218684717448679920604336918523714126233944057332733217296867019079846901644 n^{3}+12940533696025066157275093465188578481116914725024594063374536674402824996318739033955883813 n^{2}+398186102929004869235638444032741763089885498336913900076941070190384599550715138878711392916 n +5251219865009152614146056673921828886111962987381323972134088221371584913041818767683374246420\right) a \! \left(n +94\right)}{109253264616 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(173015179909867772611053465812108625894675670489743848954096348000774223388726820 n^{7}+106783736083451872946905050005626850252082886188573402746553220958001514848935337656 n^{6}+28242621403008792739017371922367592767208269653080363022573569361806519603186195736275 n^{5}+4149422448498622406631834885131570695384630306498041806368250831396071702960341661660535 n^{4}+365743218165668451793497869986910885319421278255956136197874924505799481735149052545928035 n^{3}+19340618135294905081001747491103298816077165389308461100516779010666247246210595407890299249 n^{2}+568127149088057075990890453962789788501723142980040112515543772037909255405871016033649448690 n +7151497773898752893484596882653308544410030229355725374651853282701152194098584795385714747240\right) a \! \left(n +90\right)}{109253264616 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(75673889109487791240049893524832757461439678376628864706009921303807898334299840 n^{7}+47216801859631978259475698268378477195320290893384344038593640296965838835827062330 n^{6}+12624999770074102031299767508863466561321684777542452975626152790745290113180882601757 n^{5}+1875229766284882208469450289366215560265117709705967519999538826208548167878516455360250 n^{4}+167104969676623930947431343948433158617483198249980278898807015794195528827933935274810405 n^{3}+8933789650180954253693295158306709257706267749669483731426316708395296937965211339694281985 n^{2}+265319706496820848760796106323224837083971081204742451103188573857429825328309531564047682193 n +3376650748982084453634644153429670261540219893859231302526930028247249773101544703330677986480\right) a \! \left(n +91\right)}{54626632308 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(259581391429204715126288528126265425441626014534317555380906242781140032235678332 n^{7}+163780731473270281200908693348754431742399252272767191814925602806915461352073131912 n^{6}+44283987983188930737414303778692075084944213230464256353322411135345704441470545018007 n^{5}+6651654733985887572972878786913918420037459646169278740393607745744174049996660296923820 n^{4}+599426034242286329903453751306008157000664531824463867338626806199599452344063153616522953 n^{3}+32408920054494326491909969041790487847630510474105147442151807596191793501522232390719967448 n^{2}+973403612141211160043411111772460994310220316537582059145715198548863278586240934351146063608 n +12529006926006391228323469074816974198186819292691478675151418203931518754482806038087699663440\right) a \! \left(n +92\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{2166395068749415481073467392 n \left(n -2\right) \left(2 n +3\right) \left(2 n +1\right) \left(2 n -1\right) \left(2 n -3\right) \left(n +1\right) a \! \left(n \right)}{4552219359 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{18446744073709551616 \left(440823864175700194869656656 n^{7}+33768709371013457718857669424 n^{6}+1106280616637172875695028191960 n^{5}+20090725820951011283679870122280 n^{4}+218426097304448718573942462567109 n^{3}+1421572200775520859209402500967571 n^{2}+5127947526590512248513555139386360 n +7908686383939060514188686713328600\right) a \! \left(n +11\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{4611686018427387904 \left(8069384870050307665408745824 n^{7}+674763002645416395300974055616 n^{6}+24138498730560697902156520472648 n^{5}+478851976114500431187774625507100 n^{4}+5688908741706147491428403173479556 n^{3}+40473933673082918798827680997825149 n^{2}+159661505211577929661347593729399357 n +269391379421132665684693863843057960\right) a \! \left(n +12\right)}{4552219359 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{2305843009213693952 \left(607578647403595691265534140240 n^{7}+55060084535509329673855454955056 n^{6}+2135187263383421788397844449218736 n^{5}+45929086497754957833455853512878820 n^{4}+591835334884739426969527670177774675 n^{3}+4568366671389225185308231403289364004 n^{2}+19558293095425901257548187135495716819 n +35825666243626264948917292165630789440\right) a \! \left(n +13\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(56895013138440121502541333052673195983930950861622349678410357564211133819066848 n^{7}+38272026263935429146938863043236511117549408377887144458279131243188836305439629044 n^{6}+11035277372213434746940252318905449007723039565795675007560840011838204486913971301687 n^{5}+1768008606343183128967096207089232871502814546828081726083988079949262415461092461236320 n^{4}+169984386058327924642097940006085763243918339671481007823998106085089339993021753854417677 n^{3}+9807484595302637702645570991371881916865680094513034828243580627735673568533182736289052166 n^{2}+314417563301944559370728877432334914512749592536320434443373714397834329823547006628083698708 n +4320684571474586149454281927284674843773499717561828687718845454264542664784185049600445330850\right) a \! \left(n +97\right)}{109253264616 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{576460752303423488 \left(9342768763363718584614431056224 n^{7}+911947086147859188138630984907968 n^{6}+38099830047065626796704030556333144 n^{5}+883134413587555642530978065991326980 n^{4}+12265697530551778369777195432773051376 n^{3}+102072252781441303788869450639671499627 n^{2}+471236051700544471222808020986717609261 n +931044144209077588495666150030982425800\right) a \! \left(n +14\right)}{4552219359 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{132226261520350065983488 \left(25041946867892048 n^{7}+1034728557876147472 n^{6}+18196807276594438856 n^{5}+176487007945682368480 n^{4}+1019152234131593356937 n^{3}+3502787842386531017143 n^{2}+6632224229546048577804 n +5334923772318768068700\right) a \! \left(n +6\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{33056565380087516495872 \left(2438894969413388656 n^{7}+118040129140878324400 n^{6}+2435936576675197781344 n^{5}+27778180148662567705060 n^{4}+189002594517106912264189 n^{3}+767118906383197820075740 n^{2}+1719390481959450143590521 n +1641404168308039071757590\right) a \! \left(n +7\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{1180591620717411303424 \left(1449265659458544986896 n^{7}+80389501821425141468816 n^{6}+1903531160823886919503192 n^{5}+24938259605158738060355000 n^{4}+195198534415910529494612209 n^{3}+912703078043381499634129769 n^{2}+2360169875123135820758202618 n +2603514230467265849016748500\right) a \! \left(n +8\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{295147905179352825856 \left(108742666672728453102960 n^{7}+6799410854163184274095792 n^{6}+181636044972972592402556016 n^{5}+2686883344509078614869884460 n^{4}+23767867338876796073920954665 n^{3}+125714016280499448317803249018 n^{2}+368099925154678685068622359329 n +460251600466715109791530790040\right) a \! \left(n +9\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(4688263080817523587093249881021383482166746912863493006763740117835055330546314 n^{7}+3110021168998841007277880814996904685490213087451125840252707600829782478436706456 n^{6}+884295994276725726905250365157608159561619009567123868301204958699793932629352235838 n^{5}+139707716779929595776325227650231698860223082133684347765800247276824391829130874710880 n^{4}+13245138217519024051353235090224270138339428865470164254982202974397838773939680191076616 n^{3}+753541396069126872495159385430841251307261454358901994547142058583407431491666588069912099 n^{2}+23820432161350232423438571477227377167150167494507116947238786558690647220374034595674987822 n +322760876111128643060849399264518450502434979786914975100141458955789083867133567383363957380\right) a \! \left(n +96\right)}{54626632308 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{73786976294838206464 \left(2430496857444645704845728 n^{7}+169096118198972560597438080 n^{6}+5029030090919355539531643368 n^{5}+82873621764922307363112824700 n^{4}+817185912477642714427879986752 n^{3}+4821333178973617964257567726185 n^{2}+15758058864968630081621797798727 n +22008825250341524043677705407350\right) a \! \left(n +10\right)}{4552219359 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{4231240368651202111471616 \left(268733956128 n^{7}+7296538433952 n^{6}+83576794712536 n^{5}+522749895344900 n^{4}+1925190031021152 n^{3}+4167586467596533 n^{2}+4901627062650674 n +2412265777785360\right) a \! \left(n +4\right)}{4552219359 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{528905046081400263933952 \left(220021496307344 n^{7}+7532532874227312 n^{6}+109420744767494744 n^{5}+873667577869906200 n^{4}+4138083379554565481 n^{3}+11618510476240546563 n^{2}+17892572716308640326 n +11651468547757352580\right) a \! \left(n +5\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{57344 \left(2129118502463708262400962125248338703774269470717773515582980197776261056 n^{7}+962849573566764385432694643221759089588462244490644331667046550224998387968 n^{6}+186602782398320008319929009851561303792484983643720068131083004794751199649316 n^{5}+20090139324823221002859020678749747868891078173926242025007283153333522151352770 n^{4}+1297706613226829097273625691819403445026932104860019989140369783808554716625816789 n^{3}+50291969807922932307973061554767888287104670755659171159059113781216186199098075712 n^{2}+1082743050647060645367231692497076537223374505227779833628146603575116015181974698999 n +9989697669581854243640149724526736911739639782686229078467899393568195158015822623000\right) a \! \left(n +65\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{2048 \left(100303924774798208012407507235477258348137343935958382022171783348576414720 n^{7}+46036183333655128895865891299387836314719788035002297332787809724183648421248 n^{6}+9054872842867869111399940933240027392714172543369688994995489130456839136316840 n^{5}+989398363630375517579901670886594208461433337602496548347320342554066690893835800 n^{4}+64861861762405097120485845566169891344782039248537888956972281640974980018443981170 n^{3}+2551155169524176493062575541390240038936669835689749725134899825077133226250509084547 n^{2}+55742915418882535403069653866739153080328377624444839870657425323398150836153437473355 n +521967424792031136075397826113805054173270605529187642776443340479697895783407616709240\right) a \! \left(n +66\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{1024 \left(328858874550107342659355229697341233526945324510060169912001407593915736128 n^{7}+153147188730434866861241220989475037036019553115121425316032851996631749295936 n^{6}+30564038294262523167842662766550312554913087544701207441530582805741960717589728 n^{5}+3388588505703529207986811406188844775516194672263072783508308675165712858752020520 n^{4}+225401576686117890204727558195037297388597292424153867265232548786024912217583859702 n^{3}+8995492718846979755758854157556879948254260475196871920488929491446804018351847425969 n^{2}+199433895625694150835717740350859974949490228646347011444798310982914538573800803867337 n +1894848946830380401261898125262831065736919997174614401638175795045314777916390040601260\right) a \! \left(n +67\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{512 \left(1050562179570149085651590811858435112448016796328280852348343424786640285568 n^{7}+496293279373186227123801352147603342827498669497920418525303266208485334624640 n^{6}+100474950256899848395981423851480341134554694455922455736732218092484892770373624 n^{5}+11300148349910199146039376121292357978441325962449818767972995466041287898258285380 n^{4}+762502149132733069519757568910010611261405491792878050976525038918710348405582218362 n^{3}+30869419986720079121588320126223232599429221914823075640498336725065486369573946701735 n^{2}+694260523615459729675570599400140136019886084045640634503531746993778702109393116230081 n +6691426151269899532188059907162153474305399724999062837749964300865069466754122713122520\right) a \! \left(n +68\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{1792 \left(467171532398131020810483260786538565684303855747071209721299360205653078304 n^{7}+223827090866605436217011305418395028016208404257576721505899636058897097996128 n^{6}+45957050678734922245659901626514166652339207034455687049360390047981711504460968 n^{5}+5242024517532057463959420290930207118294538629480081132300887568222014799439271260 n^{4}+358737682742826502650107995843744089703281702264826466327384078282263860294951267396 n^{3}+14729428660559822146466026356062486764871024368670424962042760897143561602169074890457 n^{2}+335971084652354572295058505603798925078314743932248994208910689553204326803187722656437 n +3284132119209347203668224447092998263851246167557235015739890318937361404796528082912240\right) a \! \left(n +69\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{1792 \left(708529914650262645170020687309479283844197404346634840597993366988429487376 n^{7}+344206946523086137023986157241617191112282233861583910629104121417964007749280 n^{6}+71661290918400115609597536869274581380924455620593002362583495631996115445366392 n^{5}+8288145512408903419072190377929235049060512792120306880180952331688036624702454200 n^{4}+575124027728660465056741224231083366909668465380488285492355350822145402891587222009 n^{3}+23944014597520536642058123133849628187930734394857706499640086205019727932412021183150 n^{2}+553783342935881746606007614446581349677432748948184404284339830207379726532680264867253 n +5488907345722317159532365943604858979084665750470420127792634076130448618710476854485310\right) a \! \left(n +70\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{128 \left(14660302363382869193432159172302374718950560284656452932520478875969352282752 n^{7}+7220009395043471602799916348613362199169135637899793475786869214310539150299392 n^{6}+1523829440859381335253345680929893034733365317227168772387551343306524788360266528 n^{5}+178666409398103942369530966223363349938274278621359221212814794998581769269319612700 n^{4}+12568431337902453536280889206007040761321617682972628132954319771719322324547976554788 n^{3}+530457717162162993599334246869861474482952652584525787557385992454493825505029502641193 n^{2}+12437358406930969497887582715779966878943309304959212332008229102792201035534971909146417 n +124970883469980821880209203665810260747381699628484786729916561055973015699246745055288270\right) a \! \left(n +71\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{896 \left(3016390705897524507042275387460532371081345359537034472694203007328311681184 n^{7}+1505658590390757752227258376235208270548176564084689131219085622826900017966912 n^{6}+322084062066460302064050715036362939188805620476182195173263066944105121455074004 n^{5}+38275420442476344972991138586795274112575609301361622701120768494804569127287631820 n^{4}+2728992720864071976532972515561125129229851251887750499438967237665781268840721381611 n^{3}+116739106906694027152202566395175833346633639772415760563107838969092827391730526504238 n^{2}+2774202072324710983746015530236520348200698380557920177355010279860576248091078907967831 n +28252909777755281969211929974216879885175587299093218698329344676385365278164374068421240\right) a \! \left(n +72\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{448 \left(8467426783568838109652398075512880019346562365204439406823621080981268898672 n^{7}+4282992565835763471277529553029535382894722728250350842681306276235165652061008 n^{6}+928425143013435969998539021715482934552367107312727185766194199687888477415998688 n^{5}+111803231238559852556217359323577354326787792058111588236575736527356291102954471060 n^{4}+8077805072024280284530872079326444794933600478397306751522594667813916555678492678183 n^{3}+350157828056031242280920049066302696639532576947780620546070760953607602748909810941307 n^{2}+8432219788761592246229406876115540803465267423781260531207117158104416855664638333412002 n +87020831446498470376200276171043983852016282286660750670492590869633878857771565512959770\right) a \! \left(n +73\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{224 \left(23163511891254949564033287979441877794896872722476739246788818999167256333296 n^{7}+11870584227399936625567021446126309405620873367231803871398785040999334445807104 n^{6}+2607012944705060276241309605874266313452401571923812086842678204530303176312940160 n^{5}+318069382974537266499667497210129083739059688781815898258868660854400823575069120520 n^{4}+23282616519848014492754468027314747776403058903487514461082183842603301436371307321299 n^{3}+1022522426885201810834441454419332053291961479505289049143535048664967654681813910312081 n^{2}+24947163853194414764463860253784128540009654970444799166739775537700244027829931520066890 n +260838932245328083316291043146926607239460473547447948365920455941837013871069557874050490\right) a \! \left(n +74\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{16 \left(432249158966691688557015715146311711986037609533621983536341648552110875004928 n^{7}+224383185412791165387592725128478780397818197382407010898895697352670069509820704 n^{6}+49917102714979180763540569816598135091518228265449729742496344565745959333459987792 n^{5}+6169010505928366375260972817314882674254132306815156935959694432956791140832759904840 n^{4}+457417074675808090456612051980860369029787352857294060574232766070228379488339912960142 n^{3}+20348848754582656873671365880837607992205428712039496679856162606117723507853761346870011 n^{2}+502891222155342843594949176596191761470108444502679188435793533362401042940547397257575283 n +5326115869675657082070218472834314045461350061332079379659204491709946116986344974456394760\right) a \! \left(n +75\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{8 \left(1122858567318786963007444945686621850366224116273437494738993076857311431982240 n^{7}+590320586969333906276579018922762056177608768961586755242405808221212225934231936 n^{6}+133000416840015372419541290733675440223759374379404538704504306965847307581774368136 n^{5}+16646557336090384682270663697285582449131348784793852913938259420334452597270431210940 n^{4}+1250045567026377668236787738402314387709379849597328170156735138501029192059832962939340 n^{3}+56319282512439402225488571790722081233657497682488127210274736858171967692111134422225629 n^{2}+1409595005021891061901022140399939781297145033403215875280601419877824842196995298758470449 n +15119350945517750330428517780218720951493023449935726721434429344662778604020320803808794280\right) a \! \left(n +76\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{4 \left(2842140603115688444058797590194347824951797125489202109639770341888708597604864 n^{7}+1512985880355716112309075913091168975917925648502977569540248762764908673362479872 n^{6}+345163971671374303878959137826855802141842301371057765449511643605467202569248751608 n^{5}+43744297109766650902776022645571559332313271445202355489485786503804594115659910500540 n^{4}+3326185292153185240233360385604561682890160423917298534977046900995409869727601341045126 n^{3}+151740075951340125401872211290537483490987591790258070557433146405169441307704927540724363 n^{2}+3845555736095881120871488101556432831293198360233156226613517582358235764344389495340763897 n +41765572989897970717194032909074805117721937426020062793957936484338268793446891706994944220\right) a \! \left(n +77\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{67699845898419233783545856 \left(2 n +1\right) \left(2 n +3\right) \left(1758028 n^{5}+19369132 n^{4}+79017937 n^{3}+141286327 n^{2}+93243334 n -171080\right) a \! \left(n +2\right)}{4552219359 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{65536 \left(47526372107542288088789751591062930511975934843847333216896662639960576 n^{7}+19556025284904397948878694475724639247203902812145986443872433112025532320 n^{6}+3448474746583497769687090800781152497112970271023718399543528230432263265200 n^{5}+337814053494915464208636223483182231958449665938979243520470382629388582960680 n^{4}+19854353039814683566306356348769487193701931828574153898362835730737389339697754 n^{3}+700100768279332742638232112256729345831670004350693449121018422733951742463891625 n^{2}+13714116659160863305165472600568873616574148232609156759652209761542575906111330425 n +115125829322951695360282035010684181822383082249190472982632440624077266412526770400\right) a \! \left(n +59\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(111607205546112044583937968983382315609038813768063606100431938230572262131582480 n^{7}+66692617582418287150902196961218840129543849936846039938863950306883680082229964888 n^{6}+17078230203703900700719874941067568975237741814661510588728674887110925464734848584994 n^{5}+2429356170137751259218937773351923115351205258872632483662426043487362746505415967393225 n^{4}+207322225493937788821871649170196839430222855929211567873076525415899435419793619230835795 n^{3}+10614663051692663161051553130774538440029990626151073567891980139405928628468575110510006907 n^{2}+301889359484949855323558539283890627279244345649730526333364512931876106358091906460364962191 n +3679303886771406823208535590252079697267999293774747841177280586839419396609002645494094519240\right) a \! \left(n +87\right)}{54626632308 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(105227936941938188855987665239265020062193128432108544780318442395500782602355868 n^{7}+63563078360959353899391275418374569463948707014674646519821083899405864529162985656 n^{6}+16453433162876808355290560442027051688422135224230976460811617859122324786741151390601 n^{5}+2365862580505021318373244187373749147271573326118404571618544624323356529271505706836060 n^{4}+204092460012224499203156719583414500719628126383347515829612339361136848146472696235798457 n^{3}+10562535393530139871921012812652885942649649570613116866817294336187123533965842782165518404 n^{2}+303660777325492984931440547900387841028570144575855913426524129057175920279467243803485347694 n +3740963872855812146028332696134493462023244944212625197954223366191367350706651670443153744620\right) a \! \left(n +88\right)}{54626632308 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(57867378465552508482085422060972856219907007626672562101755570320515721800196456 n^{7}+33830884045993759060729289777792663966486821470380629568368414638544840620840341576 n^{6}+8475742312015571350973962119242472103062259410837858862896823746482558120503034504304 n^{5}+1179589163040964760983618163500860840797861464970406585979848179899561155731028296867675 n^{4}+98490800833782983333290709849874502852064023091212104929784124445632245103901223747154794 n^{3}+4933690379941379375386548433884668019975237859128079354277473754115908662459893301395519149 n^{2}+137288807750318003812134472963005721210107018407276971397760086210666633933075223154114903356 n +1637120122389197544526430310634232385646359717924521608771317587170716301322813790220229443770\right) a \! \left(n +85\right)}{27313316154 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(115213737376638906704177008087784924130037472978417375411864685693413819545102056 n^{7}+68102427590757825153181152410506529810170701892275865546692408993319568513791271888 n^{6}+17250552170107610092259303139209311898634047211579498631408881800827501105725011160102 n^{5}+2427332090233594649684002848950198920706636690402476792323096467834027783312243803167200 n^{4}+204910564880135379747765712090041179279471133518939282501700130473197425533148453980626289 n^{3}+10377861128318113332889844711520581094855561932797141967603210892700013778776911091886103817 n^{2}+291968051579791764141053914007373263195643497247472463528030547075496465187070322681908591168 n +3519993477877352505054424441349912899229335112122514237776072251756724488310966098304881458340\right) a \! \left(n +86\right)}{54626632308 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(18854312682964670304116400118876871757007344756745688507261811347358330225992864 n^{7}+10900628310374354102722317807306589720333612286104653614611471936480521773454126912 n^{6}+2700722844861819999849486223765376400539390048496310673718490938982354837574578524864 n^{5}+371706369222088917439197303862292959879701292415869803576311286364804760863629835903300 n^{4}+30692678209609284388783417288760546565220390568230181553633186012017229654098263846358061 n^{3}+1520491163189551520864294886243740949393574524452257152132988587255565730681957357852723828 n^{2}+41843028463404989749938691724705252242941500275758641104567677997778935875352028088945797581 n +493455098379281209952789094107804231900073609509528920328969364027020172676413141559469030520\right) a \! \left(n +84\right)}{9104438718 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{2 \left(8419255457716590904906074755155569473338429703865138402346582931094597317462592 n^{7}+4592830264210502193217012981062435746940288038848670172593004747853247631957387584 n^{6}+1073706967638277284500346265050502294286817760311315592620800486755071595057955825232 n^{5}+139442094182862688204654740043293945452701473534414486525898904692264760904736676284100 n^{4}+10864964814725349133656633991464075710255837620158746818230200797888777781693200625479068 n^{3}+507912437998010099327891106465239282956220132378957589489827553013261919525084288250742631 n^{2}+13190203691765931875300123050004384147247474882144639990497946506497254367992502564448589603 n +146795178555842666681022922496115768481261147624656422496738428154991068944386481588092511070\right) a \! \left(n +79\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{2 \left(9850727246684971831270305196331747758553582038286633946056531565582194902590912 n^{7}+5438366701465657366666672637660321055550370216288241881681311250178253915197912608 n^{6}+1286665516900993880203964854684333813855143192706331017055510494327989105142862678772 n^{5}+169107886512809410814681634153515684566076921664285277616932390760667756065587382272160 n^{4}+13334803009169384279306009217240665322844924265134782448214532977185567395743635159071303 n^{3}+630860949357221565171227447752121735466955381748955773322276358183803690318923376394219217 n^{2}+16579864578546609061846078573794599912179146938839503394902187412287094191297641671447314908 n +186734288188111533950318846877172626320528106673935964884449554668631698053069536542090908160\right) a \! \left(n +80\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{8 \left(1752247621946196442217016842262285462544078574092131122537349559868663002318192 n^{7}+944348543713905625820854700683489900691279838343556232409019282178104002638431712 n^{6}+218106818791117336680120328766706988008794910032553711917607294110991080799762193048 n^{5}+27984037645922214106225732419249049681693601819959495772734295006925232137095463865500 n^{4}+2154166648797643421419186559933568907010528281934374094941308133057563164581687852476718 n^{3}+99489175723339031401080804439930242243226899203739828836271608957169324036430159887866298 n^{2}+2552560518717514977531717471500651037544039880614181162272243689032382476898770807959000767 n +28065674293580395267331907082896932443501706106775698329840453917418771846778309587785807590\right) a \! \left(n +78\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{541598767187353870268366848 \left(2 n +3\right) \left(2 n +1\right) \left(2 n -1\right) \left(n +1\right) \left(3950 n^{3}+13779 n^{2}+1972 n -19740\right) a \! \left(n +1\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{17592186044416 \left(13969932749759151455728531996584954795829355683616 n^{7}+2904218387142556171289309910858264237677020266455616 n^{6}+258729774027955764545890957545469516696176246139237112 n^{5}+12804048938384554062346446185630039321391422493143380500 n^{4}+380148354192091280204096518617982419744605419284530098484 n^{3}+6771129901029843781164611320921365195378782150207115632559 n^{2}+66995412243485768039770550764621564146295375447079609158413 n +284052113371261653451835405480480790169808118243663530008080\right) a \! \left(n +30\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{8796093022208 \left(120453712098608335208367035467377193945519108115584 n^{7}+25864449144258282176866982245005633051207146982630144 n^{6}+2380012294955408165483523049971209596700878050749727976 n^{5}+121660566145761359912118531184037998257950757109901058180 n^{4}+3731095497035212947127475011826045038182766905904910150626 n^{3}+68649328555721458765961937600248237566469439092831688283071 n^{2}+701654613274058491583185859623817371950073415689346797193319 n +3073200564986962712433698082858989628781155646814032482994860\right) a \! \left(n +31\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{4398046511104 \left(996207285088981351544860627777760154981934814920064 n^{7}+220721012721214124073848762153166048894161778406402304 n^{6}+20957546112909150176319525273077110241074815093183929288 n^{5}+1105456958449607872119051900409647723182857711070860116980 n^{4}+34983983392030902615779349373961542066619638500677908068866 n^{3}+664232777846683329731069752561930156727654223680730567586931 n^{2}+7005979172770050467360449702439632293263211217570202445676017 n +31667095955318344237450191598346265511883074460464319540557920\right) a \! \left(n +32\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{2199023255552 \left(7913623386887074100161098234843333967664354304668416 n^{7}+1807486656958555099159967489500045171530808806227209984 n^{6}+176923985079646935371130337656805028340771147460450519048 n^{5}+9620822521065718249790786062911109712731644835062003278380 n^{4}+313886784476026107331779194715000703295947575649066888153234 n^{3}+6144222082972071410008790417513194381342361812685638967420341 n^{2}+66814047872525803097942147623777774438042489777877817187260027 n +311364512571514967794024740814608907054963278212275023004248240\right) a \! \left(n +33\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{1099511627776 \left(60464019248891324565740229886218780757590097192448000 n^{7}+14224183737185582468213589019313391966913606060508416640 n^{6}+1434095418570976438791466259528000803902671604446691395528 n^{5}+80325081789164631938075334874807262493694105114209640231340 n^{4}+2699406468634231168504001565946555897922378353732067277347690 n^{3}+54428599424635513940553896776252050710520500613341359661769005 n^{2}+609679836777283317254293323366560742775124454659252743779710997 n +2926751263166999753287069199875164373149059708452052962710264780\right) a \! \left(n +34\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{1125899906842624 \left(74725127448538691661259763151349110557679824 n^{7}+12977534908251271877609356998128812263090952752 n^{6}+965667341684847393689392404202376593121180716760 n^{5}+39909219614753726164665365455973426359607921634480 n^{4}+989348750727686045177398911186532225273054663683191 n^{3}+14711350373507103409770696606827556335586102758317368 n^{2}+121494170828099551566543086102503487047285503805369395 n +429883238540622896402827190982817911997010272217538030\right) a \! \left(n +25\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{562949953421312 \left(810409170024890868817713218325358630803934608 n^{7}+146299684089574595636795054684134238502639376768 n^{6}+11316439974628855630635980976220568602131092527512 n^{5}+486188256599548133300247100121301192669631383255100 n^{4}+12529902020004618302073087222445133802684060776285187 n^{3}+193702910269392550130667318754673118719415780670986172 n^{2}+1663193946303516921258793534955944743400695161881063623 n +6118718917332087103451725898273295936239347443181238730\right) a \! \left(n +26\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{3940649673949184 \left(597882312136035613004884331644194441688096688 n^{7}+112027735637911797004437190044335939798836915136 n^{6}+8994533185586944563999500053142185940816576500172 n^{5}+401121513730751673569935319550091927061071694752190 n^{4}+10730948628048541663137116294996228026356151209005057 n^{3}+172211439129379131512351860181625230762107102248990014 n^{2}+1535043883562057614077605896106924858681003787161605323 n +5862829423196437182510552842664732913627077086830422540\right) a \! \left(n +27\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{985162418487296 \left(11780110573057229652802876905363707740355218112 n^{7}+2287897243957382474795016772660648334424586950976 n^{6}+190406232380158117976357967727929281422288127923928 n^{5}+8802064439875316534478049859840773788629971639633300 n^{4}+244099806446577354730082835824851315178221197160521758 n^{3}+4060943036759198307184835927356882777321778638368739639 n^{2}+37526347375084098006227224119140821239734402464198264857 n +148589636618751315844739835123291429366805255475520105480\right) a \! \left(n +28\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{70368744177664 \left(258659574482887917857518757765236380600082918320 n^{7}+52004858919679323255641377173148215705131106831568 n^{6}+4480533334645434852731384320078038617125233007872160 n^{5}+214430894684068075050319540101989039665267356108626300 n^{4}+6156555475563292020759174357379307180496900895194902345 n^{3}+106042084376527563945490494661675404233124593961525675282 n^{2}+1014570532979469457324208323438741609070693746736298688215 n +4159515967969714355458589351715826697649751525585479909660\right) a \! \left(n +29\right)}{4552219359 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{4503599627370496 \left(12822033338657755568938460170824911577376 n^{7}+1874115114101638375117786644912563880692192 n^{6}+117341386555823171089033487318581883407933288 n^{5}+4079631008213191893600349585951115347211693780 n^{4}+85059744840736157572696337996355619278806380504 n^{3}+1063545434657602912581597868912831805176715254793 n^{2}+7383945897268819699584293550150839768702048221617 n +21959013873113724924922186990674011143637226056520\right) a \! \left(n +21\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{4503599627370496 \left(85979983374143059112738693963390659788624 n^{7}+13159614828393606909769993947906935067092896 n^{6}+862844373688952967451479514732366244555783328 n^{5}+31417006655421224497521076604135402483177207200 n^{4}+686055720863041477589021024785229785441347433971 n^{3}+8984871314716567091199007192005208383278817982084 n^{2}+65342277047208524053230482626794392719784850013737 n +203562742504420894545016028875999628331766188392250\right) a \! \left(n +22\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{2251799813685248 \left(1090418634334899040506250937699478571265280 n^{7}+174396493041827775901049109593272656652378048 n^{6}+11949518580312180527789313931788098195802112512 n^{5}+454706531407898256855299948513554831557597979060 n^{4}+10377665320606295169658265773333676612676476691840 n^{3}+142053442931121319622268344909515234757872170216577 n^{2}+1079841073030429289095799385025519184398510985579433 n +3516542365519815902259833900864293997127166977012810\right) a \! \left(n +23\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{15762598695796736 \left(935911879788042790397024882722136033988608 n^{7}+156116747375492984617394730057880381921847360 n^{6}+11157173619881906710509351930122189933285341532 n^{5}+442842527265505402280127251284686404964790171400 n^{4}+10542770341197543787489107108974176424529755595407 n^{3}+150545124894354617892714225506329872907705868430545 n^{2}+1193871993862756715769571422689602486525854725390778 n +4056207287552548443714112355784237452702872049865240\right) a \! \left(n +24\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{252201579132747776 \left(531182370636107760564118240736577664 n^{7}+66624735466998623936651867111652856960 n^{6}+3578771318516457176589429946184799118216 n^{5}+106717629513020418901044512128468496270380 n^{4}+1907915627239651586838939196595221426890466 n^{3}+20450151729487294350276020990886659862844525 n^{2}+121679795028219759141924012917084275187128029 n +310038036690756664557021320364682811549697660\right) a \! \left(n +18\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{18014398509481984 \left(59765700567489846761559038995618537024 n^{7}+7910024823439377382186017478123573767232 n^{6}+448385563875798942428595641087068559543368 n^{5}+14111438831374453023163717549862840479864540 n^{4}+266289845685648447502568532753533412871197526 n^{3}+3012977007075500912228975514338014660110171493 n^{2}+18926300711341289091418240822641676979036975517 n +50916076068223494527266482948349202577366387720\right) a \! \left(n +19\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{9007199254740992 \left(902186263844801238350938264848220702400 n^{7}+125640752122938915273434821007768282643072 n^{6}+7494606303037274777549409645512797595548520 n^{5}+248227387812268841110273724223539338336093020 n^{4}+4930051641691311020464758259218266989052246390 n^{3}+58714984425052880107767475030481895687792161133 n^{2}+388251766354550269821277531379535144834190438755 n +1099603092483474455590924926010617859633138584360\right) a \! \left(n +20\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(101068302238895055423431789789223336604072536723844171112507471125587292970601732 n^{7}+68936964267104650412452952300268664089868546883461471255812461155273856489399637688 n^{6}+20154877418989061981457446621929680464885354879275410609572185800454048799075920663311 n^{5}+3274183093084701790233930876683694768400369412153782414762708327503003993392934895244320 n^{4}+319186095724518163928401088918883235671629917278491781480722194387280238449018984200936533 n^{3}+18672513602725686810892918879954100557260436220214571945589240558077004920575183359635368352 n^{2}+606953252866513491830465009173838323990318372766650945016454258714916213135826215764206996484 n +8456615821756868216561920051514586421374193720234276376041179342241395714483930462734123973240\right) a \! \left(n +98\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(91837719836473913833090425420674991016967960929874891412280319587378054384702244 n^{7}+63481534526531684728683043440252155915215165265489148547430025210124946895937302704 n^{6}+18808241103314551411164717645076949480149074640482108184760255068129471918526453676683 n^{5}+3096184858944977968598936715143952235267796618293210731073534026104216606484438545230895 n^{4}+305848574807489967920044048395549733939655164352850700982380058171020719399738212472406691 n^{3}+18129511220510904121129732215319219519762692188943547254047921470943457910686554592297979841 n^{2}+597091916785787689421633104490473596467922539636710579533538844216052260474037153558517426122 n +8428816876719605644436781412472545037468925426420671353375559956708328421855642769223812692060\right) a \! \left(n +99\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{288230376151711744 \left(596947054150939986988383282674816 n^{7}+62431030730424428856404028361011968 n^{6}+2795134811922905616447773308952919128 n^{5}+69444171684798517619154381578464814780 n^{4}+1033982032621290551598080641973228424494 n^{3}+9226236217158222481283533058681722501577 n^{2}+45681214649389798837235002770020659836417 n +96814278528389219803180473030795383657700\right) a \! \left(n +15\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(28264087385426978677471391108912657444667184445605018564748500553863805097917184 n^{7}+19781896492731605504698844847913430399991039544264242365151964345227824579067680848 n^{6}+5934082697544138687361535067971132952338303302069425922499583167916740874295102035245 n^{5}+988998035581288028072239810913000660716993566464943808802820894679629399468571410393610 n^{4}+98904570291613162165585324102620676891272989312226722899052074159951777519260804831577521 n^{3}+5934929541019978396513919947162435171792102408790587802635688409611329820967706547280517312 n^{2}+197864770872617877317252950933128727628875136243954068199029372171399381440161783385141724360 n +2827287631799054563070105231974652872888516871145934505724036668167001556236445893164625211240\right) a \! \left(n +100\right)}{72835509744 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{144115188075855872 \left(11788523858038241407843997989518464 n^{7}+1314943714205970688408171561656208896 n^{6}+62799769370374601619942958983749227832 n^{5}+1664588829053726899051625052089297627340 n^{4}+26446539092944192536542444254780891884686 n^{3}+251846156498195993265212903882711496836349 n^{2}+1330990139129237859934194922973574317879823 n +3011450812702615378325898113208009562486080\right) a \! \left(n +16\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(78784163001937574673543663602728422682139023389734885033958022086750848660480528 n^{7}+55777666818307975315798303772184575814150087091420374791903742797222948669615365728 n^{6}+16924438761695135726887153409904657047109322411592508469109056229478024499486488202535 n^{5}+2853017410105224608298095423974676659072333248143242867851999527440744309284981821512035 n^{4}+288571851693231377879449779769089553815741495201054706551514016832681467605160860367535707 n^{3}+17513072520575933943770708957098419577534680980182416191567276063943566843335678531086419667 n^{2}+590480080976861527382401717846097848668259388972916447309388628760993299126112176717649692040 n +8532530673472277994328860259176427716210426736050554165630532574391479301759952015816419702400\right) a \! \left(n +101\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{72057594037927936 \left(216660329981387042795377675256617600 n^{7}+25672517985866675835201369947980809088 n^{6}+1302615880188562052031857378873648464312 n^{5}+36687597640920612396237292761350808259540 n^{4}+619431472950459950944104364217321182022710 n^{3}+6269473962232565605882837354992647618180467 n^{2}+35221041762782710599914654843802971636240613 n +84721932780168740823754160218079331552897600\right) a \! \left(n +17\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(53803864833649229478163675099178568113399309443322860185254073771086394740655040 n^{7}+30757439373955904272392377052888089476909887486186425886574671475619782003157030624 n^{6}+7534895205933600033416352849818906622600995167689544709372589252972601377849597770092 n^{5}+1025412227522175757147504592355650011406531262233875819140380287798010417683977051820550 n^{4}+83721570545768678219328561215615564168217297702739594170428527986057219927553259682325750 n^{3}+4101034659142923156353725073823696661221655188074056184683008259138043300386666438355353451 n^{2}+111594436386854214800436105893288464976592462192492723276841589942921434014750672485874112263 n +1301307623541930742446879378310854861596714181248672516340413822576967647900696736984037358010\right) a \! \left(n +83\right)}{27313316154 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{16384 \left(716545876185188469835445803413201335935156872665472814966348029104432448 n^{7}+304629220575320682544394133015656131514754279673871395186642841314181427904 n^{6}+55500735088297141810559229716867777662808388732552197475690734083813291292424 n^{5}+5617323088009793451302603590002058311563228504753621004876213258147707512510420 n^{4}+341104088635647575513602898050183376834025299736133440920964285931634549224760622 n^{3}+12427132110850674279532224521162160454190444783503030320503061039206766871229618221 n^{2}+251511151084490092067589614888000026680299583263528777629927618395122308765230227571 n +2181429944153738387016027457983910846086267470213627320826863757140323274349686519500\right) a \! \left(n +61\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{32768 \left(669029476006122826172645502285522736891649730773643849136294312122130240 n^{7}+288976339515588973462492962554909467082199380237418734375729589437679224256 n^{6}+53490791253717622587904344679708549485556390344799458213680047234155598724248 n^{5}+5500465082893375508396045987770210093622749287659947684278479858485939557139200 n^{4}+339349246076041749938095989094493549088857654095413936472281873435888051630054385 n^{3}+12560910982583350564418783447035929732366363602637236369681682857654380160785635009 n^{2}+258284353691726070358383045268235867331147176829916957646872085758071442807864547157 n +2276004898737283030749038344048517911582778353775157436833126225102242666868527631840\right) a \! \left(n +62\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{8192 \left(4868848174885081835691117355763429272017544109893148421710740450753677248 n^{7}+2136031798400619952261062521302732359309241433321054625947269751390166502976 n^{6}+401595852684460491892213052255744589249070293351544286717780219781428910565376 n^{5}+41944474629713134864164037959227414292121274878103503267363222649102780871066500 n^{4}+2628378009900200978178046096474526960668798514516601765263959530141904204064130152 n^{3}+98816202426651119050672742397172441687458143335845846150513394080285515644317040799 n^{2}+2063819712394461120187472127172876713988182066697287128491114864598673931452720089859 n +18472007235061112107121948109261830745328281063256316961885559560686022090713090594010\right) a \! \left(n +63\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{8192 \left(2876752684832857575372638984672091415012130351502456791716659983878340992 n^{7}+1281531897729081838002148229006443315214839808067307066859776467573189956704 n^{6}+244656531173972188392438514764308284470752011326542012009540667934879570082012 n^{5}+25947096428816844365405778934192865228800314703733802342383293284584355517984700 n^{4}+1651006619747437935902495684428024744168267292004167449299492136720568756426032913 n^{3}+63028467514508644024954434733930347685113732477375723848162621763841086072222508866 n^{2}+1336683546617635108252343027976659256032252524120552262290919027526782561356081286023 n +12148422724745675688173076872609648769257282505594423746050439636774385058638876600960\right) a \! \left(n +64\right)}{4552219359 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{1073741824 \left(6739264622561242466184061720149308024718248714456917394839072 n^{7}+2056520886546493919264785415466406577245207989299428113835912000 n^{6}+268982553876219229147118421032039987601281706717629494716283089544 n^{5}+19547314848013034008917160112883420623413968168314527841399722365340 n^{4}+852399533675197971838652772690516583609401547282274984995663710103288 n^{3}+22304357829962945353800944055820755931790017873983418975272574349070205 n^{2}+324265118378736862429178357545785622193585483942095349977217637140545881 n +2020541484277329197595928748323133953541774066229973169301691296210622920\right) a \! \left(n +44\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{536870912 \left(37165859074758590290063817720553912410681866958411460870408208 n^{7}+11608615443608133590779133249735565216449799698168193080311504752 n^{6}+1554123980759126738759708587311700947800593753820832386132313790432 n^{5}+115600951376069775604737495256011766600610648723147322475797010737180 n^{4}+5159749919776506960260733686008762818115806235459519444250282055319507 n^{3}+138192549148894231222272487890193305908249554614143039715055946692218978 n^{2}+2056377362265542311013289628888979430493357776538356020728501974715936353 n +13115238026694746354582520734017356078439352148476425965147730829251159200\right) a \! \left(n +45\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{134217728 \left(401393468942098398020308869502988874007462286101295353695252896 n^{7}+128269523292674818674986094346799013264876538978516269100734650688 n^{6}+17568816392887135417310430525353251495702454426803699612392278828744 n^{5}+1336992030068059729515121585308066834678263024915674636405815255569580 n^{4}+61052485558705380761755149345276830231048326928388284111328179179900424 n^{3}+1672874180952176215329865236974433282406881248410171329047215381165330617 n^{2}+25467249615468349188397266713906622137224769801775330769671616730989379991 n +166169986730267867817259499062613827330313453006402094761048171535529377960\right) a \! \left(n +46\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{8589934592 \left(103595109578458226931453299017137250088733946441653154048928 n^{7}+30133376651226113578118221237427185010749127594204939593834368 n^{6}+3756854820643269049071608410536137016050439628808014922510839400 n^{5}+260238167972389435085471878557818164511116408171752152270550688140 n^{4}+10817051248952753646067701469818084794137032645806312716981931536412 n^{3}+269796096344623331168408849267499373141437787510517268783696294391887 n^{2}+3738738644789094101911518117714099444671921408390909636259590213065005 n +22206007187515658153428720615019622201030319252413333181595944659724620\right) a \! \left(n +42\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{4294967296 \left(597725736960509515324656056884876327478214214397796031455760 n^{7}+178120094438186415179259813972732709831021359890550680598402736 n^{6}+22750654405638735947984852112413673600714407630123095385479537792 n^{5}+1614531986149789668962279172887582997822015025568894331089172655060 n^{4}+68753120530804094673558996026644489853059146222862258072971465270655 n^{3}+1756825469991074392812603055454571537774279693091651627582158013349494 n^{2}+24941865942913090550539159436956339331375727994350357480749878166619363 n +151770204577708862160154441060462602942015212609389700439173712383515920\right) a \! \left(n +43\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{137438953472 \left(231079604086734752522716280871436873360662422262814343488 n^{7}+62338124410960148593971095549741906406541680592622187558304 n^{6}+7207769928469254174473854308505351451339071389025090815548020 n^{5}+463025970141111269531003214956676491217398367083855746964196040 n^{4}+17847963222261616707710065809056078258085921051669421805268972817 n^{3}+412808561399598571464201921706470219867078239881167322235259141211 n^{2}+5304683985333528508780004189825431386060445244690465013452564536215 n +29215589252653110697732874962777001695344501147431026532664519009105\right) a \! \left(n +39\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{34359738368 \left(2885318465003310999094101222441078825416951429755564758784 n^{7}+798550914370150482292642761434247652310816225837869853703424 n^{6}+94726569600981976362474092191355648855467095643057182877541824 n^{5}+6243145672420133452553617097315140072217266882054642154063120260 n^{4}+246898894337637468634167534270017943380420528676002109816059282056 n^{3}+5858907142528620879519957868539676097143157811716972830589281272301 n^{2}+77244910545566634091856237805119527759063047470873042766397228255581 n +436488069185277339058974748420505214381269985067394589839215404306720\right) a \! \left(n +40\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{17179869184 \left(17517298011857070248143093473135755891436760451979985408032 n^{7}+4971385969172112437722083182339313760130256561807344595925600 n^{6}+604717590500403347552260815343051308065134301531498484787314840 n^{5}+40869045835450174738911436293847162865083927547034181683446620540 n^{4}+1657389698696613230499086401467542150702455773922699082016722018088 n^{3}+40331158075266412280215211220385413549156869299260972548656533201565 n^{2}+545276238714406313555492751068819679099550255973693059027566103816785 n +3159698449763633654397731941239390731401379468442157526910188456770980\right) a \! \left(n +41\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{549755813888 \left(444967833551602449630189038609227959849803139144721216 n^{7}+107731514356096082696319967975561778543351263432877018944 n^{6}+11178542287943095294530111922890267698955096826339341002680 n^{5}+644403657274119711473936655659367959724031895569793550986500 n^{4}+22288602777293428844182568776107625505295385624422458476708594 n^{3}+462548805915491576053002047072784118234647164002994106157083691 n^{2}+5332811597428026040891841860797921098841938451073266124785860475 n +26349503245848813670444002889985090554980653906739535640595225720\right) a \! \left(n +35\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{274877906944 \left(3158671216434912003731871457801634084544337999191080896 n^{7}+786470303377912936174707547198838451468207049862675603584 n^{6}+83925881906161552665496330169703285163033697589067652827768 n^{5}+4975621981971678616845587289688289732901136984429198878485620 n^{4}+176993931744822715641387725504481171849317614328612730205383994 n^{3}+3777694159715319639950201801686777732961796649399986023065378831 n^{2}+44794712026419456268198884234362113361683984102563841506583397097 n +227641702221823685765125445169431670362672321076773859325079971800\right) a \! \left(n +36\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{137438953472 \left(21661249217322499132240974743826702788911620774043557792 n^{7}+5542814253926113947688134719388789386085173697684598934368 n^{6}+607882706374999569252911792510163522962255437551792649660440 n^{5}+37038561551133003952766942890594169014389085917511613354689660 n^{4}+1354113192972497872731303428067397507221219163677722209693083948 n^{3}+29704364047613613708248080746949825929053267565852468534750435727 n^{2}+362012949974641655616622629650220909617266382397990679175608178475 n +1890863166000472083218887122455086178079899032420475345180410890840\right) a \! \left(n +37\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{962072674304 \left(10266535749688633594603171333599741401575147701253509360 n^{7}+2698163941017299155906226823649621728658872324693455650016 n^{6}+303921809723681910305864343639805630319896460366170784676072 n^{5}+19019834774678275274321783087594341981139919989719092575623340 n^{4}+714207848873807310619448739314013154348229648793703963341028395 n^{3}+16092124642095308212741524533250824813582236244880237678219054629 n^{2}+201440669948734587269594921141326721934524282479444565480202942048 n +1080735696875377237729352045010475049274834460747037742916288938930\right) a \! \left(n +38\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(77251350193228776716927560462204313978726442060330423734371968189244505471797058 n^{7}+50556671516641001812598574860946709313121511332801593014217390029812361858549650816 n^{6}+14181137982855254137491875509928060060372949396843160530096890701915261934061085209893 n^{5}+2210088234415851627614259689089839858802296381314134499014773663661767361004474402741805 n^{4}+206680381481611102167782996928746483178795989760812482587611827432739977783513483745598332 n^{3}+11597955880062495364039810430032442381218492006655559182691338991738187476361094117552561229 n^{2}+361604562455462135091167513032831876382266504702815167341423446904802893573085565479650378527 n +4832298774568624770108332705395116963417157880393991272155224876069469554975459848473180653000\right) a \! \left(n +95\right)}{109253264616 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{4194304 \left(1359525448125484464678063715340224719674035148249990575541604919104 n^{7}+483417795227784172123890129425576526339536720189476864806986414358848 n^{6}+73670070736275053208517731197397392740891878576253135159399992398369160 n^{5}+6237271920773317939429794102796032539553309262405004823893195652088124540 n^{4}+316850870471954690204051065378024129498563240823171770841564857975527861046 n^{3}+9657607632553301156933963973652748791325154638175355901824889919620703675677 n^{2}+163535754774254136572995541516021794850648433093973724769227439107558739722085 n +1186801272487912038610728634760230468866099303719369175502631465888991556819080\right) a \! \left(n +51\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{2097152 \left(6489630317901672723044349564127759866949555056128478440710228437440 n^{7}+2353798096951487127789443949485490682812528972899117450105423215975552 n^{6}+365884999428298825081073558551407071654713196794190036767867945606735592 n^{5}+31597183436190721668850543224261559709499605952041013986207861502907592860 n^{4}+1637201943766774264791536367921596556974182859771996247978974310538839828710 n^{3}+50898417627396550013112089881539405249362266256094641204267962317065355234973 n^{2}+879080786407942480244679046091550009217472800693905661537010177066554553147523 n +6506832488908726067157389201775340619122417338374790283243512426423738602400360\right) a \! \left(n +52\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{1048576 \left(30298428041822560502533225030458493155149564729727346330677960966560 n^{7}+11203880205546825571491838510455907972633290697827958508203055066195296 n^{6}+1775565274958939926029359938899029059906246640289205877130283282438374440 n^{5}+156324530844134376255876645183267600905967968152864380416507863788135734740 n^{4}+8257753750245963228011972156427745800961883959353705974751755898284737928480 n^{3}+261721446559780672406305177718636812917893871181299462154259356531229908652689 n^{2}+4608226994597128163826006507129191797821500037610936230387331508860659703202625 n +34772801476829809806932779283038042334049200811023464506712625276808277869249480\right) a \! \left(n +53\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{1048576 \left(69127963149725767948329327616265782616545063740919492498832704427152 n^{7}+26049193596111845752678678832040843115916244121448659652894298145430048 n^{6}+4206774017061924474816993124581960743633631633974431786750892136289716880 n^{5}+377416766663709460609215413942664511364260131688060319411060200228328971400 n^{4}+20315735522822143538827716556596485718637540289203339603453437029202264229723 n^{3}+656117764683427906100721177402944092979945262798921528764345682565341337242722 n^{2}+11771823597801478520802132769775945823295504233036938762322070214525920649624355 n +90513369084899948285274265181486807743492539253169715803003083575740919691756890\right) a \! \left(n +54\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{67108864 \left(2123766514929156247041669152365569258194961407194045387702218880 n^{7}+694019080659748198889846708639237802225858843122959108899357438208 n^{6}+97206909474597664264799698990103196666956077582876282100536529264536 n^{5}+7564589597140743908226577309030558955069204347561028187187372991860540 n^{4}+353229556540392751317730404356904532600161886720445369876879288319900670 n^{3}+9897130932656154175308789064384309414028213085173825487254899852454665177 n^{2}+154069142694521410880812550459879273770818570258666530331854979037954982769 n +1027943035107430751823713699133253402907427134563615209323056004986225875060\right) a \! \left(n +47\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{33554432 \left(11013266143830159105153061409921589200105993285481596744530580608 n^{7}+3678574434062934879811159934487449520215480210677824697232108398080 n^{6}+526620745195635762692929176112887648389576342073466610634319755659320 n^{5}+41886382358917102584302332649171342211629301418269962454336698832323820 n^{4}+1999057073128436992048023417609611829273434087774941160427627880037455822 n^{3}+57246934816841636072757524967411407471544397961289284831669819377832024805 n^{2}+910809434501783246448232677501249284921731348734220739591980410745527675735 n +6210750584035007210509200559333434095700304576961419210899558161255619198720\right) a \! \left(n +48\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{16777216 \left(55975097444365063596613980233419854602104547763600362874181255552 n^{7}+19100215178432054785436229715026303465180384602479798184197400056960 n^{6}+2793377767231411221092738136889331019487613513049131920714404695329912 n^{5}+226971162109442816108938429167110489471095682087450625429839957109535540 n^{4}+11065789018427962997472633170871984865469191610915103323871736023123892438 n^{3}+323714511810205368334826728695554271145214639523864767536612968716789352475 n^{2}+5261186562561727678207163874464548794236225403118247147529031241382199380333 n +36647147694838374159185074863439820493074116372128210874106277806743209171360\right) a \! \left(n +49\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{8388608 \left(278754706156220384691032993260397076925893750298229232897227234944 n^{7}+97123226907794924542091694325831297737853475500402635985068133191552 n^{6}+14503224758170780942396105899985018044849949887649402593736290680688376 n^{5}+1203229271191050230311870666285828762735371446646590901752232611186680980 n^{4}+59895723331672021663259208832143653786915754014293419940248841777556618926 n^{3}+1788975616520871109857765347558191209278437970048564935035150636071942779443 n^{2}+29685753025237591218167122126786253625151100659704385069961069528229606572019 n +211115512154986577752123357575154298086233582822118655592468334864046704509540\right) a \! \left(n +50\right)}{13656658077 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(3206630771 n +641991095449\right) a \! \left(n +205\right)}{12488942 n +2585210994}+\frac{\left(1428639636162189781165667503460850539444275094853086121312873478722258949093148 n^{7}+1163169171734057829980567908560395637639996740334766120266864851587091578371519936 n^{6}+405863516755304534185866527381610576342615493475850260385627690429179406499524619994 n^{5}+78675293817760487694167256917951810631557922829705975618049148803148875561287709713605 n^{4}+9150434612873394128290626257423231634929028321766158013875019796479675316889445182654782 n^{3}+638542876784057779127683840268701722645975056028053655562191097750696701665435976831939459 n^{2}+24754813005223532468016434914953236840811589074955861730155753059223909707849497970952986096 n +411288155397597613558918413693866765628215016186227296368385566880334707304334798828444418440\right) a \! \left(n +117\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(1778907866868173329560143794733935128191671612533496821008407516212583056832760 n^{7}+1460051776586864665419013728517413405517344051224312636913037808553872247118993408 n^{6}+513571151110919690315687414235110489393096510310950395994122764401699540142867364871 n^{5}+100358654315470291706830920138773122222917683050783029925645511064989326763717244521920 n^{4}+11766699010382232093647548297747062123731341620811934010144885668027042650795010913582605 n^{3}+827751676657545414832597701428257387835087193379439697350817972838250744586090998144737432 n^{2}+32349483516817487904087718067745389504323636002754512282309647277005619848120883347455146924 n +541816483849355180387407876380876385808031340563581632435707557177606654789695272532419797880\right) a \! \left(n +118\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(6819245078395551549924103134607216999858952088180439788785108967951809045837860 n^{7}+5462765521662696786549699296905840074509426248432431530297434996712735631382991600 n^{6}+1875444464133817909869822005937727441527364780392749242296749822059029678859537590952 n^{5}+357697200175313509499194334311931826640945359062397544466445663257723515435161440920595 n^{4}+40932693922849508596738967838521608636299523561365195834351604075731938149007991917481790 n^{3}+2810402900211759658278832338771669501080059373430119477525166999343312368447877918647147965 n^{2}+107197972320572079680253868642586292757432901190422650557082509774307471918221751025249980998 n +1752346634858090444799510888460772880026868063287068744813340246768321929332626084048075217480\right) a \! 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\left(n +112\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(14647178806496513851445972153757483239298883042991291046322927937028279034363924 n^{7}+11542772470404040546386533715451942733929709023964286936975160768869886049771687672 n^{6}+3898338145324597721180407045180151910874017141292512084022086572421200707133993165965 n^{5}+731419306424948297472698503179811677745220935552329075843810859104612219626593099963505 n^{4}+82336929097597699989741721127516815030819294376459224158817943224692444133389113210258701 n^{3}+5561145798656977358571404214866063769360783159355229058268214162158844867943685410639497423 n^{2}+208665931940509595683107810557769544630944371950243005198737594961172234415172635224953753690 n +3355461229458637734325202614038540503642265892616422660608629782902371741028749650367832043200\right) a \! \left(n +113\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(10127836659937875361469809027773936011304540087057443145427410270880387148018940 n^{7}+8047160016488607434587919397322997880358220282039247715685277244734140435066708504 n^{6}+2740204528338218043261318834629571513154980401066169829671098740658853882531104762019 n^{5}+518372580556717702602825064176905709280263356984206687898308663496818846847304604497920 n^{4}+58836054659735725026311797385093303589938117324286393183320519727107385870003238248258585 n^{3}+4006706848493658605043750450249552601465322809176464702113775883714066441381064603406950556 n^{2}+151582954130199099251985746658411184413883947563613665604394903936529532194273637019463449596 n +2457693272279789285614847996972144293833410477249617064720672078311734086116487020512433411680\right) a \! 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\left(n +102\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(66769544682563444665188537842769755585728074012731070247762510095419158720131680 n^{7}+48254192282749187127454007043980583020281397499531962421409334464976801357587203768 n^{6}+14945127661577348973619464024063204505399396100298798726562993176046522583110976824685 n^{5}+2571440046895461274290938132458333454186953322238554706431131778984570214158955207788220 n^{4}+265453894961808398056698581507595503959680565497218404867405253260003171081208138822104295 n^{3}+16441358581875114338999266186028285296100240236792007646715408700227859815846166490579096822 n^{2}+565715948787335028425005087957617842295240217915287880075531339109033256147208840224649911870 n +8341938133624915031814727713076686709321442977352698258420863713681706302316959729357901624360\right) a \! \left(n +103\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(20012732621648786001035060471576930268073981135474968490447644072853696442758988 n^{7}+14600517582575871469308635196875781351649445719397316014907872222223073355937466328 n^{6}+4564919832413259962670227902811012800102634364375015871550697864472013682674745158006 n^{5}+792876422784253501736266385096492103335045344536595113469252796734107808570081877323305 n^{4}+82624562295023630074215442082222372344627559116555999394026042910602898139151502279721992 n^{3}+5165879553086753800711910285243995336438405866292122838213896601514395261059271551250711117 n^{2}+179426743832236686159412621679243018549454743834613649200675108868155230588812666548654029424 n +2670752872950397175679401930298152001174758059008666599790136402883351454337472464311733562220\right) a \! 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\left(n +135\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(7425911195927505781797113024694920156663603178806604852871298294204949428 n^{7}+7025656485802369192889412418020862616691196650260671018627096431027419576624 n^{6}+2848805033978905880994089358084932289747860531203285252482985011995992622750831 n^{5}+641773266299171004494523567791725818553790910431832946843472324223428475759402050 n^{4}+86749601469934461857241043854685272388975158764171085239941566820706254439074694777 n^{3}+7035913050886111100128994066644461203101990604879490786838245665545667358499071013586 n^{2}+317042094815513023421625248171119937107811819353345509643095650496913324389048652390104 n +6122837549739753490608723853377453769557386150024428064688729638581847909217225978182040\right) a \! \left(n +136\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(87716798726453999491075443071925045676118170331258015070576743859057001876 n^{7}+81046257782640080789219110458173882472461251046284259951163234197034914212744 n^{6}+32093632111084234959665055573653381891476533013988369375324445804907633105482067 n^{5}+7060654433658076085419489899734159250054849256040291883802859373194463921664584760 n^{4}+932041336720079005940253949126992672914561714035112669738767415202742986500367162349 n^{3}+73822664201222390643844144064515044267271934448510792349792166913854981328974123395396 n^{2}+3248516027329538881213907144155727085983147670438897046176583678459180628395844440265688 n +61265641150462930039312452148068819530294259967989431314775714356295527238459246564429280\right) a \! 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\left(n +129\right)}{145671019488 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(917382782794921403597797959641763508763851967058226079018125694557880566008 n^{7}+827709467603056955302478384419600358822954353474637350381795937453244567559784 n^{6}+320062787281448691957954715909430069493106681796645325954514122424241400869733324 n^{5}+68758567160719063399173908663134609862983827511353676224931766006547668425881062045 n^{4}+8862918509199769917792787445599922689912796062788165867724558141819767709872148404762 n^{3}+685464821180281177388569924256843266236283024791527105541514868350793950927067913032951 n^{2}+29452928427297682199152806697582022076818761655455017676958382923748433169591823626374926 n +542378647155462339524811135686492060111794909005315366630896055825888857019100516111386360\right) a \! \left(n +130\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(425989646330806182502269371264892293931039493393276662980182964118160413620 n^{7}+387400661836764519228689206741778384336528592311280894178567322423962720937704 n^{6}+150991888154316164651471134791306720428834653246589278037698009655094718512893018 n^{5}+32695146196843498543566027656096124143083770567778210622656201292279825096685515935 n^{4}+4247890410502534838133881719330601191016227436899546034921701551445763218600238591180 n^{3}+331149317971594784871616499281165041232753789335990602511211334358741834994403119282561 n^{2}+14342055508732753234200250026968774237050124313996714390841950623098833409093236730695822 n +266214566343425195425824065633434054736908760535398298418404373455950138662168079731501920\right) a \! \left(n +131\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{5 \left(38941732538129284059835451927350077014642453332898989705475932810736241988 n^{7}+35695943638135462598374794705767736468247448524548092247414049480914692619016 n^{6}+14023498898947184117262775426960873470975319741486173644167413204738675615599191 n^{5}+3060781279724153498789441649298486315127370788002831140434752822445568070448808949 n^{4}+400839537296392235848462188827496345899479427110417454996528188360276348621198014175 n^{3}+31497156337122258296029064123036204669282045313387864681654924128739112239150409311199 n^{2}+1375026655416372197691846580956043748462304279898679909163048313825198982916558559420362 n +25726800559341154551623206604615423296046955359344351720714242293893739092125320276683776\right) a \! \left(n +132\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(672569331906089000984441261887367919609838012888600126740100813825227610702 n^{7}+597344674221811997152972200663016090652191231989381398343510665520137758650480 n^{6}+227373121455201306911970292603949843445379384734645866361853321895851487759595912 n^{5}+48082147325020493026658209219257702403916799313733285483323395978606447171575303055 n^{4}+6100747844692991519938296084716720583307289704593089840025661131069139841023143631348 n^{3}+464447807456007900537008627305354120883957835009921208543178087306356407994145247913455 n^{2}+19643630559378902694451312654996235259874135649975158092323859668286174632030680218262708 n +356068414381350235542115932659291041803571930561338429969573187940910171073732540271672040\right) a \! \left(n +128\right)}{72835509744 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(32022748500908808466054820693159596936893805870622343673040843815806897471804 n^{7}+27779888064878145522668820303127386380624301146618987888208853008523649132488472 n^{6}+10328196879631054683134210555048128246920740589619903184232697912458772259561017551 n^{5}+2133265946381681011639000167604639924847344658794147183300914608566196743014027145775 n^{4}+264372204089748176790911723408315932495847250710830500936647602762175212044245200842951 n^{3}+19657892160127395466790530111882621384902837326030491693407155446902991620031567953594893 n^{2}+812053760782702558299725840197895738680738889846857987977572197914539681694490925619442434 n +14376563284885999355803196971383396099076957948813953407779254790310387954205747706117592160\right) a \! \left(n +125\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(5467957069648141719279863076610301602778049401744923285389485618190849078340 n^{7}+4780800412234082702196855787619088307176279079429120878174143346064274361685232 n^{6}+1791428149243369701795515040586672668116212432326622621683658845011178467517510263 n^{5}+372928698051111695129795913624423503422814782785802408882188765349162117825833349020 n^{4}+46580450858524751011578637791055197252674738413159430775930548940878882235808204986225 n^{3}+3490865608138837502388597413271119157576666357495856497929157294435742497397825981982248 n^{2}+145341775878686708205207723724365597877964631012263063544716491893043124341239505003408752 n +2593411868166116131355504396409140573644092658878255218911194159143832067150279820607103800\right) a \! \left(n +126\right)}{145671019488 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(8221490483642587745980524877766174609699656596877717792271695286083953785992 n^{7}+7244865032356329071359914913099799137593453944533156958593971119013003797419400 n^{6}+2736116943954449622667422765778436423500911735901979705826607890684699476069326633 n^{5}+574074181496835470940943634213013286601099011778547201988141756328336609957844348335 n^{4}+72269365571994497206036304900715852041769633625772362418122982134449212759543937432553 n^{3}+5458753022306117333588875261640335765208602168483263450813254705965818055057103919549125 n^{2}+229066710392526337760734721489728969985789186506474759327800685095482822706237797347703442 n +4119605917262367212852490807108412028304857960204043564187780680069452809046327647831454040\right) a \! \left(n +127\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(61113059588362669961645731142822136327391980877832691947786387529246660544000 n^{7}+52601662928092803133955707875693772700265927059487870773998452101906371436255784 n^{6}+19403769641821994457535855453311684964387327611078053305363517217819334557869328814 n^{5}+3976475078598133727133401388204971825416421350278024917539366639629905757630558353895 n^{4}+488944700850256991591417048757179941801955210622962110268653641122700570286619105787520 n^{3}+36072031019562857097588347753473550232055458240304954877553853114206605945308009816260501 n^{2}+1478451613878690302302436515182762703959146845230006117938936873088156463499409355651845606 n +25969588804347727985745008508209271372776601420094004252367103817825005864066868648675493720\right) a \! \left(n +124\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(638666874262549284254233162653316735845207133623577252751724541026802238246884 n^{7}+532632288761485382375080068297889279177920869072117560360004130393066715655135184 n^{6}+190370316801304664041490943707719956510238762612649212516804849154375584833587082904 n^{5}+37800183459428972137880582697642298781049839302898589106632823021887110783165028888765 n^{4}+4503345626999580908678637744983406094895253262825224780350713689701758179253744406085526 n^{3}+321901765075892660372557947108598885434107411243630958338343323497853658582141403800743811 n^{2}+12783047274924402544634471984981536848023554591504181881997660025459068151019519357394466846 n +217552520256564990118850314346999616126432798217318124210284092240787996581300937678424855640\right) a \! \left(n +120\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{7 \left(17547469874166595884323314353249401676606327581115059846262638275745991367000 n^{7}+14750732364996251168229883194610718125976907520854156746996821691342852389639792 n^{6}+5314125863873739304951118123858004720341537087324309587996531827692187364121849500 n^{5}+1063588322007419217192851272559748645509285522004612923114663370530482350247789057505 n^{4}+127721063311155605091052294164716564514981440175038361015210076211781171915438190168710 n^{3}+9202349999928452965364555675472292100252328213534634981694228831954561854614987714181383 n^{2}+368348142506707488870104677954334112111233469840627982940518595354226279338843157542462110 n +6318841632004896931700940054123669371452716573336171049352434344175433573939168727772843560\right) a \! \left(n +121\right)}{145671019488 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(207417367871825173424590976853571341630091563977705713452334653082597683982424 n^{7}+175742506431974310512195223983385774312203129485005140361955973860945105657499616 n^{6}+63815806769972604409573106032370474752210958340432604865624236461358684120994657186 n^{5}+12873711342401950247416123569567662820944144294627918440459964348993392265997656233125 n^{4}+1558214008415593410633793376915840032259312654487356814146944683224688287990129974897796 n^{3}+113161396840241712609023744871989980398324500701787817634371740575792354997334542406709959 n^{2}+4565555441454900586587124548590898583936200014953376688862899338687362106527364977811790414 n +78942124764079346292759035037142071004376944052193053229938697470486814369907463878979961720\right) a \! \left(n +122\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(113940381832936816373952659547112813898626865957099945772525362107231975568168 n^{7}+97303995249247655418061051732972121373554917263649117252266449163352155485426944 n^{6}+35612632939718580298110241885181066857457712464400052291878145549515771959965105322 n^{5}+7241061211499204377051521753248545510769095071089685245798962215304528063829947024975 n^{4}+883382658015592742891469112529832385855968975628150310516732269990196159190811908736172 n^{3}+64661246152785661773065210652412796887846135221313348497802329347321131191119640353207941 n^{2}+2629445060194769499401551507798384001658913376581836940156857933048703994167750263722599638 n +45825236725864214323372399641831462275493624857427952821754650633773656339279240891781982960\right) a \! \left(n +123\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(1079500538291487366774642926183490932304637548134485437840005532350053891682640 n^{7}+893130602294857520032439768170063699185039645006284234856558653342269089636398248 n^{6}+316683323880833545225592198861783726566252578435154136956250074700655104932247251398 n^{5}+62381788509789780607238386471050896498214648006000578482295208637167644891251118787055 n^{4}+7372870626639787189426070884086481304024588769638581815832320300271577941333773672030480 n^{3}+522831293114499805695786406150763489309441841393215928002863627520300583327277581338909737 n^{2}+20597236327544734649401813050125611587423619334326360728148191446201759815344232327633585722 n +347755872568436699328582124841212786589528735657872047526720765923716767584209383563641965080\right) a \! \left(n +119\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(1927069094386999028040 n^{6}+2285886061926617871176024 n^{5}+1129786047206879473059835323 n^{4}+297805111030086307292634908402 n^{3}+44155642397567157201079599954993 n^{2}+3491681311666713881641278280304738 n +115044896916089570711266198534656720\right) a \! \left(n +200\right)}{5395222944 \left(n +202\right) \left(n +203\right) \left(n +204\right) \left(n +205\right) \left(n +206\right) \left(n +207\right)}-\frac{\left(312628341439839024 n^{4}+248477594016252266744 n^{3}+74058490725175604210325 n^{2}+9810190514110523114204947 n +487313879641418977211763000\right) a \! \left(n +202\right)}{1798407648 \left(n +204\right) \left(n +205\right) \left(n +206\right) \left(n +207\right)}-\frac{\left(17525921273035561582343149098 n^{7}+23836039988498768599202241891332 n^{6}+13893316117257728805968713375103379 n^{5}+4498840387259573149096679764091959205 n^{4}+874061269849858546380243070097097328647 n^{3}+101889587643786421292717332469489568931763 n^{2}+6598430180774569794112296603850713577536216 n +183134460137908390173801413220547708574905800\right) a \! \left(n +196\right)}{72835509744 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{7 \left(210564873451668607102729468 n^{7}+287805171730477004415770193672 n^{6}+168589133267877024654824150349055 n^{5}+54863456758514014436235777522668790 n^{4}+10712309932559934823625053034849690197 n^{3}+1254958818549481945291526227742326723818 n^{2}+81676752069897909341151560214241605135840 n +2278168354002148757651381304798518459016240\right) a \! \left(n +197\right)}{145671019488 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{5 \left(409023831911623025164348 n^{7}+561839235479139834685710416 n^{6}+330745229622228786093460165357 n^{5}+108167670538935784481854177729169 n^{4}+21224989980598249877717657271448981 n^{3}+2498869923374303011659558183446341703 n^{2}+163441447373847539052640040163305775474 n +4581406979201547242212085205504285068136\right) a \! \left(n +198\right)}{5395222944 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(67433342051029302255896 n^{7}+93085097057813891221138416 n^{6}+55068527909652838811020049189 n^{5}+18098763568547033681870293257000 n^{4}+3568948154829500395939252550944079 n^{3}+422257598319245727726809195507128584 n^{2}+27754720776620187360074105290125354756 n +781833249156952089713030110062538056480\right) a \! \left(n +199\right)}{5395222944 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(63051154156626909290045723976559744 n^{7}+83621868687751581426155310758733118288 n^{6}+47529873742819194908320382237957842061371 n^{5}+15008514732584242299951598074966592552288710 n^{4}+2843523409597939066806056269786503039610466361 n^{3}+323239149511331579433574457411673628779692378582 n^{2}+20413403550101216793383472596498641800950352415504 n +552493208251226074520642709433989522888093645575040\right) a \! \left(n +191\right)}{145671019488 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(1798592629998580042946304299213792 n^{7}+2397520963579099007313681816649901912 n^{6}+1369656547294129792487624267978382278438 n^{5}+434695256029704094939820012154985688471135 n^{4}+82776270286294118995264716611389270734463628 n^{3}+9457460928233162116596688401040878259326092153 n^{2}+600298512527592492760651100642656772140751672862 n +16329757135837376402745501056926980133942188595920\right) a \! \left(n +192\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(773575478331159858079970853252964 n^{7}+1036397113570459457113564945466112632 n^{6}+595071381824068245857367734402483460490 n^{5}+189817216400846434581025951967880997987415 n^{4}+36328676249341946736051735742833625000287676 n^{3}+4171680116913246332520127743124798431958104773 n^{2}+266131412884476270174315109175748325965135903210 n +7276134689147984528685464501459003134791090624000\right) a \! \left(n +193\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(43656280231494935878484382770748 n^{7}+58783495936762184547813864857434336 n^{6}+33922135364435951329827303261386250351 n^{5}+10875127071158950293113091815985526672225 n^{4}+2091860180227112533088670405867249911006127 n^{3}+241422718541625589301482120474619733064949599 n^{2}+15479147860735835996039975285735390632005996174 n +425338922017375603972515378438619283434653209640\right) a \! \left(n +194\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(1124892890812304003081986379636 n^{7}+1522286591757704976507207106685244 n^{6}+882877591060587414104348297141799671 n^{5}+284464241231798495296181986820374967865 n^{4}+54992283339463684630794232854115506708269 n^{3}+6378561132299137526927354201009050253517621 n^{2}+411023684808696350483087521720139193839401134 n +11350888683361597510943005645747477331486599440\right) a \! \left(n +195\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(4697214630827629055086261752087046727048 n^{7}+6103245000754395457557333134839514529667712 n^{6}+3398619379672115572656967523628429658932946163 n^{5}+1051404629100246964592647630493673344820372239450 n^{4}+195158130265895466647164411988030159342371626201497 n^{3}+21734659683221488618505808164588293178586007799503898 n^{2}+1344759869098689872049776550244547815805811032659304352 n +35658090192873947447071195022399435880125937658108117920\right) a \! \left(n +187\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(413825295392979233785578507079077246744 n^{7}+540479593728695122001205251766882443094320 n^{6}+302525878029538564759851377394988921087425186 n^{5}+94074305712368742254218846143540641954175352595 n^{4}+17552078565282269213849488417023289260686502708876 n^{3}+1964876005864101154937813340506660015775277333593425 n^{2}+122198837319723076711447289689148028825581279827096734 n +3257017332076054839765307492535628180307502112973609320\right) a \! \left(n +188\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(34165812256583797249730955229027801816 n^{7}+44852361683705725522893321690278897533264 n^{6}+25234778347577789884728718705533813761949583 n^{5}+7887485747191604018840525730240107197772672875 n^{4}+1479198204733589574386958343786725160594264012519 n^{3}+166441977119522251491503248227450295221718311095341 n^{2}+10404574824753767195045841942599890579306444055169042 n +278744641345306429621141973403713268818583392822154720\right) a \! \left(n +189\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(94104340953222686109596111225749012 n^{7}+124172260238250394249170131256097944212 n^{6}+70219833756505725348125797162951026652216 n^{5}+22060715243054293244610571012752972885327695 n^{4}+4158414123176540505006381375637055767920959938 n^{3}+470310052467806547455746425179311859394654036833 n^{2}+29550540316822159111469724756567192459264762098244 n +795732269823807800095283509956465295523734893691590\right) a \! \left(n +190\right)}{109253264616 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(4789678103901355255515671058807126134059468 n^{7}+6126715613532484312890472023041227074457138240 n^{6}+3358703557192646289320691767668084396020819042979 n^{5}+1022921935369382253190126048879391316582262772796160 n^{4}+186923522806775591309646505018402362897151350578757397 n^{3}+20494442014124798595598614651241183528534756938208557280 n^{2}+1248346614742699457868448844105299897620054266283857291316 n +32587944836180155853688077293653952422248865002063528421480\right) a \! \left(n +184\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(503949651405709282868162737546701941069712 n^{7}+648020005297773634404136908785219165843002360 n^{6}+357118047616680558318930892343295867200521324203 n^{5}+109335604661131354036549067741063779334372550287665 n^{4}+20084528106803655384035597194830390341257929817470243 n^{3}+2213664947851814577881580837443305431034844759889472975 n^{2}+135546606683280892588245367744205068910257651933370208642 n +3557031102733258658753418619802122995320176665706408468080\right) a \! \left(n +185\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(25056861826114449690190981573362631392690 n^{7}+32388720038498049352648708051759887290380216 n^{6}+17942485545337733301464322760742886015306083067 n^{5}+5522013210258337329772918402861828566792419244535 n^{4}+1019675711011352564868835529676936214402972088382705 n^{3}+112973485798545240483250919587956513331735573934383429 n^{2}+6953718004744144737807168181050578576824943764926683178 n +183433839160329364163851508203409100796390032513957550860\right) a \! \left(n +186\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(369170188517581816471395292526827447611131564 n^{7}+467237976819780361308972696549995494075210361680 n^{6}+253438843732683934546696050385150396041367394522684 n^{5}+76372334503594445387936187685377839855862655020792925 n^{4}+13808629715170705586918774935165738457343172733134800326 n^{3}+1498017074039517520642263534984536013663345535454000189695 n^{2}+90284018263544671929171972118963613421607367637781895206446 n +2332000743743559846139721888801021632604288662491827863407600\right) a \! \left(n +182\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(43138734202252813245124182155746024779783992 n^{7}+54889971114885382360855342329702633223533738680 n^{6}+29932406382935408801593668005128627484196091520723 n^{5}+9068127107481695423644634754880375255237206272089085 n^{4}+1648331982447554018526650638300864709283161599302857183 n^{3}+179772360531940225019245413976894539689388602187079441115 n^{2}+10892525366621458467913407763022348381734874805531271416582 n +282850799884622105958118251328131582813490251062577239032680\right) a \! \left(n +183\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(23448279135911596513401706105346665328488506708 n^{7}+29358052912999305156605993849661886852983619829848 n^{6}+15753178722095586777417668124520681619617285743953391 n^{5}+4696108752061960794572597757351097831307323028387891785 n^{4}+839964394795830937631493432968566884951972182444288592627 n^{3}+90143918085176658282861190743520006326700335161600842706707 n^{2}+5374537367404125536021815121433713748228978411340145684055534 n +137331638361554722914383426038594664371394308273966337820297480\right) a \! \left(n +180\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(3009995243945459768984418236523910252224626748 n^{7}+3789151900797105621840602400789777229903535669144 n^{6}+2044289057032683733671532923968708778448182031813911 n^{5}+612732600130805312633716113555560054093755782413868860 n^{4}+110192454033853339677183452940516509171311529135795790597 n^{3}+11890084483793181298771886870792230344376792499261047290596 n^{2}+712765255372493953250133220532491787237376828972847751142384 n +18311855421926180396129006177025622234942699176599614933873440\right) a \! \left(n +181\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(125925390630917746057824185088059817420034841824712 n^{7}+153262070784974757237617966418640471272345797681714488 n^{6}+79943670413753554406663819195559277121741659874847109465 n^{5}+23166788681199725293078826161593964937458665727933146985505 n^{4}+4028132710731112493753886082250658464084604364879882216800633 n^{3}+420240543058761316914838291886645517607177039742342821265699607 n^{2}+24357049742594654364713042870654020868019409570374641555705995350 n +605033967739022684348589417885346496449527232911914585825044530120\right) a \! \left(n +175\right)}{145671019488 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(4155028699126928736997880076425991954831648877518 n^{7}+5086624290608156912895313247713838246428980315264416 n^{6}+2668779441159329390958957278691428497598920562874050769 n^{5}+777906558185622653782843390970835104701746982153004281040 n^{4}+136049741736474141424045874637805793775929333178139658591997 n^{3}+14276561047175584065643471301951861101179974675693397249389804 n^{2}+832302863992007921262481224047095042497308111663996599141928736 n +20795379238505981687788296256549654840599155076275354384714984460\right) a \! \left(n +176\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(8690865607810357659617970733818698182972767969352 n^{7}+10700736612331116521740049751862498474794820132182496 n^{6}+5646651928521175062379476881297141938282816615035199963 n^{5}+1655386442901870836817273668819379345171509971153657579390 n^{4}+291180715560201075804267807987911137014631080048215615574013 n^{3}+30731284401040431148979557729563385127210118763163733393147034 n^{2}+1801897142623630343890700402580892675184479469846197420198868712 n +45279980633596281626002102963629999221131402606068498106684696200\right) a \! \left(n +177\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(1256037242690621102803944692650538234330884557328 n^{7}+1555284109842405827420992365359982203902632895160136 n^{6}+825359120776849790455899820583578094787500106747628924 n^{5}+243336076484907637572942414548425082314062000958111018095 n^{4}+43045144849439763567512736903365930388980375721280853895322 n^{3}+4568735498020602645887465696196136007370664917447156007477689 n^{2}+269400449600455890884141574402998596081356330855903916956807786 n +6808114297686843611308522610176700744969547351664760728578090120\right) a \! \left(n +178\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{7 \left(25006098825369503978104746415460763382429065420 n^{7}+31136791325680049860772803432397894574846282656248 n^{6}+16616023184072138841429782119445831423720154475869420 n^{5}+4926176445274225045552537989872956936670875176807304075 n^{4}+876286805900384444065218195772068543461786221267368175170 n^{3}+93526796076835752172078094306958076824511610549631416466457 n^{2}+5545690145656925310251790398772128438930138577678060254490090 n +140929094757164097515365190275403606772193331041484355084106200\right) a \! \left(n +179\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(14704482250948365979707677468321594189355979068810916 n^{7}+17684537191542348035840146206118144779602306394115257672 n^{6}+9115206048242492728984846822661890640412279425350322805613 n^{5}+2610192153056572931771992456277414129777895344885531285961315 n^{4}+448472182117650738300647705964991628847257465826315791903793049 n^{3}+46233382413784890316282800878694936761705083854099662199332863053 n^{2}+2647946974526179455211270881779489293114265403485350112919011099862 n +64996828550800626443880732085654106004103300443449288583290178242400\right) a \! \left(n +173\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(2386900773259723948548091445571592292820388126098740 n^{7}+2887910957075774428728889382796617840803489672451444656 n^{6}+1497482458830073455053880967160092353498569589160658133887 n^{5}+431392467567262720895613928787759012875045130922789909148990 n^{4}+74565866965091557085596204823564327426536440354291908417953865 n^{3}+7733291158186931224868231726899548955051811657035049181436248094 n^{2}+445575956259738399214175103917727578931197075620209515419436301768 n +11002921776463633393943485567753731139677990573169389856890897018360\right) a \! \left(n +174\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(16758051022517045356830067748518583896750684825960705600 n^{7}+19667804263238494131377820206361242548193201367826853264256 n^{6}+9892729727464847513733918566118886312212207891964231766239552 n^{5}+2764449797010913849031069045761971077350225920521901313701797655 n^{4}+463508221709018680567933609596525993333786598830518816876888995210 n^{3}+46629683488462079195176769523848458538338526929392195544029564034509 n^{2}+2606154441033861159163107457548290777490197630254692169021363398520578 n +62426117423077391586465645140114567898374273890277055987776699999318520\right) a \! \left(n +169\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(426739084961825187737698778714912406752499606674600864 n^{7}+503918495713490672244899872299963143046199415823723928192 n^{6}+255027256568120470633166791499536261331383645874805068625788 n^{5}+71704385293904477900179758063210564428029632305973175785034165 n^{4}+12096549959152232311599042142758437213254714103592390447178412666 n^{3}+1224430483971012762742075876051581593971019159601096234131715223963 n^{2}+68855701479250899619730272322608655877393650499859399452144523514442 n +1659490153351635502892084954268254355831788720345567445898599531385560\right) a \! \left(n +170\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{7 \left(74285956168453676383847771019306958716504386431903192 n^{7}+88260574655696068384555167658236948721469819952695944976 n^{6}+44942328091569775158189420708490123717348284157670969352526 n^{5}+12713863692275510316096027326493249156779477124572952922824845 n^{4}+2158025485780610139940464685879404205077460503239203628031350848 n^{3}+219782307494261768292468768082402152855407664433813392036575836199 n^{2}+12435475084788750853572335875758626193864024845931725600547854110854 n +301551404791309224348452730016260885713535465488014742762626743408600\right) a \! \left(n +171\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(12636742425045515173429279411636055455737434598485768 n^{7}+15105900617369843390453403838981599583669488360017132424 n^{6}+7739039044523286277051519576057013290407522422345540120810 n^{5}+2202727407771081074765418809170676896467811180676902176857505 n^{4}+376176473120491303802630524228538285764009479771873962844163172 n^{3}+38546039322121054979406343717632880002373139718056465553463892511 n^{2}+2194327709799497069873894711177847886784615603566599961834274915610 n +53536827235528125488609667196042607211034523468072321523870994969560\right) a \! \left(n +172\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(6392117237813444940325195142160578232862198481720978615900 n^{7}+7320840377658671258809667211270242123959028313443511500931360 n^{6}+3593375371931590343402390030848733778520564204510488020924038463 n^{5}+979882650468842816945362043101130574230771968688722543818055490010 n^{4}+160324260810736848855132905389542892132718651202557699213104626807785 n^{3}+15739039698356157671039682228386718763041041510215269519554393330271390 n^{2}+858395390651038561458591398993036431596114159922564903774685423513852832 n +20064230833615415505222697312991333641373956159431704441383942121169463320\right) a \! \left(n +165\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(2536455729760473890910328625928408483753709738697649445448 n^{7}+2922723594737195639678809567487950475985536570546372539943744 n^{6}+1443358450156786795411559766472864069496492310591653803007467739 n^{5}+395996220974644310956828080336061936914127030066397193117218746640 n^{4}+65187172286716090830740615510997192794336575885723187051511612345317 n^{3}+6438543250579960600205543109398557967466211069057774758507344662803476 n^{2}+353300153857006600481934073485836321190193400744180432018871663230806476 n +8308576181288832667086703112504502294067097514518583348237452748691384920\right) a \! \left(n +166\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{7 \left(23284763837560585964884333932506022831185512688311077696 n^{7}+26994988126706847985529938897376537164049215705563787457224 n^{6}+13412849860277520071539672971273032959552959017160159524880456 n^{5}+3702456825532078342108136023207693994517455066437475058065061555 n^{4}+613216502359670076122560637287749229714745991704840626553713105454 n^{3}+60938628367104870040308878171169731988817903703580455433682270604321 n^{2}+3364363325169238408440094613906028321548082845033426708085986752295614 n +79604995095315202277784315232339905280749474208496740001240033217464640\right) a \! \left(n +167\right)}{145671019488 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(13101667487616104660524330765647797534982245363249749996 n^{7}+15282542904240307008747527240574383228252727834221539883424 n^{6}+7639975178379465085689173759934557414400213526639893735040252 n^{5}+2121875726617675031878510868827615636682281743226105723362115605 n^{4}+353592863136769128705742492533064294198975978411137066640870753654 n^{3}+35354337738367576231927769942230950195610609121965369390687513152531 n^{2}+1963875524263744807452811841940116645630681326225422882110721962779218 n +46753387796399966332103710415459923199838660248843361262311545060087520\right) a \! \left(n +168\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(296664146606978008070968351396771521383603939691840780687908 n^{7}+335665044779467074131192675929758172463745101452721022268379152 n^{6}+162769047998189386062181852746097937195110520079267569946213781502 n^{5}+43849693013491550984639103804949304660383005340906955175659635546195 n^{4}+7087844343451127984720549501223200385816937405013303679014371217380172 n^{3}+687408286899244462836484931474067370370195434849738990428148912159717393 n^{2}+37037756810846831967122407032248261658798849268286231793927572639162492598 n +855263084762073917786358252788118748110470761819998226797009005485149457320\right) a \! \left(n +163\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(8934134027174889736554332335935203422896308402424968265928 n^{7}+10170201690516786381812393804890437265458613581602921095841392 n^{6}+4961713228046720523895714977842728941500685097779941433654963505 n^{5}+1344816806966552926982094418478349911919105981753463966600687174765 n^{4}+218699519751558917721485032227310230545516243829208727815679811399217 n^{3}+21339579991288590315454460797477059378156708501657920742138471340714243 n^{2}+1156787510297644984260399141468145328236305985860129232903958273666885670 n +26874898030816950318714259503711359681303032619887698043716361363992644640\right) a \! \left(n +164\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(26179101012741833634593836237300015003980069731054370866886980 n^{7}+29085886201648371495913739621651453131786036424334739967715660184 n^{6}+13849501704583748798815139216460217006118854700632908769300639351322 n^{5}+3663655515098293968569104642849592090420021707149848490982405140456325 n^{4}+581497143685803070623003613713752478271534580334093815256304230584045960 n^{3}+55377467704318667276581421544665579824771302278855399779358801120609215831 n^{2}+2929864103333276488157772756909950823510765431294495381879942740140561757398 n +66433409227338542601965188323861433721283167753566207337261329854992534058000\right) a \! \left(n +160\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(6071968867534127200472559173846943461161947749147454442417284 n^{7}+6787317361060489757900155999137760935014698431953962237461069064 n^{6}+3251554803219487724291547586583256328551227954185599586426497984783 n^{5}+865391582609617718838919818329256290972955602395152598669502854312375 n^{4}+138193228326296573018214389886910234327684265905798877756309008270697031 n^{3}+13240776398635197494016052908668807956795477912526038680815784119947751941 n^{2}+704805143253694393154187592146623378458942818602304693530148513116553505362 n +16078643585750944836954648607825293803582667641299307829066422796598808334960\right) a \! \left(n +161\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(1363720914418590731047181894679602688005395394152921669048148 n^{7}+1533667423419495397218091425492606353096978743069422114682330136 n^{6}+739198893450407338439105007591503760675670364116564836437159037443 n^{5}+197933916150058857442860534363599565713839391965160775653361212168540 n^{4}+31800340261238403457239480881724493984908208179273534768371102546455397 n^{3}+3065462786761341946938293355831540324956820229211160208155016447193156984 n^{2}+164168336738194793805523714576823747425394993759060937989559385829639536272 n +3767971669130791844596390961067125594205334523397462857775438068814259014240\right) a \! \left(n +162\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(3275750523226241369861685061222573744230903273604425900211381492 n^{7}+3551370237179437576213316609972931447365786139901657359252239932644 n^{6}+1650083734334096071932125383501609417490862565807520932118132801521645 n^{5}+425936895869844522734314730669235521169087248428323022172115106662434730 n^{4}+65968651373808738002029513743462063830805012694042308381844161905508741403 n^{3}+6130319090138577263717092709969295853459850581946235822065122702857433631286 n^{2}+316488545066569873924171882489213659237945302739721707432712938806090377758600 n +7002580923301533966975455018654780967379841421817912163054544102470986342575120\right) a \! \left(n +156\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(864261455916754229689308135030583367827450113078911439086727230 n^{7}+942770530024994115998290957519760355514807942741093706015621721964 n^{6}+440749175789017951158445998456282942947439500083013603492097987020327 n^{5}+114473780034699906677490771977686557233378019134436646979351760158020195 n^{4}+17839117543934396613504371313568888200674988006476865686574280494682460015 n^{3}+1667990630469018934492140457283483013090752543643777577289162061864495361291 n^{2}+86644910158343777131542301409681227669422422404839093523294150964983316361378 n +1928934596499519603049092121019791115581591089940128737892470743465928121621720\right) a \! \left(n +157\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(63096653237641461348849314133296397394289690509475784745338220 n^{7}+69251914258326912481825195316875633828752266855708864687081334576 n^{6}+32574796091397460689108840235733850049755426384236652910847719903195 n^{5}+8512565079794429691301325234913308338726182271194204485189131064347740 n^{4}+1334725100531319825117269094716582701242804260414569302170771275389336865 n^{3}+125567117731486418390326723359537094130091510180234581816779892861163850764 n^{2}+6562798274195071694303695105949524119841257109070300456202238439390688557160 n +147003274574319146562306426838840694574161594158354489492779150514020235121040\right) a \! \left(n +158\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(109281370780570127232153306598939811272299542042855498055049072 n^{7}+120677583966870525102037078482323229768044604858396529969289921944 n^{6}+57112531885569394250902466895786370822157131632194346156207692696200 n^{5}+15016368240776600821469383527968746961064091863335565368763928658913625 n^{4}+2368922902733227535075451078413829682350167819387229421730225521290128938 n^{3}+224227843611188983400547733189832980847507031941326425955893752616003272791 n^{2}+11791174634805128915213284807748273599762266976096367015887254513738232531710 n +265735341294161394684397202752210683260199397487045370264899911354564439675880\right) a \! \left(n +159\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(3205571953726729539612490446806790549089261959441313266089917575592 n^{7}+3368180067188650873285187770323735081710489238400144733023192872911664 n^{6}+1516742252690405772403273227764378702100660411092352344066804055516475829 n^{5}+379454155279225757514485596352726398747682741086499885082213759137545029630 n^{4}+56958912804624085777498298924434395807168276193214199800161927161081442514423 n^{3}+5130018967432753911153171684380031420906113129337855431910393937302460401071586 n^{2}+256689111929583298801366159309647948539424030644059673526727879904035018350872556 n +5504563568868519212514160448317411173684713650656686171216536026316980785181203040\right) a \! \left(n +151\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(141085885403122984761989058961381476127994212346291903705678088008 n^{7}+149185382691339494106283685650442922136034870659312287579118625032144 n^{6}+67607558969196444746435133039632265357229257415793368918433271307295789 n^{5}+17021383269941101361815858437397913806241210452967740485781151493386959765 n^{4}+2571277013931507168169059182445244788122666613779907431052106235681754868217 n^{3}+233054428127202979128853246209959171603050465845554476706970544476033001724731 n^{2}+11735365596027310917346571119604385082693116282193886445801420409457429388429546 n +253257569670996233549128457523728475852147173445093547661092547328469564088564400\right) a \! \left(n +152\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(295230140845034324515215237128652840563929843998425664231934741352 n^{7}+314150535601316949891258664815611459533188761867453109548862661925848 n^{6}+143265228145138218250209458111405188583839641852863202690183005799845699 n^{5}+36297273502782423161564156977774140147673517395668195848750328633799747240 n^{4}+5517740107289763092492461125326546275216567766834514747188805179607915455273 n^{3}+503271761201336423113296966393736226541000411697958274403161724193162781385192 n^{2}+25502001685799165815722973171196815227017372068067587190371647977691743883653676 n +553824468306432398346119314403034305173962684290660553090272665884591408926947560\right) a \! \left(n +153\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(85592012121935313727138680750820801334598782152216880985916537412 n^{7}+91649035275926470922119900687325060226031467923641847483424034544448 n^{6}+42057947724029194829846830585252859897761901102258934031334290990428398 n^{5}+10722550794931333013809485579294334075408284468318763997433601084864904145 n^{4}+1640218924567008759918745415041277923790505824510687633704635295465542058268 n^{3}+150542545179623883896574702017033582847145224777736922811295639608591619758747 n^{2}+7676207807449956553899559143114613804575489532386965894994883147402920682962582 n +167749024871046942538988137299988023760835510274714462499805552848541824406529600\right) a \! \left(n +154\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(24055478185638181124767864363982265081142323525898220825813575272 n^{7}+25918559374677062740425488809071701398484895831995988497833469866336 n^{6}+11968312279389341198731118242379852961495407134201374724118878344120471 n^{5}+3070326051576904911201197681770412980257228106313087209502723461743767725 n^{4}+472595336182833569042546961583174633213721043856256661157880908689062352843 n^{3}+43646334409330223487175927938081223753649562335252613595564479176123991027619 n^{2}+2239421466958139210762663506680257895921509945934957620684518756706423892643734 n +49243554860739676716334988111769891488432137956247165295562783034020807142699920\right) a \! \left(n +155\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(10101112086929866459586936513314016292334913571180660947612333168612 n^{7}+10545947066864224352910904692890107905989878503095273463173232581559888 n^{6}+4718773924544631553574726141629297992861120659250105994600526958320781881 n^{5}+1173016903846304959438613642355328965271708587178916713973693405792082243045 n^{4}+174958356517840702940443117036826138682171737836138121976633762404880717165293 n^{3}+15657430009613653523610765477871612155832543059407578741300021717672137657540447 n^{2}+778462916634857018146516989375557375769984348187386178523349719718400635295621674 n +16587571520827307548033962326111448093413105074638979403806780774440914121455364120\right) a \! \left(n +150\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(133182122713159099806242698692767633036826309522777378934159167512672 n^{7}+136362540954101277073744268512819565205927715215058735286662524338889724 n^{6}+59837464298687974054319067552834908412248876342535049329105326051259557492 n^{5}+14587623411509523964786521282499885879934036572671471497834325411844272085255 n^{4}+2133796348753148282679675141206536017432447171905847280224812326035069362181518 n^{3}+187274435106380568786574412744111869965869303817668211761025787829146116595267531 n^{2}+9131400949848203126257209373886643821671356758168969181950592437215523272160752968 n +190820697153012121267997547663935212865992264400669241339014699248354239878343184680\right) a \! \left(n +147\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{7 \left(3286006624899124979554038204150333273685826582062329115103540496541 n^{7}+3386627261968277855380760874026000581596466810941786581910529084856054 n^{6}+1495872768643650882136788972425284034248237507438817440299337153830482131 n^{5}+367074763312637891043514360650929673197655578902644893954721778809118120850 n^{4}+54046903001246477558683194919380526116786366451251045235976423339060720669809 n^{3}+4774672151126129155395205627525338887308800003535925029773220637116745200023716 n^{2}+234341413608953868949730132113346266144748322196268760746718487300403340907172799 n +4929274937965911779786955381244282567819986763426975494399335384719370055600185640\right) a \! \left(n +148\right)}{109253264616 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(10306700725966344832595764319923577279841400929264278710906528909756 n^{7}+10691533660623520004398177437285480422037220668484344667542057527365608 n^{6}+4753221567625550655388938204874039560079200303137703645465544447479326937 n^{5}+1174000134770195864969605589615657077136519063711953035114946019811787376070 n^{4}+173981901257076486319324685520997799102164557417227414131195377555718855472139 n^{3}+15470198353338214174986519653286468052232676851345604195686356405164146734011522 n^{2}+764222580920505163108631271991749028592818907156220730484825042256516534712876808 n +16179749335219468262631795903000751746148037957843401507073562319979130295763907600\right) a \! \left(n +149\right)}{145671019488 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{7 \left(2072890081332511602421571978794491605808630027260950709152953755448504 n^{7}+2065674529561506303316057120175611232659552278958855648082094342332228992 n^{6}+882226408077423854564874063278024848483487732734474277176472958344230040331 n^{5}+209331733064667708142551860515938421594290918131459523533647173729042523356460 n^{4}+29802365297455542387151329377657253208465929387878210569488735107288664637290921 n^{3}+2545816424916479505783381134503761682618249843942227625341540238176774771754604668 n^{2}+120820436447195262592845448481894417746374005521662586295659346653453972817297754204 n +2457459880310155848622450184205204798325254009836843699402936440081853638576165842360\right) a \! \left(n +143\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(5535161922554165804154540057412686071172859879843252214789890291554584 n^{7}+5554187757397807009409165708983018486043568970818113799042663619688030184 n^{6}+2388593564298501465556565723387336791594433206315789479196977150249178272050 n^{5}+570689327395428929870852623144055998654202798688668100880168298753968834885215 n^{4}+81811965773105938968241814430478937745113128471256996441438961859198918831931156 n^{3}+7037096807224802775234870938134343787543700740138092968876134489987351506870070681 n^{2}+336283936970199571092343459970888687984966243740230257385093748927332085310891367330 n +6887321800526580782710756031413646856826846992959324491137578552985509763372312439800\right) a \! \left(n +144\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(2063640252010786079973584115241933613979599881306649113473007880745668 n^{7}+2084890018348897485677145372177017720867287563761472215945421655458197064 n^{6}+902740304425079975714353120123575692420233963537955196920773659479147255990 n^{5}+217158761799042744493704127467541903558347200253423549464211977580590655809805 n^{4}+31343718283341454168974680827494286221235472281936386237830146654129097622673232 n^{3}+2714453118504896144427166471101332023463635388895047954937620946125136011912174211 n^{2}+130601789571672925436734333953240699066241560230203642956294028141130880944596122990 n +2693063653306175106061044274035780418739469475369231554377943169912220386152476924280\right) a \! \left(n +145\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(750915956395753555545261078459846685930138179706256656322206016857444 n^{7}+763762976118356162698218558165776100397037997969284488171258352198987984 n^{6}+332932010712646606790202739084148796591578717719735064725906991389102351933 n^{5}+80628115330162079318579597380724264772249333520792125465209523048601942946255 n^{4}+11715889333475079872423378533152882594184703741996812429255128823894391591008621 n^{3}+1021461141176611589537564076306090039613615967535389005811387568188442081026551781 n^{2}+49476908782502603240410305339583829861676630484319880645879780744890209482687596502 n +1027100978957037229382663202891162723381467641528878130032851462453952301216721312040\right) a \! \left(n +146\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(31222524727031177516936307955510233671699599500393746019375975518023984 n^{7}+30675312801861295913138458254713455135255710262655497236148940622385814016 n^{6}+12916501566504894914568188961474523865016602368481062919565102724052029624991 n^{5}+3021621406370653207488991885602433436135156002700911024894579270233055386776215 n^{4}+424129269186066939252117780725482342399697642535576905462355279632054969381683531 n^{3}+35720664756457139214882687024948133102628401858884912123063963903033646987607339609 n^{2}+1671399242856854489623791124884982412668409706601530303485395803301985537273652618734 n +33517839098164394362195781899297655270355144908095178915457011687689025021800486461360\right) a \! \left(n +141\right)}{145671019488 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(18616325918770980594235817321863254021123958009183138986691092439229092 n^{7}+18421481774685120116252288754105870344535348633693501427248989883015752400 n^{6}+7812478714112474104354236043098195259140136530859033134968199899162697451309 n^{5}+1840734507636689476585249997361438104626874286417970519175898795994268559146850 n^{4}+260228750829534491814499665387043300510872037343044870253758816993028922333165463 n^{3}+22074011024120785915559608995993282079563853181972698462293402634639450661929697610 n^{2}+1040268314776968534024652225858415758115796157275451528341959350520127635413810935156 n +21010838283625724034759056055087082622565198249690451104797391209648070974580777877500\right) a \! \left(n +142\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(673526453391028117877013446546980300537738796511409800899213922596932414 n^{7}+647145073696872615755012449260565438342252793207269581796667459196059832096 n^{6}+266493574589349811005274602247862426773489949096319494675241899091370382951560 n^{5}+60969735136422832030228349504777540924157506900886786878375149760571886147511625 n^{4}+8369667280072947688991823858642868807047648849805437535049117806712561931571884286 n^{3}+689395567913454157801531937429433934901935710031814235408196357217551313010215883459 n^{2}+31547977262150733793901951578707678737604210672511547196682205334414928601318534526300 n +618746983365533808394282012611487443532789591877200212577488304663901747727545325079380\right) a \! \left(n +138\right)}{218506529232 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(562489706945430723445082001887171692367157577762899161485394575072287056 n^{7}+544556869072883251174298854244841429854163209088962231508561816564068754416 n^{6}+225948328269474981582586215682999867237621061168969605202909682947665509299975 n^{5}+52085472441608113930989936435502788669351447440697864252143426567812937890548800 n^{4}+7204261904688967293200316879718398509612307750862088957510904967032221402475857309 n^{3}+597899040589055924665728264407314141735910822840382426704788146567966650054025726704 n^{2}+27568174593269834484649048972824266018782833521507174015390315971599037929301635795420 n +544785751129792461789087824534809686330113419003060031872134227738983739703541584741360\right) a \! \left(n +139\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}-\frac{\left(231424262183343368508118986329468040990417521945586489474296201664583904 n^{7}+225716254788293257798081194078711309259825017513840342072603701901865462688 n^{6}+94352391583777935767381003400138053267724147605935013945642980706997015481358 n^{5}+21912072552875488885001169100991006762932491714685545540427660377042241253060225 n^{4}+3053361885802521846108425940583903720552091328661203226462311572133521568212506676 n^{3}+255292135302040445855948709700798924677620446037437035733408773301073117198119198967 n^{2}+11858703801089444243977124851292335678088504866097238848085273592565498803899626174502 n +236087725737362541987790384097746989604712016315682215743087169473098154644148595986880\right) a \! \left(n +140\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}+\frac{\left(3182667344644018335885936856390564809899582475954068439472079138209022072 n^{7}+3034625611000835334401318442838849433737702116551646257639564920660907424616 n^{6}+1240102552344184661069908772781801521065241635849421176664551754007175636779137 n^{5}+281548418304218547176410955437816311969765436164867000960444515365465195793442115 n^{4}+38354423542837324333214022272171612455747484432589422440252683396030885754155938513 n^{3}+3135052493832644285851888670085538128068031950349842586067711794624046790769082603729 n^{2}+142369683145938975424106033505735229879887411953505053214250617537914700276098929391298 n +2770954482352189700339252473698050099024689760626612264519446613862489555986625684840400\right) a \! \left(n +137\right)}{437013058464 \left(n +207\right) \left(n +206\right) \left(n +205\right) \left(n +204\right) \left(n +203\right) \left(n +202\right) \left(n +201\right)}, \quad n \geq 206
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/193/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[28,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[28,x]*F[7,x]
F[7,x] = F[515,x]+F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[0,x]^2
F[10,x] = F[11,x]+F[479,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[28,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[0,x]+F[11,x]
F[15,x] = -F[30,x]+F[16,x]
F[16,x] = 1/F[28,x]*F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]+F[2,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[28,x]
F[21,x] = F[11,x]+F[22,x]
F[22,x] = -F[29,x]+F[23,x]
F[23,x] = 1/F[28,x]*F[24,x]
F[24,x] = F[25,x]
F[25,x] = -F[0,x]+F[26,x]
F[26,x] = 1/F[28,x]*F[27,x]
F[27,x] = F[2,x]
F[28,x] = x
F[29,x] = F[11,x]+F[26,x]
F[30,x] = F[31,x]+F[4,x]
F[31,x] = F[32,x]
F[32,x] = F[28,x]*F[33,x]
F[33,x] = 1/F[28,x]*F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[28,x]*F[37,x]
F[37,x] = F[38,x]+F[477,x]
F[38,x] = 1/F[28,x]*F[39,x]
F[39,x] = F[40,x]
F[40,x] = -F[187,x]+F[41,x]
F[41,x] = F[42,x]+F[67,x]
F[42,x] = F[0,x]*F[43,x]
F[43,x] = F[1,x]+F[44,x]
F[44,x] = F[28,x]*F[45,x]
F[45,x] = F[43,x]+F[46,x]
F[46,x] = F[28,x]*F[47,x]
F[47,x] = F[48,x]+F[52,x]
F[48,x] = F[49,x]^2
F[49,x] = F[1,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[28,x]*F[49,x]
F[52,x] = F[53,x]
F[53,x] = F[49,x]^2*F[28,x]*F[54,x]
F[54,x] = F[55,x]+F[62,x]
F[55,x] = F[49,x]+F[56,x]
F[56,x] = F[50,x]+F[57,x]
F[57,x] = F[58,x]+F[59,x]+F[61,x]
F[58,x] = 0
F[59,x] = F[28,x]*F[60,x]
F[60,x] = F[50,x]+F[57,x]
F[61,x] = F[28,x]*F[56,x]
F[62,x] = F[50,x]+F[63,x]
F[63,x] = F[58,x]+F[64,x]+F[65,x]
F[64,x] = F[28,x]*F[62,x]
F[65,x] = F[28,x]*F[66,x]
F[66,x] = F[50,x]+F[63,x]
F[67,x] = F[68,x]
F[68,x] = F[28,x]*F[69,x]
F[69,x] = 1/F[28,x]*F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[449,x]+F[72,x]
F[72,x] = F[73,x]+F[75,x]
F[73,x] = F[74,x]
F[74,x] = F[2,x]*F[49,x]
F[75,x] = F[76,x]
F[76,x] = F[28,x]*F[77,x]
F[77,x] = F[447,x]+F[78,x]
F[78,x] = F[446,x]+F[79,x]
F[79,x] = 1/F[28,x]*F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[28,x]*F[83,x]
F[83,x] = F[101,x]+F[84,x]
F[84,x] = F[85,x]+F[86,x]
F[85,x] = F[2,x]*F[43,x]
F[86,x] = -F[445,x]+F[87,x]
F[87,x] = -F[99,x]+F[88,x]
F[88,x] = 1/F[28,x]*F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[2,x]+F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[28,x]*F[93,x]
F[93,x] = F[94,x]+F[95,x]
F[94,x] = F[2,x]*F[26,x]
F[95,x] = -F[98,x]+F[96,x]
F[96,x] = 1/F[28,x]*F[97,x]
F[97,x] = F[25,x]
F[98,x] = F[0,x]*F[26,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[0,x]*F[43,x]
F[101,x] = -F[102,x]+F[88,x]
F[102,x] = -F[105,x]+F[103,x]
F[103,x] = 1/F[28,x]*F[104,x]
F[104,x] = F[90,x]
F[105,x] = F[106,x]+F[430,x]
F[106,x] = F[0,x]*F[107,x]
F[107,x] = F[108,x]+F[2,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]*F[28,x]
F[110,x] = F[107,x]+F[111,x]
F[111,x] = F[112,x]+F[40,x]
F[112,x] = F[113,x]+F[425,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[28,x]
F[115,x] = F[116,x]+F[117,x]
F[116,x] = F[113,x]+F[2,x]
F[117,x] = F[118,x]
F[118,x] = F[119,x]*F[28,x]
F[119,x] = F[120,x]+F[125,x]
F[120,x] = F[121,x]*F[123,x]
F[121,x] = F[122,x]+F[43,x]
F[122,x] = F[2,x]+F[81,x]
F[123,x] = F[0,x]+F[124,x]
F[124,x] = F[113,x]+F[50,x]
F[125,x] = F[126,x]
F[126,x] = F[127,x]*F[28,x]*F[49,x]
F[127,x] = F[128,x]+F[398,x]
F[128,x] = F[129,x]+F[253,x]
F[129,x] = 1/F[28,x]*F[130,x]
F[130,x] = F[131,x]
F[131,x] = F[132,x]
F[132,x] = F[133,x]*F[28,x]
F[133,x] = 1/F[28,x]*F[134,x]
F[134,x] = F[135,x]
F[135,x] = F[124,x]+F[136,x]
F[136,x] = F[137,x]
F[137,x] = F[138,x]*F[28,x]
F[138,x] = F[139,x]+F[181,x]
F[139,x] = F[140,x]+F[142,x]
F[140,x] = F[141,x]
F[141,x] = F[50,x]*F[55,x]
F[142,x] = F[143,x]
F[143,x] = F[144,x]*F[28,x]
F[144,x] = F[145,x]+F[149,x]
F[145,x] = F[142,x]+F[146,x]
F[146,x] = F[116,x]+F[147,x]
F[147,x] = F[148,x]
F[148,x] = F[145,x]*F[28,x]
F[149,x] = -F[150,x]+F[133,x]
F[150,x] = 1/F[28,x]*F[151,x]
F[151,x] = F[152,x]
F[152,x] = F[153,x]+F[154,x]
F[153,x] = F[0,x]*F[50,x]
F[154,x] = F[155,x]
F[155,x] = F[156,x]*F[28,x]
F[156,x] = F[157,x]+F[248,x]
F[157,x] = F[158,x]*F[50,x]
F[158,x] = F[159,x]+F[160,x]
F[159,x] = F[117,x]+F[123,x]
F[160,x] = 1/F[50,x]*F[161,x]
F[161,x] = -F[166,x]+F[162,x]
F[162,x] = 1/F[28,x]*F[163,x]
F[163,x] = F[164,x]
F[164,x] = -F[165,x]+F[131,x]
F[165,x] = F[4,x]*F[50,x]
F[166,x] = F[167,x]+F[188,x]
F[167,x] = F[168,x]*F[50,x]
F[168,x] = F[159,x]+F[169,x]
F[169,x] = 1/F[28,x]*F[170,x]
F[170,x] = F[171,x]
F[171,x] = F[172,x]*F[28,x]
F[172,x] = -F[179,x]+F[173,x]
F[173,x] = 1/F[28,x]*F[174,x]
F[174,x] = F[175,x]
F[175,x] = -F[178,x]+F[176,x]
F[176,x] = 1/F[28,x]*F[177,x]
F[177,x] = F[18,x]
F[178,x] = F[123,x]+F[18,x]
F[179,x] = F[180,x]+F[181,x]
F[180,x] = F[139,x]+F[176,x]
F[181,x] = -F[182,x]+F[173,x]
F[182,x] = F[139,x]+F[183,x]
F[183,x] = 1/F[28,x]*F[184,x]
F[184,x] = F[185,x]
F[185,x] = -F[4,x]+F[186,x]
F[186,x] = F[117,x]+F[187,x]
F[187,x] = F[107,x]+F[43,x]
F[188,x] = -F[237,x]+F[189,x]
F[189,x] = 1/F[28,x]*F[190,x]
F[190,x] = F[191,x]
F[191,x] = F[192,x]
F[192,x] = F[193,x]*F[28,x]
F[193,x] = 1/F[28,x]*F[194,x]
F[194,x] = F[195,x]
F[195,x] = -F[236,x]+F[196,x]
F[196,x] = F[197,x]+F[41,x]
F[197,x] = F[198,x]
F[198,x] = F[199,x]*F[28,x]
F[199,x] = F[200,x]+F[226,x]
F[200,x] = F[201,x]+F[202,x]
F[201,x] = F[4,x]*F[49,x]
F[202,x] = F[203,x]
F[203,x] = F[204,x]*F[28,x]*F[49,x]
F[204,x] = F[200,x]+F[205,x]
F[205,x] = 1/F[49,x]*F[206,x]
F[206,x] = -F[207,x]+F[193,x]
F[207,x] = 1/F[28,x]*F[208,x]
F[208,x] = F[209,x]
F[209,x] = -F[225,x]+F[210,x]
F[210,x] = -F[212,x]+F[211,x]
F[211,x] = F[191,x]+F[201,x]
F[212,x] = -F[223,x]+F[213,x]
F[213,x] = -F[217,x]+F[214,x]
F[214,x] = 1/F[28,x]*F[215,x]
F[215,x] = F[216,x]
F[216,x] = -F[41,x]+F[176,x]
F[217,x] = F[218,x]
F[218,x] = F[219,x]*F[28,x]
F[219,x] = F[214,x]+F[220,x]
F[220,x] = F[221,x]
F[221,x] = F[159,x]*F[222,x]*F[50,x]
F[222,x] = F[49,x]+F[66,x]
F[223,x] = F[123,x]+F[224,x]
F[224,x] = F[147,x]+F[56,x]
F[225,x] = F[0,x]*F[49,x]
F[226,x] = F[227,x]
F[227,x] = F[228,x]*F[28,x]
F[228,x] = F[229,x]+F[230,x]
F[229,x] = F[200,x]*F[49,x]
F[230,x] = F[231,x]
F[231,x] = F[232,x]*F[49,x]*F[66,x]
F[232,x] = F[233,x]+F[4,x]
F[233,x] = F[234,x]
F[234,x] = F[235,x]*F[28,x]
F[235,x] = F[172,x]+F[232,x]
F[236,x] = F[201,x]
F[237,x] = F[238,x]+F[240,x]
F[238,x] = F[167,x]+F[239,x]
F[239,x] = F[169,x]+F[186,x]
F[240,x] = -F[241,x]+F[189,x]
F[241,x] = F[242,x]+F[244,x]
F[242,x] = F[211,x]+F[243,x]
F[243,x] = F[213,x]*F[50,x]
F[244,x] = F[245,x]*F[49,x]
F[245,x] = 1/F[28,x]/F[49,x]*F[246,x]
F[246,x] = F[247,x]
F[247,x] = F[205,x]*F[28,x]*F[49,x]
F[248,x] = F[131,x]+F[249,x]
F[249,x] = F[250,x]*F[50,x]
F[250,x] = F[224,x]+F[251,x]
F[251,x] = F[252,x]
F[252,x] = F[149,x]*F[28,x]
F[253,x] = F[254,x]
F[254,x] = F[129,x]*F[255,x]*F[28,x]
F[255,x] = F[121,x]+F[256,x]
F[256,x] = F[257,x]
F[257,x] = F[258,x]*F[28,x]
F[258,x] = 1/F[28,x]*F[259,x]
F[259,x] = F[260,x]
F[260,x] = -F[397,x]+F[261,x]
F[261,x] = 1/F[28,x]*F[262,x]
F[262,x] = F[263,x]
F[263,x] = 1/F[11,x]/F[49,x]*F[264,x]
F[264,x] = F[265,x]
F[265,x] = -F[346,x]+F[266,x]
F[266,x] = -F[339,x]+F[267,x]
F[267,x] = 1/F[28,x]*F[268,x]
F[268,x] = F[269,x]
F[269,x] = -F[272,x]+F[270,x]
F[270,x] = 1/F[28,x]*F[271,x]
F[271,x] = F[90,x]
F[272,x] = F[26,x]+F[273,x]
F[273,x] = -F[274,x]+F[270,x]
F[274,x] = F[26,x]+F[275,x]
F[275,x] = F[276,x]
F[276,x] = F[277,x]*F[28,x]
F[277,x] = 1/F[28,x]*F[278,x]
F[278,x] = F[279,x]
F[279,x] = -F[280,x]+F[96,x]
F[280,x] = 1/F[28,x]/F[49,x]*F[281,x]
F[281,x] = F[282,x]
F[282,x] = 1/F[0,x]*F[283,x]
F[283,x] = F[284,x]
F[284,x] = -F[285,x]+F[35,x]
F[285,x] = -F[338,x]+F[286,x]
F[286,x] = -F[287,x]+F[7,x]
F[287,x] = F[288,x]
F[288,x] = F[0,x]*F[289,x]
F[289,x] = 1/F[50,x]*F[290,x]
F[290,x] = -F[26,x]+F[291,x]
F[291,x] = F[292,x]+F[295,x]
F[292,x] = F[293,x]+F[48,x]
F[293,x] = F[294,x]
F[294,x] = F[28,x]*F[49,x]*F[5,x]
F[295,x] = F[25,x]+F[296,x]
F[296,x] = -F[319,x]+F[297,x]
F[297,x] = F[298,x]
F[298,x] = F[28,x]*F[299,x]
F[299,x] = F[300,x]+F[308,x]
F[300,x] = -F[13,x]+F[301,x]
F[301,x] = -F[304,x]+F[302,x]
F[302,x] = 1/F[28,x]*F[303,x]
F[303,x] = F[10,x]
F[304,x] = F[305,x]
F[305,x] = F[28,x]*F[306,x]
F[306,x] = 1/F[28,x]*F[307,x]
F[307,x] = F[95,x]
F[308,x] = F[309,x]
F[309,x] = F[28,x]*F[310,x]
F[310,x] = F[311,x]+F[315,x]
F[311,x] = F[26,x]*F[312,x]
F[312,x] = -F[13,x]+F[313,x]
F[313,x] = 1/F[28,x]*F[314,x]
F[314,x] = F[15,x]
F[315,x] = F[316,x]
F[316,x] = F[317,x]*F[318,x]*F[49,x]
F[317,x] = -F[279,x]+F[93,x]
F[318,x] = -F[123,x]+F[232,x]
F[319,x] = F[320,x]
F[320,x] = F[28,x]*F[321,x]
F[321,x] = F[322,x]+F[336,x]
F[322,x] = F[26,x]*F[323,x]
F[323,x] = F[324,x]
F[324,x] = F[28,x]*F[325,x]
F[325,x] = F[312,x]+F[326,x]
F[326,x] = F[323,x]+F[327,x]
F[327,x] = F[328,x]
F[328,x] = F[28,x]*F[329,x]*F[49,x]
F[329,x] = F[330,x]+F[4,x]
F[330,x] = F[331,x]+F[332,x]
F[331,x] = F[153,x]
F[332,x] = F[333,x]
F[333,x] = F[28,x]*F[334,x]
F[334,x] = F[202,x]+F[335,x]
F[335,x] = F[18,x]*F[49,x]
F[336,x] = F[337,x]
F[337,x] = F[113,x]*F[317,x]*F[49,x]
F[338,x] = F[18,x]+F[332,x]
F[339,x] = 1/F[28,x]*F[340,x]
F[340,x] = F[341,x]
F[341,x] = -F[26,x]+F[342,x]
F[342,x] = -F[345,x]+F[343,x]
F[343,x] = 1/F[28,x]*F[344,x]
F[344,x] = F[18,x]
F[345,x] = F[15,x]+F[297,x]
F[346,x] = F[347,x]+F[348,x]
F[347,x] = F[0,x]*F[273,x]
F[348,x] = F[349,x]+F[351,x]
F[349,x] = F[350,x]
F[350,x] = F[266,x]*F[28,x]
F[351,x] = F[352,x]
F[352,x] = F[28,x]*F[353,x]
F[353,x] = F[354,x]+F[376,x]
F[354,x] = F[273,x]*F[355,x]
F[355,x] = F[356,x]+F[372,x]
F[356,x] = F[357,x]
F[357,x] = F[28,x]*F[358,x]
F[358,x] = F[222,x]+F[359,x]
F[359,x] = F[360,x]+F[74,x]
F[360,x] = F[361,x]
F[361,x] = F[28,x]*F[362,x]*F[49,x]
F[362,x] = F[359,x]+F[363,x]
F[363,x] = -F[358,x]+F[364,x]
F[364,x] = -F[367,x]+F[365,x]
F[365,x] = 1/F[28,x]*F[366,x]
F[366,x] = F[87,x]
F[367,x] = F[368,x]
F[368,x] = F[28,x]*F[369,x]
F[369,x] = F[365,x]+F[370,x]
F[370,x] = F[371,x]
F[371,x] = F[261,x]*F[50,x]*F[55,x]
F[372,x] = F[373,x]+F[374,x]
F[373,x] = F[327,x]+F[91,x]
F[374,x] = -F[375,x]+F[22,x]
F[375,x] = F[19,x]+F[282,x]
F[376,x] = F[377,x]
F[377,x] = F[263,x]*F[378,x]*F[49,x]
F[378,x] = F[379,x]
F[379,x] = F[28,x]*F[380,x]
F[380,x] = 1/F[28,x]*F[381,x]
F[381,x] = F[382,x]
F[382,x] = -F[385,x]+F[383,x]
F[383,x] = 1/F[28,x]*F[384,x]
F[384,x] = F[374,x]
F[385,x] = -F[388,x]+F[386,x]
F[386,x] = 1/F[28,x]*F[387,x]
F[387,x] = F[31,x]
F[388,x] = F[389,x]
F[389,x] = F[31,x]+F[390,x]
F[390,x] = F[391,x]+F[392,x]
F[391,x] = F[289,x]*F[49,x]
F[392,x] = F[393,x]
F[393,x] = F[28,x]*F[394,x]*F[49,x]
F[394,x] = 1/F[28,x]*F[395,x]
F[395,x] = F[396,x]
F[396,x] = -F[289,x]+F[280,x]
F[397,x] = F[0,x]+F[263,x]
F[398,x] = F[399,x]
F[399,x] = F[28,x]*F[400,x]
F[400,x] = 1/F[28,x]/F[49,x]*F[401,x]
F[401,x] = F[402,x]
F[402,x] = F[125,x]+F[403,x]
F[403,x] = F[404,x]
F[404,x] = F[160,x]*F[28,x]*F[405,x]
F[405,x] = F[406,x]+F[409,x]
F[406,x] = F[358,x]+F[407,x]
F[407,x] = F[408,x]
F[408,x] = F[28,x]*F[405,x]
F[409,x] = -F[418,x]+F[410,x]
F[410,x] = 1/F[28,x]*F[411,x]
F[411,x] = F[412,x]
F[412,x] = -F[417,x]+F[413,x]
F[413,x] = 1/F[28,x]*F[414,x]
F[414,x] = F[415,x]
F[415,x] = F[416,x]+F[81,x]
F[416,x] = F[44,x]
F[417,x] = F[121,x]+F[260,x]
F[418,x] = 1/F[28,x]*F[419,x]
F[419,x] = F[420,x]
F[420,x] = -F[121,x]+F[421,x]
F[421,x] = -F[363,x]+F[422,x]
F[422,x] = F[417,x]+F[423,x]
F[423,x] = F[424,x]
F[424,x] = F[28,x]*F[410,x]
F[425,x] = F[426,x]
F[426,x] = F[28,x]*F[427,x]
F[427,x] = F[112,x]+F[428,x]
F[428,x] = F[142,x]+F[429,x]
F[429,x] = F[113,x]*F[66,x]
F[430,x] = F[431,x]
F[431,x] = F[28,x]*F[432,x]
F[432,x] = F[433,x]+F[440,x]
F[433,x] = F[434,x]
F[434,x] = F[28,x]*F[364,x]*F[435,x]
F[435,x] = F[187,x]+F[436,x]
F[436,x] = F[437,x]
F[437,x] = F[28,x]*F[438,x]
F[438,x] = 1/F[28,x]*F[439,x]
F[439,x] = F[117,x]
F[440,x] = F[441,x]
F[441,x] = F[28,x]*F[442,x]
F[442,x] = F[432,x]+F[443,x]
F[443,x] = F[444,x]
F[444,x] = F[142,x]*F[261,x]
F[445,x] = F[46,x]
F[446,x] = F[2,x]*F[50,x]*F[55,x]
F[447,x] = F[448,x]+F[86,x]
F[448,x] = F[360,x]*F[50,x]
F[449,x] = F[450,x]+F[451,x]
F[450,x] = F[122,x]*F[2,x]
F[451,x] = F[452,x]
F[452,x] = F[28,x]*F[453,x]
F[453,x] = F[454,x]+F[466,x]
F[454,x] = F[455,x]+F[456,x]
F[455,x] = F[2,x]*F[359,x]
F[456,x] = F[457,x]
F[457,x] = F[28,x]*F[458,x]
F[458,x] = F[453,x]+F[459,x]
F[459,x] = F[460,x]
F[460,x] = F[461,x]*F[49,x]*F[50,x]
F[461,x] = F[462,x]+F[464,x]
F[462,x] = F[463,x]
F[463,x] = F[146,x]*F[255,x]*F[28,x]
F[464,x] = F[465,x]
F[465,x] = F[212,x]*F[255,x]*F[28,x]
F[466,x] = F[467,x]+F[468,x]
F[467,x] = F[18,x]*F[359,x]
F[468,x] = F[469,x]
F[469,x] = F[28,x]*F[470,x]
F[470,x] = F[471,x]+F[472,x]
F[471,x] = F[172,x]*F[359,x]
F[472,x] = F[473,x]
F[473,x] = F[474,x]*F[476,x]*F[49,x]
F[474,x] = F[475,x]
F[475,x] = F[255,x]*F[28,x]*F[49,x]
F[476,x] = -F[172,x]+F[205,x]
F[477,x] = F[478,x]
F[478,x] = F[228,x]*F[28,x]
F[479,x] = F[480,x]
F[480,x] = F[28,x]*F[481,x]
F[481,x] = F[482,x]+F[95,x]
F[482,x] = F[483,x]+F[488,x]
F[483,x] = F[484,x]
F[484,x] = F[0,x]*F[485,x]
F[485,x] = F[11,x]+F[486,x]
F[486,x] = F[487,x]
F[487,x] = F[123,x]*F[28,x]*F[49,x]*F[50,x]
F[488,x] = F[489,x]
F[489,x] = F[28,x]*F[490,x]
F[490,x] = F[491,x]+F[508,x]
F[491,x] = -F[498,x]+F[492,x]
F[492,x] = 1/F[28,x]*F[493,x]
F[493,x] = F[494,x]
F[494,x] = -F[495,x]+F[93,x]
F[495,x] = F[496,x]
F[496,x] = F[0,x]*F[497,x]
F[497,x] = F[11,x]+F[2,x]
F[498,x] = F[499,x]+F[507,x]
F[499,x] = F[500,x]+F[93,x]
F[500,x] = F[501,x]
F[501,x] = F[28,x]*F[502,x]
F[502,x] = 1/F[28,x]*F[503,x]
F[503,x] = F[504,x]
F[504,x] = F[351,x]+F[505,x]
F[505,x] = -F[341,x]+F[506,x]
F[506,x] = -F[96,x]+F[339,x]
F[507,x] = F[2,x]*F[273,x]
F[508,x] = F[509,x]
F[509,x] = F[123,x]*F[28,x]*F[49,x]*F[50,x]*F[510,x]
F[510,x] = 1/F[28,x]/F[49,x]*F[511,x]
F[511,x] = F[512,x]
F[512,x] = -F[513,x]+F[280,x]
F[513,x] = F[514,x]
F[514,x] = F[0,x]*F[49,x]
F[515,x] = F[516,x]+F[518,x]
F[516,x] = F[517,x]
F[517,x] = F[2,x]*F[289,x]
F[518,x] = F[519,x]
F[519,x] = F[28,x]*F[520,x]
F[520,x] = F[521,x]+F[522,x]
F[521,x] = F[289,x]*F[49,x]*F[50,x]
F[522,x] = F[523,x]+F[530,x]
F[523,x] = F[524,x]+F[529,x]
F[524,x] = F[515,x]+F[525,x]
F[525,x] = F[526,x]+F[527,x]
F[526,x] = F[356,x]*F[5,x]
F[527,x] = F[528,x]
F[528,x] = F[28,x]*F[312,x]*F[397,x]*F[50,x]
F[529,x] = F[289,x]*F[323,x]
F[530,x] = -F[524,x]+F[531,x]
F[531,x] = F[532,x]+F[541,x]
F[532,x] = -F[536,x]+F[533,x]
F[533,x] = 1/F[28,x]*F[534,x]
F[534,x] = F[535,x]
F[535,x] = -F[4,x]+F[30,x]
F[536,x] = F[537,x]+F[7,x]
F[537,x] = F[538,x]+F[539,x]
F[538,x] = F[0,x]*F[15,x]
F[539,x] = F[540,x]
F[540,x] = F[124,x]*F[356,x]*F[49,x]
F[541,x] = F[542,x]+F[543,x]
F[542,x] = F[356,x]*F[535,x]
F[543,x] = F[544,x]
F[544,x] = F[28,x]*F[397,x]*F[49,x]*F[545,x]
F[545,x] = -F[535,x]+F[546,x]
F[546,x] = -F[549,x]+F[547,x]
F[547,x] = 1/F[28,x]/F[49,x]*F[548,x]
F[548,x] = F[338,x]
F[549,x] = F[330,x]+F[550,x]
F[550,x] = F[15,x]+F[4,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{28}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{515}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{0} \left(x \right)^{2}
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{479}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{28}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{0}\! \left(x \right)+F_{11}\! \left(x \right)
F_{15}\! \left(x \right) = -F_{30}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = \frac{F_{17}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{2}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{28}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = -F_{29}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = \frac{F_{24}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = \frac{F_{27}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{27}\! \left(x \right) = F_{2}\! \left(x \right)
F_{28}\! \left(x \right) = x
F_{29}\! \left(x \right) = F_{11}\! \left(x \right)+F_{26}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{28}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = \frac{F_{34}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{28}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{477}\! \left(x \right)
F_{38}\! \left(x \right) = \frac{F_{39}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = -F_{187}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{67}\! \left(x \right)
F_{42}\! \left(x \right) = F_{0}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{1}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{28}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{28}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{52}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49} \left(x \right)^{2}
F_{49}\! \left(x \right) = F_{1}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{28}\! \left(x \right) F_{49}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{49} \left(x \right)^{2} F_{28}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{62}\! \left(x \right)
F_{55}\! \left(x \right) = F_{49}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{50}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)+F_{61}\! \left(x \right)
F_{58}\! \left(x \right) = 0
F_{59}\! \left(x \right) = F_{28}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{50}\! \left(x \right)+F_{57}\! \left(x \right)
F_{61}\! \left(x \right) = F_{28}\! \left(x \right) F_{56}\! \left(x \right)
F_{62}\! \left(x \right) = F_{50}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{58}\! \left(x \right)+F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{28}\! \left(x \right) F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{28}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{50}\! \left(x \right)+F_{63}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{28}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = \frac{F_{70}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{449}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{75}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{2}\! \left(x \right) F_{49}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{28}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{447}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{446}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = \frac{F_{80}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{28}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{101}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{86}\! \left(x \right)
F_{85}\! \left(x \right) = F_{2}\! \left(x \right) F_{43}\! \left(x \right)
F_{86}\! \left(x \right) = -F_{445}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = -F_{99}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = \frac{F_{89}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{2}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{28}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{95}\! \left(x \right)
F_{94}\! \left(x \right) = F_{2}\! \left(x \right) F_{26}\! \left(x \right)
F_{95}\! \left(x \right) = -F_{98}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = \frac{F_{97}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{97}\! \left(x \right) = F_{25}\! \left(x \right)
F_{98}\! \left(x \right) = F_{0}\! \left(x \right) F_{26}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{0}\! \left(x \right) F_{43}\! \left(x \right)
F_{101}\! \left(x \right) = -F_{102}\! \left(x \right)+F_{88}\! \left(x \right)
F_{102}\! \left(x \right) = -F_{105}\! \left(x \right)+F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = \frac{F_{104}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{104}\! \left(x \right) = F_{90}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{430}\! \left(x \right)
F_{106}\! \left(x \right) = F_{0}\! \left(x \right) F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{2}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{28}\! \left(x \right)
F_{110}\! \left(x \right) = F_{107}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{40}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{425}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{28}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{117}\! \left(x \right)
F_{116}\! \left(x \right) = F_{113}\! \left(x \right)+F_{2}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{28}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{125}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{123}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{43}\! \left(x \right)
F_{122}\! \left(x \right) = F_{2}\! \left(x \right)+F_{81}\! \left(x \right)
F_{123}\! \left(x \right) = F_{0}\! \left(x \right)+F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{113}\! \left(x \right)+F_{50}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{28}\! \left(x \right) F_{49}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{398}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{253}\! \left(x \right)
F_{129}\! \left(x \right) = \frac{F_{130}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{28}\! \left(x \right)
F_{133}\! \left(x \right) = \frac{F_{134}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{124}\! \left(x \right)+F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{28}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{181}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{142}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{50}\! \left(x \right) F_{55}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right) F_{28}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{149}\! \left(x \right)
F_{145}\! \left(x \right) = F_{142}\! \left(x \right)+F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{116}\! \left(x \right)+F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{145}\! \left(x \right) F_{28}\! \left(x \right)
F_{149}\! \left(x \right) = -F_{150}\! \left(x \right)+F_{133}\! \left(x \right)
F_{150}\! \left(x \right) = \frac{F_{151}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{154}\! \left(x \right)
F_{153}\! \left(x \right) = F_{0}\! \left(x \right) F_{50}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right) F_{28}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)+F_{248}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right) F_{50}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{160}\! \left(x \right)
F_{159}\! \left(x \right) = F_{117}\! \left(x \right)+F_{123}\! \left(x \right)
F_{160}\! \left(x \right) = \frac{F_{161}\! \left(x \right)}{F_{50}\! \left(x \right)}
F_{161}\! \left(x \right) = -F_{166}\! \left(x \right)+F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = \frac{F_{163}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)
F_{164}\! \left(x \right) = -F_{165}\! \left(x \right)+F_{131}\! \left(x \right)
F_{165}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{188}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right) F_{50}\! \left(x \right)
F_{168}\! \left(x \right) = F_{159}\! \left(x \right)+F_{169}\! \left(x \right)
F_{169}\! \left(x \right) = \frac{F_{170}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right) F_{28}\! \left(x \right)
F_{172}\! \left(x \right) = -F_{179}\! \left(x \right)+F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = \frac{F_{174}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = -F_{178}\! \left(x \right)+F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = \frac{F_{177}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{177}\! \left(x \right) = F_{18}\! \left(x \right)
F_{178}\! \left(x \right) = F_{123}\! \left(x \right)+F_{18}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)+F_{181}\! \left(x \right)
F_{180}\! \left(x \right) = F_{139}\! \left(x \right)+F_{176}\! \left(x \right)
F_{181}\! \left(x \right) = -F_{182}\! \left(x \right)+F_{173}\! \left(x \right)
F_{182}\! \left(x \right) = F_{139}\! \left(x \right)+F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = \frac{F_{184}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)
F_{185}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{117}\! \left(x \right)+F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{107}\! \left(x \right)+F_{43}\! \left(x \right)
F_{188}\! \left(x \right) = -F_{237}\! \left(x \right)+F_{189}\! \left(x \right)
F_{189}\! \left(x \right) = \frac{F_{190}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right) F_{28}\! \left(x \right)
F_{193}\! \left(x \right) = \frac{F_{194}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)
F_{195}\! \left(x \right) = -F_{236}\! \left(x \right)+F_{196}\! \left(x \right)
F_{196}\! \left(x \right) = F_{197}\! \left(x \right)+F_{41}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right) F_{28}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)+F_{226}\! \left(x \right)
F_{200}\! \left(x \right) = F_{201}\! \left(x \right)+F_{202}\! \left(x \right)
F_{201}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{202}\! \left(x \right) = F_{203}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right) F_{28}\! \left(x \right) F_{49}\! \left(x \right)
F_{204}\! \left(x \right) = F_{200}\! \left(x \right)+F_{205}\! \left(x \right)
F_{205}\! \left(x \right) = \frac{F_{206}\! \left(x \right)}{F_{49}\! \left(x \right)}
F_{206}\! \left(x \right) = -F_{207}\! \left(x \right)+F_{193}\! \left(x \right)
F_{207}\! \left(x \right) = \frac{F_{208}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)
F_{209}\! \left(x \right) = -F_{225}\! \left(x \right)+F_{210}\! \left(x \right)
F_{210}\! \left(x \right) = -F_{212}\! \left(x \right)+F_{211}\! \left(x \right)
F_{211}\! \left(x \right) = F_{191}\! \left(x \right)+F_{201}\! \left(x \right)
F_{212}\! \left(x \right) = -F_{223}\! \left(x \right)+F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = -F_{217}\! \left(x \right)+F_{214}\! \left(x \right)
F_{214}\! \left(x \right) = \frac{F_{215}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{215}\! \left(x \right) = F_{216}\! \left(x \right)
F_{216}\! \left(x \right) = -F_{41}\! \left(x \right)+F_{176}\! \left(x \right)
F_{217}\! \left(x \right) = F_{218}\! \left(x \right)
F_{218}\! \left(x \right) = F_{219}\! \left(x \right) F_{28}\! \left(x \right)
F_{219}\! \left(x \right) = F_{214}\! \left(x \right)+F_{220}\! \left(x \right)
F_{220}\! \left(x \right) = F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = F_{159}\! \left(x \right) F_{222}\! \left(x \right) F_{50}\! \left(x \right)
F_{222}\! \left(x \right) = F_{49}\! \left(x \right)+F_{66}\! \left(x \right)
F_{223}\! \left(x \right) = F_{123}\! \left(x \right)+F_{224}\! \left(x \right)
F_{224}\! \left(x \right) = F_{147}\! \left(x \right)+F_{56}\! \left(x \right)
F_{225}\! \left(x \right) = F_{0}\! \left(x \right) F_{49}\! \left(x \right)
F_{226}\! \left(x \right) = F_{227}\! \left(x \right)
F_{227}\! \left(x \right) = F_{228}\! \left(x \right) F_{28}\! \left(x \right)
F_{228}\! \left(x \right) = F_{229}\! \left(x \right)+F_{230}\! \left(x \right)
F_{229}\! \left(x \right) = F_{200}\! \left(x \right) F_{49}\! \left(x \right)
F_{230}\! \left(x \right) = F_{231}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right) F_{49}\! \left(x \right) F_{66}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right)+F_{4}\! \left(x \right)
F_{233}\! \left(x \right) = F_{234}\! \left(x \right)
F_{234}\! \left(x \right) = F_{235}\! \left(x \right) F_{28}\! \left(x \right)
F_{235}\! \left(x \right) = F_{172}\! \left(x \right)+F_{232}\! \left(x \right)
F_{236}\! \left(x \right) = F_{201}\! \left(x \right)
F_{237}\! \left(x \right) = F_{238}\! \left(x \right)+F_{240}\! \left(x \right)
F_{238}\! \left(x \right) = F_{167}\! \left(x \right)+F_{239}\! \left(x \right)
F_{239}\! \left(x \right) = F_{169}\! \left(x \right)+F_{186}\! \left(x \right)
F_{240}\! \left(x \right) = -F_{241}\! \left(x \right)+F_{189}\! \left(x \right)
F_{241}\! \left(x \right) = F_{242}\! \left(x \right)+F_{244}\! \left(x \right)
F_{242}\! \left(x \right) = F_{211}\! \left(x \right)+F_{243}\! \left(x \right)
F_{243}\! \left(x \right) = F_{213}\! \left(x \right) F_{50}\! \left(x \right)
F_{244}\! \left(x \right) = F_{245}\! \left(x \right) F_{49}\! \left(x \right)
F_{245}\! \left(x \right) = \frac{F_{246}\! \left(x \right)}{F_{28}\! \left(x \right) F_{49}\! \left(x \right)}
F_{246}\! \left(x \right) = F_{247}\! \left(x \right)
F_{247}\! \left(x \right) = F_{205}\! \left(x \right) F_{28}\! \left(x \right) F_{49}\! \left(x \right)
F_{248}\! \left(x \right) = F_{131}\! \left(x \right)+F_{249}\! \left(x \right)
F_{249}\! \left(x \right) = F_{250}\! \left(x \right) F_{50}\! \left(x \right)
F_{250}\! \left(x \right) = F_{224}\! \left(x \right)+F_{251}\! \left(x \right)
F_{251}\! \left(x \right) = F_{252}\! \left(x \right)
F_{252}\! \left(x \right) = F_{149}\! \left(x \right) F_{28}\! \left(x \right)
F_{253}\! \left(x \right) = F_{254}\! \left(x \right)
F_{254}\! \left(x \right) = F_{129}\! \left(x \right) F_{255}\! \left(x \right) F_{28}\! \left(x \right)
F_{255}\! \left(x \right) = F_{121}\! \left(x \right)+F_{256}\! \left(x \right)
F_{256}\! \left(x \right) = F_{257}\! \left(x \right)
F_{257}\! \left(x \right) = F_{258}\! \left(x \right) F_{28}\! \left(x \right)
F_{258}\! \left(x \right) = \frac{F_{259}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{259}\! \left(x \right) = F_{260}\! \left(x \right)
F_{260}\! \left(x \right) = -F_{397}\! \left(x \right)+F_{261}\! \left(x \right)
F_{261}\! \left(x \right) = \frac{F_{262}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{262}\! \left(x \right) = F_{263}\! \left(x \right)
F_{263}\! \left(x \right) = \frac{F_{264}\! \left(x \right)}{F_{11}\! \left(x \right) F_{49}\! \left(x \right)}
F_{264}\! \left(x \right) = F_{265}\! \left(x \right)
F_{265}\! \left(x \right) = -F_{346}\! \left(x \right)+F_{266}\! \left(x \right)
F_{266}\! \left(x \right) = -F_{339}\! \left(x \right)+F_{267}\! \left(x \right)
F_{267}\! \left(x \right) = \frac{F_{268}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{268}\! \left(x \right) = F_{269}\! \left(x \right)
F_{269}\! \left(x \right) = -F_{272}\! \left(x \right)+F_{270}\! \left(x \right)
F_{270}\! \left(x \right) = \frac{F_{271}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{271}\! \left(x \right) = F_{90}\! \left(x \right)
F_{272}\! \left(x \right) = F_{26}\! \left(x \right)+F_{273}\! \left(x \right)
F_{273}\! \left(x \right) = -F_{274}\! \left(x \right)+F_{270}\! \left(x \right)
F_{274}\! \left(x \right) = F_{26}\! \left(x \right)+F_{275}\! \left(x \right)
F_{275}\! \left(x \right) = F_{276}\! \left(x \right)
F_{276}\! \left(x \right) = F_{277}\! \left(x \right) F_{28}\! \left(x \right)
F_{277}\! \left(x \right) = \frac{F_{278}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{278}\! \left(x \right) = F_{279}\! \left(x \right)
F_{279}\! \left(x \right) = -F_{280}\! \left(x \right)+F_{96}\! \left(x \right)
F_{280}\! \left(x \right) = \frac{F_{281}\! \left(x \right)}{F_{28}\! \left(x \right) F_{49}\! \left(x \right)}
F_{281}\! \left(x \right) = F_{282}\! \left(x \right)
F_{282}\! \left(x \right) = \frac{F_{283}\! \left(x \right)}{F_{0}\! \left(x \right)}
F_{283}\! \left(x \right) = F_{284}\! \left(x \right)
F_{284}\! \left(x \right) = -F_{285}\! \left(x \right)+F_{35}\! \left(x \right)
F_{285}\! \left(x \right) = -F_{338}\! \left(x \right)+F_{286}\! \left(x \right)
F_{286}\! \left(x \right) = -F_{287}\! \left(x \right)+F_{7}\! \left(x \right)
F_{287}\! \left(x \right) = F_{288}\! \left(x \right)
F_{288}\! \left(x \right) = F_{0}\! \left(x \right) F_{289}\! \left(x \right)
F_{289}\! \left(x \right) = \frac{F_{290}\! \left(x \right)}{F_{50}\! \left(x \right)}
F_{290}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{291}\! \left(x \right)
F_{291}\! \left(x \right) = F_{292}\! \left(x \right)+F_{295}\! \left(x \right)
F_{292}\! \left(x \right) = F_{293}\! \left(x \right)+F_{48}\! \left(x \right)
F_{293}\! \left(x \right) = F_{294}\! \left(x \right)
F_{294}\! \left(x \right) = F_{28}\! \left(x \right) F_{49}\! \left(x \right) F_{5}\! \left(x \right)
F_{295}\! \left(x \right) = F_{25}\! \left(x \right)+F_{296}\! \left(x \right)
F_{296}\! \left(x \right) = -F_{319}\! \left(x \right)+F_{297}\! \left(x \right)
F_{297}\! \left(x \right) = F_{298}\! \left(x \right)
F_{298}\! \left(x \right) = F_{28}\! \left(x \right) F_{299}\! \left(x \right)
F_{299}\! \left(x \right) = F_{300}\! \left(x \right)+F_{308}\! \left(x \right)
F_{300}\! \left(x \right) = -F_{13}\! \left(x \right)+F_{301}\! \left(x \right)
F_{301}\! \left(x \right) = -F_{304}\! \left(x \right)+F_{302}\! \left(x \right)
F_{302}\! \left(x \right) = \frac{F_{303}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{303}\! \left(x \right) = F_{10}\! \left(x \right)
F_{304}\! \left(x \right) = F_{305}\! \left(x \right)
F_{305}\! \left(x \right) = F_{28}\! \left(x \right) F_{306}\! \left(x \right)
F_{306}\! \left(x \right) = \frac{F_{307}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{307}\! \left(x \right) = F_{95}\! \left(x \right)
F_{308}\! \left(x \right) = F_{309}\! \left(x \right)
F_{309}\! \left(x \right) = F_{28}\! \left(x \right) F_{310}\! \left(x \right)
F_{310}\! \left(x \right) = F_{311}\! \left(x \right)+F_{315}\! \left(x \right)
F_{311}\! \left(x \right) = F_{26}\! \left(x \right) F_{312}\! \left(x \right)
F_{312}\! \left(x \right) = -F_{13}\! \left(x \right)+F_{313}\! \left(x \right)
F_{313}\! \left(x \right) = \frac{F_{314}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{314}\! \left(x \right) = F_{15}\! \left(x \right)
F_{315}\! \left(x \right) = F_{316}\! \left(x \right)
F_{316}\! \left(x \right) = F_{317}\! \left(x \right) F_{318}\! \left(x \right) F_{49}\! \left(x \right)
F_{317}\! \left(x \right) = -F_{279}\! \left(x \right)+F_{93}\! \left(x \right)
F_{318}\! \left(x \right) = -F_{123}\! \left(x \right)+F_{232}\! \left(x \right)
F_{319}\! \left(x \right) = F_{320}\! \left(x \right)
F_{320}\! \left(x \right) = F_{28}\! \left(x \right) F_{321}\! \left(x \right)
F_{321}\! \left(x \right) = F_{322}\! \left(x \right)+F_{336}\! \left(x \right)
F_{322}\! \left(x \right) = F_{26}\! \left(x \right) F_{323}\! \left(x \right)
F_{323}\! \left(x \right) = F_{324}\! \left(x \right)
F_{324}\! \left(x \right) = F_{28}\! \left(x \right) F_{325}\! \left(x \right)
F_{325}\! \left(x \right) = F_{312}\! \left(x \right)+F_{326}\! \left(x \right)
F_{326}\! \left(x \right) = F_{323}\! \left(x \right)+F_{327}\! \left(x \right)
F_{327}\! \left(x \right) = F_{328}\! \left(x \right)
F_{328}\! \left(x \right) = F_{28}\! \left(x \right) F_{329}\! \left(x \right) F_{49}\! \left(x \right)
F_{329}\! \left(x \right) = F_{330}\! \left(x \right)+F_{4}\! \left(x \right)
F_{330}\! \left(x \right) = F_{331}\! \left(x \right)+F_{332}\! \left(x \right)
F_{331}\! \left(x \right) = F_{153}\! \left(x \right)
F_{332}\! \left(x \right) = F_{333}\! \left(x \right)
F_{333}\! \left(x \right) = F_{28}\! \left(x \right) F_{334}\! \left(x \right)
F_{334}\! \left(x \right) = F_{202}\! \left(x \right)+F_{335}\! \left(x \right)
F_{335}\! \left(x \right) = F_{18}\! \left(x \right) F_{49}\! \left(x \right)
F_{336}\! \left(x \right) = F_{337}\! \left(x \right)
F_{337}\! \left(x \right) = F_{113}\! \left(x \right) F_{317}\! \left(x \right) F_{49}\! \left(x \right)
F_{338}\! \left(x \right) = F_{18}\! \left(x \right)+F_{332}\! \left(x \right)
F_{339}\! \left(x \right) = \frac{F_{340}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{340}\! \left(x \right) = F_{341}\! \left(x \right)
F_{341}\! \left(x \right) = -F_{26}\! \left(x \right)+F_{342}\! \left(x \right)
F_{342}\! \left(x \right) = -F_{345}\! \left(x \right)+F_{343}\! \left(x \right)
F_{343}\! \left(x \right) = \frac{F_{344}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{344}\! \left(x \right) = F_{18}\! \left(x \right)
F_{345}\! \left(x \right) = F_{15}\! \left(x \right)+F_{297}\! \left(x \right)
F_{346}\! \left(x \right) = F_{347}\! \left(x \right)+F_{348}\! \left(x \right)
F_{347}\! \left(x \right) = F_{0}\! \left(x \right) F_{273}\! \left(x \right)
F_{348}\! \left(x \right) = F_{349}\! \left(x \right)+F_{351}\! \left(x \right)
F_{349}\! \left(x \right) = F_{350}\! \left(x \right)
F_{350}\! \left(x \right) = F_{266}\! \left(x \right) F_{28}\! \left(x \right)
F_{351}\! \left(x \right) = F_{352}\! \left(x \right)
F_{352}\! \left(x \right) = F_{28}\! \left(x \right) F_{353}\! \left(x \right)
F_{353}\! \left(x \right) = F_{354}\! \left(x \right)+F_{376}\! \left(x \right)
F_{354}\! \left(x \right) = F_{273}\! \left(x \right) F_{355}\! \left(x \right)
F_{355}\! \left(x \right) = F_{356}\! \left(x \right)+F_{372}\! \left(x \right)
F_{356}\! \left(x \right) = F_{357}\! \left(x \right)
F_{357}\! \left(x \right) = F_{28}\! \left(x \right) F_{358}\! \left(x \right)
F_{358}\! \left(x \right) = F_{222}\! \left(x \right)+F_{359}\! \left(x \right)
F_{359}\! \left(x \right) = F_{360}\! \left(x \right)+F_{74}\! \left(x \right)
F_{360}\! \left(x \right) = F_{361}\! \left(x \right)
F_{361}\! \left(x \right) = F_{28}\! \left(x \right) F_{362}\! \left(x \right) F_{49}\! \left(x \right)
F_{362}\! \left(x \right) = F_{359}\! \left(x \right)+F_{363}\! \left(x \right)
F_{363}\! \left(x \right) = -F_{358}\! \left(x \right)+F_{364}\! \left(x \right)
F_{364}\! \left(x \right) = -F_{367}\! \left(x \right)+F_{365}\! \left(x \right)
F_{365}\! \left(x \right) = \frac{F_{366}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{366}\! \left(x \right) = F_{87}\! \left(x \right)
F_{367}\! \left(x \right) = F_{368}\! \left(x \right)
F_{368}\! \left(x \right) = F_{28}\! \left(x \right) F_{369}\! \left(x \right)
F_{369}\! \left(x \right) = F_{365}\! \left(x \right)+F_{370}\! \left(x \right)
F_{370}\! \left(x \right) = F_{371}\! \left(x \right)
F_{371}\! \left(x \right) = F_{261}\! \left(x \right) F_{50}\! \left(x \right) F_{55}\! \left(x \right)
F_{372}\! \left(x \right) = F_{373}\! \left(x \right)+F_{374}\! \left(x \right)
F_{373}\! \left(x \right) = F_{327}\! \left(x \right)+F_{91}\! \left(x \right)
F_{374}\! \left(x \right) = -F_{375}\! \left(x \right)+F_{22}\! \left(x \right)
F_{375}\! \left(x \right) = F_{19}\! \left(x \right)+F_{282}\! \left(x \right)
F_{376}\! \left(x \right) = F_{377}\! \left(x \right)
F_{377}\! \left(x \right) = F_{263}\! \left(x \right) F_{378}\! \left(x \right) F_{49}\! \left(x \right)
F_{378}\! \left(x \right) = F_{379}\! \left(x \right)
F_{379}\! \left(x \right) = F_{28}\! \left(x \right) F_{380}\! \left(x \right)
F_{380}\! \left(x \right) = \frac{F_{381}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{381}\! \left(x \right) = F_{382}\! \left(x \right)
F_{382}\! \left(x \right) = -F_{385}\! \left(x \right)+F_{383}\! \left(x \right)
F_{383}\! \left(x \right) = \frac{F_{384}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{384}\! \left(x \right) = F_{374}\! \left(x \right)
F_{385}\! \left(x \right) = -F_{388}\! \left(x \right)+F_{386}\! \left(x \right)
F_{386}\! \left(x \right) = \frac{F_{387}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{387}\! \left(x \right) = F_{31}\! \left(x \right)
F_{388}\! \left(x \right) = F_{389}\! \left(x \right)
F_{389}\! \left(x \right) = F_{31}\! \left(x \right)+F_{390}\! \left(x \right)
F_{390}\! \left(x \right) = F_{391}\! \left(x \right)+F_{392}\! \left(x \right)
F_{391}\! \left(x \right) = F_{289}\! \left(x \right) F_{49}\! \left(x \right)
F_{392}\! \left(x \right) = F_{393}\! \left(x \right)
F_{393}\! \left(x \right) = F_{28}\! \left(x \right) F_{394}\! \left(x \right) F_{49}\! \left(x \right)
F_{394}\! \left(x \right) = \frac{F_{395}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{395}\! \left(x \right) = F_{396}\! \left(x \right)
F_{396}\! \left(x \right) = -F_{289}\! \left(x \right)+F_{280}\! \left(x \right)
F_{397}\! \left(x \right) = F_{0}\! \left(x \right)+F_{263}\! \left(x \right)
F_{398}\! \left(x \right) = F_{399}\! \left(x \right)
F_{399}\! \left(x \right) = F_{28}\! \left(x \right) F_{400}\! \left(x \right)
F_{400}\! \left(x \right) = \frac{F_{401}\! \left(x \right)}{F_{28}\! \left(x \right) F_{49}\! \left(x \right)}
F_{401}\! \left(x \right) = F_{402}\! \left(x \right)
F_{402}\! \left(x \right) = F_{125}\! \left(x \right)+F_{403}\! \left(x \right)
F_{403}\! \left(x \right) = F_{404}\! \left(x \right)
F_{404}\! \left(x \right) = F_{160}\! \left(x \right) F_{28}\! \left(x \right) F_{405}\! \left(x \right)
F_{405}\! \left(x \right) = F_{406}\! \left(x \right)+F_{409}\! \left(x \right)
F_{406}\! \left(x \right) = F_{358}\! \left(x \right)+F_{407}\! \left(x \right)
F_{407}\! \left(x \right) = F_{408}\! \left(x \right)
F_{408}\! \left(x \right) = F_{28}\! \left(x \right) F_{405}\! \left(x \right)
F_{409}\! \left(x \right) = -F_{418}\! \left(x \right)+F_{410}\! \left(x \right)
F_{410}\! \left(x \right) = \frac{F_{411}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{411}\! \left(x \right) = F_{412}\! \left(x \right)
F_{412}\! \left(x \right) = -F_{417}\! \left(x \right)+F_{413}\! \left(x \right)
F_{413}\! \left(x \right) = \frac{F_{414}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{414}\! \left(x \right) = F_{415}\! \left(x \right)
F_{415}\! \left(x \right) = F_{416}\! \left(x \right)+F_{81}\! \left(x \right)
F_{416}\! \left(x \right) = F_{44}\! \left(x \right)
F_{417}\! \left(x \right) = F_{121}\! \left(x \right)+F_{260}\! \left(x \right)
F_{418}\! \left(x \right) = \frac{F_{419}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{419}\! \left(x \right) = F_{420}\! \left(x \right)
F_{420}\! \left(x \right) = -F_{121}\! \left(x \right)+F_{421}\! \left(x \right)
F_{421}\! \left(x \right) = -F_{363}\! \left(x \right)+F_{422}\! \left(x \right)
F_{422}\! \left(x \right) = F_{417}\! \left(x \right)+F_{423}\! \left(x \right)
F_{423}\! \left(x \right) = F_{424}\! \left(x \right)
F_{424}\! \left(x \right) = F_{28}\! \left(x \right) F_{410}\! \left(x \right)
F_{425}\! \left(x \right) = F_{426}\! \left(x \right)
F_{426}\! \left(x \right) = F_{28}\! \left(x \right) F_{427}\! \left(x \right)
F_{427}\! \left(x \right) = F_{112}\! \left(x \right)+F_{428}\! \left(x \right)
F_{428}\! \left(x \right) = F_{142}\! \left(x \right)+F_{429}\! \left(x \right)
F_{429}\! \left(x \right) = F_{113}\! \left(x \right) F_{66}\! \left(x \right)
F_{430}\! \left(x \right) = F_{431}\! \left(x \right)
F_{431}\! \left(x \right) = F_{28}\! \left(x \right) F_{432}\! \left(x \right)
F_{432}\! \left(x \right) = F_{433}\! \left(x \right)+F_{440}\! \left(x \right)
F_{433}\! \left(x \right) = F_{434}\! \left(x \right)
F_{434}\! \left(x \right) = F_{28}\! \left(x \right) F_{364}\! \left(x \right) F_{435}\! \left(x \right)
F_{435}\! \left(x \right) = F_{187}\! \left(x \right)+F_{436}\! \left(x \right)
F_{436}\! \left(x \right) = F_{437}\! \left(x \right)
F_{437}\! \left(x \right) = F_{28}\! \left(x \right) F_{438}\! \left(x \right)
F_{438}\! \left(x \right) = \frac{F_{439}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{439}\! \left(x \right) = F_{117}\! \left(x \right)
F_{440}\! \left(x \right) = F_{441}\! \left(x \right)
F_{441}\! \left(x \right) = F_{28}\! \left(x \right) F_{442}\! \left(x \right)
F_{442}\! \left(x \right) = F_{432}\! \left(x \right)+F_{443}\! \left(x \right)
F_{443}\! \left(x \right) = F_{444}\! \left(x \right)
F_{444}\! \left(x \right) = F_{142}\! \left(x \right) F_{261}\! \left(x \right)
F_{445}\! \left(x \right) = F_{46}\! \left(x \right)
F_{446}\! \left(x \right) = F_{2}\! \left(x \right) F_{50}\! \left(x \right) F_{55}\! \left(x \right)
F_{447}\! \left(x \right) = F_{448}\! \left(x \right)+F_{86}\! \left(x \right)
F_{448}\! \left(x \right) = F_{360}\! \left(x \right) F_{50}\! \left(x \right)
F_{449}\! \left(x \right) = F_{450}\! \left(x \right)+F_{451}\! \left(x \right)
F_{450}\! \left(x \right) = F_{122}\! \left(x \right) F_{2}\! \left(x \right)
F_{451}\! \left(x \right) = F_{452}\! \left(x \right)
F_{452}\! \left(x \right) = F_{28}\! \left(x \right) F_{453}\! \left(x \right)
F_{453}\! \left(x \right) = F_{454}\! \left(x \right)+F_{466}\! \left(x \right)
F_{454}\! \left(x \right) = F_{455}\! \left(x \right)+F_{456}\! \left(x \right)
F_{455}\! \left(x \right) = F_{2}\! \left(x \right) F_{359}\! \left(x \right)
F_{456}\! \left(x \right) = F_{457}\! \left(x \right)
F_{457}\! \left(x \right) = F_{28}\! \left(x \right) F_{458}\! \left(x \right)
F_{458}\! \left(x \right) = F_{453}\! \left(x \right)+F_{459}\! \left(x \right)
F_{459}\! \left(x \right) = F_{460}\! \left(x \right)
F_{460}\! \left(x \right) = F_{461}\! \left(x \right) F_{49}\! \left(x \right) F_{50}\! \left(x \right)
F_{461}\! \left(x \right) = F_{462}\! \left(x \right)+F_{464}\! \left(x \right)
F_{462}\! \left(x \right) = F_{463}\! \left(x \right)
F_{463}\! \left(x \right) = F_{146}\! \left(x \right) F_{255}\! \left(x \right) F_{28}\! \left(x \right)
F_{464}\! \left(x \right) = F_{465}\! \left(x \right)
F_{465}\! \left(x \right) = F_{212}\! \left(x \right) F_{255}\! \left(x \right) F_{28}\! \left(x \right)
F_{466}\! \left(x \right) = F_{467}\! \left(x \right)+F_{468}\! \left(x \right)
F_{467}\! \left(x \right) = F_{18}\! \left(x \right) F_{359}\! \left(x \right)
F_{468}\! \left(x \right) = F_{469}\! \left(x \right)
F_{469}\! \left(x \right) = F_{28}\! \left(x \right) F_{470}\! \left(x \right)
F_{470}\! \left(x \right) = F_{471}\! \left(x \right)+F_{472}\! \left(x \right)
F_{471}\! \left(x \right) = F_{172}\! \left(x \right) F_{359}\! \left(x \right)
F_{472}\! \left(x \right) = F_{473}\! \left(x \right)
F_{473}\! \left(x \right) = F_{474}\! \left(x \right) F_{476}\! \left(x \right) F_{49}\! \left(x \right)
F_{474}\! \left(x \right) = F_{475}\! \left(x \right)
F_{475}\! \left(x \right) = F_{255}\! \left(x \right) F_{28}\! \left(x \right) F_{49}\! \left(x \right)
F_{476}\! \left(x \right) = -F_{172}\! \left(x \right)+F_{205}\! \left(x \right)
F_{477}\! \left(x \right) = F_{478}\! \left(x \right)
F_{478}\! \left(x \right) = F_{228}\! \left(x \right) F_{28}\! \left(x \right)
F_{479}\! \left(x \right) = F_{480}\! \left(x \right)
F_{480}\! \left(x \right) = F_{28}\! \left(x \right) F_{481}\! \left(x \right)
F_{481}\! \left(x \right) = F_{482}\! \left(x \right)+F_{95}\! \left(x \right)
F_{482}\! \left(x \right) = F_{483}\! \left(x \right)+F_{488}\! \left(x \right)
F_{483}\! \left(x \right) = F_{484}\! \left(x \right)
F_{484}\! \left(x \right) = F_{0}\! \left(x \right) F_{485}\! \left(x \right)
F_{485}\! \left(x \right) = F_{11}\! \left(x \right)+F_{486}\! \left(x \right)
F_{486}\! \left(x \right) = F_{487}\! \left(x \right)
F_{487}\! \left(x \right) = F_{123}\! \left(x \right) F_{28}\! \left(x \right) F_{49}\! \left(x \right) F_{50}\! \left(x \right)
F_{488}\! \left(x \right) = F_{489}\! \left(x \right)
F_{489}\! \left(x \right) = F_{28}\! \left(x \right) F_{490}\! \left(x \right)
F_{490}\! \left(x \right) = F_{491}\! \left(x \right)+F_{508}\! \left(x \right)
F_{491}\! \left(x \right) = -F_{498}\! \left(x \right)+F_{492}\! \left(x \right)
F_{492}\! \left(x \right) = \frac{F_{493}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{493}\! \left(x \right) = F_{494}\! \left(x \right)
F_{494}\! \left(x \right) = -F_{495}\! \left(x \right)+F_{93}\! \left(x \right)
F_{495}\! \left(x \right) = F_{496}\! \left(x \right)
F_{496}\! \left(x \right) = F_{0}\! \left(x \right) F_{497}\! \left(x \right)
F_{497}\! \left(x \right) = F_{11}\! \left(x \right)+F_{2}\! \left(x \right)
F_{498}\! \left(x \right) = F_{499}\! \left(x \right)+F_{507}\! \left(x \right)
F_{499}\! \left(x \right) = F_{500}\! \left(x \right)+F_{93}\! \left(x \right)
F_{500}\! \left(x \right) = F_{501}\! \left(x \right)
F_{501}\! \left(x \right) = F_{28}\! \left(x \right) F_{502}\! \left(x \right)
F_{502}\! \left(x \right) = \frac{F_{503}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{503}\! \left(x \right) = F_{504}\! \left(x \right)
F_{504}\! \left(x \right) = F_{351}\! \left(x \right)+F_{505}\! \left(x \right)
F_{505}\! \left(x \right) = -F_{341}\! \left(x \right)+F_{506}\! \left(x \right)
F_{506}\! \left(x \right) = -F_{96}\! \left(x \right)+F_{339}\! \left(x \right)
F_{507}\! \left(x \right) = F_{2}\! \left(x \right) F_{273}\! \left(x \right)
F_{508}\! \left(x \right) = F_{509}\! \left(x \right)
F_{509}\! \left(x \right) = F_{123}\! \left(x \right) F_{28}\! \left(x \right) F_{49}\! \left(x \right) F_{50}\! \left(x \right) F_{510}\! \left(x \right)
F_{510}\! \left(x \right) = \frac{F_{511}\! \left(x \right)}{F_{28}\! \left(x \right) F_{49}\! \left(x \right)}
F_{511}\! \left(x \right) = F_{512}\! \left(x \right)
F_{512}\! \left(x \right) = -F_{513}\! \left(x \right)+F_{280}\! \left(x \right)
F_{513}\! \left(x \right) = F_{514}\! \left(x \right)
F_{514}\! \left(x \right) = F_{0}\! \left(x \right) F_{49}\! \left(x \right)
F_{515}\! \left(x \right) = F_{516}\! \left(x \right)+F_{518}\! \left(x \right)
F_{516}\! \left(x \right) = F_{517}\! \left(x \right)
F_{517}\! \left(x \right) = F_{2}\! \left(x \right) F_{289}\! \left(x \right)
F_{518}\! \left(x \right) = F_{519}\! \left(x \right)
F_{519}\! \left(x \right) = F_{28}\! \left(x \right) F_{520}\! \left(x \right)
F_{520}\! \left(x \right) = F_{521}\! \left(x \right)+F_{522}\! \left(x \right)
F_{521}\! \left(x \right) = F_{289}\! \left(x \right) F_{49}\! \left(x \right) F_{50}\! \left(x \right)
F_{522}\! \left(x \right) = F_{523}\! \left(x \right)+F_{530}\! \left(x \right)
F_{523}\! \left(x \right) = F_{524}\! \left(x \right)+F_{529}\! \left(x \right)
F_{524}\! \left(x \right) = F_{515}\! \left(x \right)+F_{525}\! \left(x \right)
F_{525}\! \left(x \right) = F_{526}\! \left(x \right)+F_{527}\! \left(x \right)
F_{526}\! \left(x \right) = F_{356}\! \left(x \right) F_{5}\! \left(x \right)
F_{527}\! \left(x \right) = F_{528}\! \left(x \right)
F_{528}\! \left(x \right) = F_{28}\! \left(x \right) F_{312}\! \left(x \right) F_{397}\! \left(x \right) F_{50}\! \left(x \right)
F_{529}\! \left(x \right) = F_{289}\! \left(x \right) F_{323}\! \left(x \right)
F_{530}\! \left(x \right) = -F_{524}\! \left(x \right)+F_{531}\! \left(x \right)
F_{531}\! \left(x \right) = F_{532}\! \left(x \right)+F_{541}\! \left(x \right)
F_{532}\! \left(x \right) = -F_{536}\! \left(x \right)+F_{533}\! \left(x \right)
F_{533}\! \left(x \right) = \frac{F_{534}\! \left(x \right)}{F_{28}\! \left(x \right)}
F_{534}\! \left(x \right) = F_{535}\! \left(x \right)
F_{535}\! \left(x \right) = -F_{4}\! \left(x \right)+F_{30}\! \left(x \right)
F_{536}\! \left(x \right) = F_{537}\! \left(x \right)+F_{7}\! \left(x \right)
F_{537}\! \left(x \right) = F_{538}\! \left(x \right)+F_{539}\! \left(x \right)
F_{538}\! \left(x \right) = F_{0}\! \left(x \right) F_{15}\! \left(x \right)
F_{539}\! \left(x \right) = F_{540}\! \left(x \right)
F_{540}\! \left(x \right) = F_{124}\! \left(x \right) F_{356}\! \left(x \right) F_{49}\! \left(x \right)
F_{541}\! \left(x \right) = F_{542}\! \left(x \right)+F_{543}\! \left(x \right)
F_{542}\! \left(x \right) = F_{356}\! \left(x \right) F_{535}\! \left(x \right)
F_{543}\! \left(x \right) = F_{544}\! \left(x \right)
F_{544}\! \left(x \right) = F_{28}\! \left(x \right) F_{397}\! \left(x \right) F_{49}\! \left(x \right) F_{545}\! \left(x \right)
F_{545}\! \left(x \right) = -F_{535}\! \left(x \right)+F_{546}\! \left(x \right)
F_{546}\! \left(x \right) = -F_{549}\! \left(x \right)+F_{547}\! \left(x \right)
F_{547}\! \left(x \right) = \frac{F_{548}\! \left(x \right)}{F_{28}\! \left(x \right) F_{49}\! \left(x \right)}
F_{548}\! \left(x \right) = F_{338}\! \left(x \right)
F_{549}\! \left(x \right) = F_{330}\! \left(x \right)+F_{550}\! \left(x \right)
F_{550}\! \left(x \right) = F_{15}\! \left(x \right)+F_{4}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_28(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_28(x)*F_7(x))
Eq(F_7(x), F_515(x) + F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_0(x)**2)
Eq(F_10(x), F_11(x) + F_479(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_28(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_0(x) + F_11(x))
Eq(F_15(x), F_16(x) - F_30(x))
Eq(F_16(x), F_17(x)/F_28(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x) + F_2(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_28(x))
Eq(F_21(x), F_11(x) + F_22(x))
Eq(F_22(x), F_23(x) - F_29(x))
Eq(F_23(x), F_24(x)/F_28(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), -F_0(x) + F_26(x))
Eq(F_26(x), F_27(x)/F_28(x))
Eq(F_27(x), F_2(x))
Eq(F_28(x), x)
Eq(F_29(x), F_11(x) + F_26(x))
Eq(F_30(x), F_31(x) + F_4(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_28(x)*F_33(x))
Eq(F_33(x), F_34(x)/F_28(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_28(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_477(x))
Eq(F_38(x), F_39(x)/F_28(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), -F_187(x) + F_41(x))
Eq(F_41(x), F_42(x) + F_67(x))
Eq(F_42(x), F_0(x)*F_43(x))
Eq(F_43(x), F_1(x) + F_44(x))
Eq(F_44(x), F_28(x)*F_45(x))
Eq(F_45(x), F_43(x) + F_46(x))
Eq(F_46(x), F_28(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_52(x))
Eq(F_48(x), F_49(x)**2)
Eq(F_49(x), F_1(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_28(x)*F_49(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_28(x)*F_49(x)**2*F_54(x))
Eq(F_54(x), F_55(x) + F_62(x))
Eq(F_55(x), F_49(x) + F_56(x))
Eq(F_56(x), F_50(x) + F_57(x))
Eq(F_57(x), F_58(x) + F_59(x) + F_61(x))
Eq(F_58(x), 0)
Eq(F_59(x), F_28(x)*F_60(x))
Eq(F_60(x), F_50(x) + F_57(x))
Eq(F_61(x), F_28(x)*F_56(x))
Eq(F_62(x), F_50(x) + F_63(x))
Eq(F_63(x), F_58(x) + F_64(x) + F_65(x))
Eq(F_64(x), F_28(x)*F_62(x))
Eq(F_65(x), F_28(x)*F_66(x))
Eq(F_66(x), F_50(x) + F_63(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_28(x)*F_69(x))
Eq(F_69(x), F_70(x)/F_28(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_449(x) + F_72(x))
Eq(F_72(x), F_73(x) + F_75(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_2(x)*F_49(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_28(x)*F_77(x))
Eq(F_77(x), F_447(x) + F_78(x))
Eq(F_78(x), F_446(x) + F_79(x))
Eq(F_79(x), F_80(x)/F_28(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_28(x)*F_83(x))
Eq(F_83(x), F_101(x) + F_84(x))
Eq(F_84(x), F_85(x) + F_86(x))
Eq(F_85(x), F_2(x)*F_43(x))
Eq(F_86(x), -F_445(x) + F_87(x))
Eq(F_87(x), F_88(x) - F_99(x))
Eq(F_88(x), F_89(x)/F_28(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_2(x) + F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_28(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_95(x))
Eq(F_94(x), F_2(x)*F_26(x))
Eq(F_95(x), F_96(x) - F_98(x))
Eq(F_96(x), F_97(x)/F_28(x))
Eq(F_97(x), F_25(x))
Eq(F_98(x), F_0(x)*F_26(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_0(x)*F_43(x))
Eq(F_101(x), -F_102(x) + F_88(x))
Eq(F_102(x), F_103(x) - F_105(x))
Eq(F_103(x), F_104(x)/F_28(x))
Eq(F_104(x), F_90(x))
Eq(F_105(x), F_106(x) + F_430(x))
Eq(F_106(x), F_0(x)*F_107(x))
Eq(F_107(x), F_108(x) + F_2(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x)*F_28(x))
Eq(F_110(x), F_107(x) + F_111(x))
Eq(F_111(x), F_112(x) + F_40(x))
Eq(F_112(x), F_113(x) + F_425(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_28(x))
Eq(F_115(x), F_116(x) + F_117(x))
Eq(F_116(x), F_113(x) + F_2(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_119(x)*F_28(x))
Eq(F_119(x), F_120(x) + F_125(x))
Eq(F_120(x), F_121(x)*F_123(x))
Eq(F_121(x), F_122(x) + F_43(x))
Eq(F_122(x), F_2(x) + F_81(x))
Eq(F_123(x), F_0(x) + F_124(x))
Eq(F_124(x), F_113(x) + F_50(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_127(x)*F_28(x)*F_49(x))
Eq(F_127(x), F_128(x) + F_398(x))
Eq(F_128(x), F_129(x) + F_253(x))
Eq(F_129(x), F_130(x)/F_28(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_133(x)*F_28(x))
Eq(F_133(x), F_134(x)/F_28(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_124(x) + F_136(x))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_138(x)*F_28(x))
Eq(F_138(x), F_139(x) + F_181(x))
Eq(F_139(x), F_140(x) + F_142(x))
Eq(F_140(x), F_141(x))
Eq(F_141(x), F_50(x)*F_55(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_144(x)*F_28(x))
Eq(F_144(x), F_145(x) + F_149(x))
Eq(F_145(x), F_142(x) + F_146(x))
Eq(F_146(x), F_116(x) + F_147(x))
Eq(F_147(x), F_148(x))
Eq(F_148(x), F_145(x)*F_28(x))
Eq(F_149(x), F_133(x) - F_150(x))
Eq(F_150(x), F_151(x)/F_28(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_153(x) + F_154(x))
Eq(F_153(x), F_0(x)*F_50(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), F_156(x)*F_28(x))
Eq(F_156(x), F_157(x) + F_248(x))
Eq(F_157(x), F_158(x)*F_50(x))
Eq(F_158(x), F_159(x) + F_160(x))
Eq(F_159(x), F_117(x) + F_123(x))
Eq(F_160(x), F_161(x)/F_50(x))
Eq(F_161(x), F_162(x) - F_166(x))
Eq(F_162(x), F_163(x)/F_28(x))
Eq(F_163(x), F_164(x))
Eq(F_164(x), F_131(x) - F_165(x))
Eq(F_165(x), F_4(x)*F_50(x))
Eq(F_166(x), F_167(x) + F_188(x))
Eq(F_167(x), F_168(x)*F_50(x))
Eq(F_168(x), F_159(x) + F_169(x))
Eq(F_169(x), F_170(x)/F_28(x))
Eq(F_170(x), F_171(x))
Eq(F_171(x), F_172(x)*F_28(x))
Eq(F_172(x), F_173(x) - F_179(x))
Eq(F_173(x), F_174(x)/F_28(x))
Eq(F_174(x), F_175(x))
Eq(F_175(x), F_176(x) - F_178(x))
Eq(F_176(x), F_177(x)/F_28(x))
Eq(F_177(x), F_18(x))
Eq(F_178(x), F_123(x) + F_18(x))
Eq(F_179(x), F_180(x) + F_181(x))
Eq(F_180(x), F_139(x) + F_176(x))
Eq(F_181(x), F_173(x) - F_182(x))
Eq(F_182(x), F_139(x) + F_183(x))
Eq(F_183(x), F_184(x)/F_28(x))
Eq(F_184(x), F_185(x))
Eq(F_185(x), F_186(x) - F_4(x))
Eq(F_186(x), F_117(x) + F_187(x))
Eq(F_187(x), F_107(x) + F_43(x))
Eq(F_188(x), F_189(x) - F_237(x))
Eq(F_189(x), F_190(x)/F_28(x))
Eq(F_190(x), F_191(x))
Eq(F_191(x), F_192(x))
Eq(F_192(x), F_193(x)*F_28(x))
Eq(F_193(x), F_194(x)/F_28(x))
Eq(F_194(x), F_195(x))
Eq(F_195(x), F_196(x) - F_236(x))
Eq(F_196(x), F_197(x) + F_41(x))
Eq(F_197(x), F_198(x))
Eq(F_198(x), F_199(x)*F_28(x))
Eq(F_199(x), F_200(x) + F_226(x))
Eq(F_200(x), F_201(x) + F_202(x))
Eq(F_201(x), F_4(x)*F_49(x))
Eq(F_202(x), F_203(x))
Eq(F_203(x), F_204(x)*F_28(x)*F_49(x))
Eq(F_204(x), F_200(x) + F_205(x))
Eq(F_205(x), F_206(x)/F_49(x))
Eq(F_206(x), F_193(x) - F_207(x))
Eq(F_207(x), F_208(x)/F_28(x))
Eq(F_208(x), F_209(x))
Eq(F_209(x), F_210(x) - F_225(x))
Eq(F_210(x), F_211(x) - F_212(x))
Eq(F_211(x), F_191(x) + F_201(x))
Eq(F_212(x), F_213(x) - F_223(x))
Eq(F_213(x), F_214(x) - F_217(x))
Eq(F_214(x), F_215(x)/F_28(x))
Eq(F_215(x), F_216(x))
Eq(F_216(x), F_176(x) - F_41(x))
Eq(F_217(x), F_218(x))
Eq(F_218(x), F_219(x)*F_28(x))
Eq(F_219(x), F_214(x) + F_220(x))
Eq(F_220(x), F_221(x))
Eq(F_221(x), F_159(x)*F_222(x)*F_50(x))
Eq(F_222(x), F_49(x) + F_66(x))
Eq(F_223(x), F_123(x) + F_224(x))
Eq(F_224(x), F_147(x) + F_56(x))
Eq(F_225(x), F_0(x)*F_49(x))
Eq(F_226(x), F_227(x))
Eq(F_227(x), F_228(x)*F_28(x))
Eq(F_228(x), F_229(x) + F_230(x))
Eq(F_229(x), F_200(x)*F_49(x))
Eq(F_230(x), F_231(x))
Eq(F_231(x), F_232(x)*F_49(x)*F_66(x))
Eq(F_232(x), F_233(x) + F_4(x))
Eq(F_233(x), F_234(x))
Eq(F_234(x), F_235(x)*F_28(x))
Eq(F_235(x), F_172(x) + F_232(x))
Eq(F_236(x), F_201(x))
Eq(F_237(x), F_238(x) + F_240(x))
Eq(F_238(x), F_167(x) + F_239(x))
Eq(F_239(x), F_169(x) + F_186(x))
Eq(F_240(x), F_189(x) - F_241(x))
Eq(F_241(x), F_242(x) + F_244(x))
Eq(F_242(x), F_211(x) + F_243(x))
Eq(F_243(x), F_213(x)*F_50(x))
Eq(F_244(x), F_245(x)*F_49(x))
Eq(F_245(x), F_246(x)/(F_28(x)*F_49(x)))
Eq(F_246(x), F_247(x))
Eq(F_247(x), F_205(x)*F_28(x)*F_49(x))
Eq(F_248(x), F_131(x) + F_249(x))
Eq(F_249(x), F_250(x)*F_50(x))
Eq(F_250(x), F_224(x) + F_251(x))
Eq(F_251(x), F_252(x))
Eq(F_252(x), F_149(x)*F_28(x))
Eq(F_253(x), F_254(x))
Eq(F_254(x), F_129(x)*F_255(x)*F_28(x))
Eq(F_255(x), F_121(x) + F_256(x))
Eq(F_256(x), F_257(x))
Eq(F_257(x), F_258(x)*F_28(x))
Eq(F_258(x), F_259(x)/F_28(x))
Eq(F_259(x), F_260(x))
Eq(F_260(x), F_261(x) - F_397(x))
Eq(F_261(x), F_262(x)/F_28(x))
Eq(F_262(x), F_263(x))
Eq(F_263(x), F_264(x)/(F_11(x)*F_49(x)))
Eq(F_264(x), F_265(x))
Eq(F_265(x), F_266(x) - F_346(x))
Eq(F_266(x), F_267(x) - F_339(x))
Eq(F_267(x), F_268(x)/F_28(x))
Eq(F_268(x), F_269(x))
Eq(F_269(x), F_270(x) - F_272(x))
Eq(F_270(x), F_271(x)/F_28(x))
Eq(F_271(x), F_90(x))
Eq(F_272(x), F_26(x) + F_273(x))
Eq(F_273(x), F_270(x) - F_274(x))
Eq(F_274(x), F_26(x) + F_275(x))
Eq(F_275(x), F_276(x))
Eq(F_276(x), F_277(x)*F_28(x))
Eq(F_277(x), F_278(x)/F_28(x))
Eq(F_278(x), F_279(x))
Eq(F_279(x), -F_280(x) + F_96(x))
Eq(F_280(x), F_281(x)/(F_28(x)*F_49(x)))
Eq(F_281(x), F_282(x))
Eq(F_282(x), F_283(x)/F_0(x))
Eq(F_283(x), F_284(x))
Eq(F_284(x), -F_285(x) + F_35(x))
Eq(F_285(x), F_286(x) - F_338(x))
Eq(F_286(x), -F_287(x) + F_7(x))
Eq(F_287(x), F_288(x))
Eq(F_288(x), F_0(x)*F_289(x))
Eq(F_289(x), F_290(x)/F_50(x))
Eq(F_290(x), -F_26(x) + F_291(x))
Eq(F_291(x), F_292(x) + F_295(x))
Eq(F_292(x), F_293(x) + F_48(x))
Eq(F_293(x), F_294(x))
Eq(F_294(x), F_28(x)*F_49(x)*F_5(x))
Eq(F_295(x), F_25(x) + F_296(x))
Eq(F_296(x), F_297(x) - F_319(x))
Eq(F_297(x), F_298(x))
Eq(F_298(x), F_28(x)*F_299(x))
Eq(F_299(x), F_300(x) + F_308(x))
Eq(F_300(x), -F_13(x) + F_301(x))
Eq(F_301(x), F_302(x) - F_304(x))
Eq(F_302(x), F_303(x)/F_28(x))
Eq(F_303(x), F_10(x))
Eq(F_304(x), F_305(x))
Eq(F_305(x), F_28(x)*F_306(x))
Eq(F_306(x), F_307(x)/F_28(x))
Eq(F_307(x), F_95(x))
Eq(F_308(x), F_309(x))
Eq(F_309(x), F_28(x)*F_310(x))
Eq(F_310(x), F_311(x) + F_315(x))
Eq(F_311(x), F_26(x)*F_312(x))
Eq(F_312(x), -F_13(x) + F_313(x))
Eq(F_313(x), F_314(x)/F_28(x))
Eq(F_314(x), F_15(x))
Eq(F_315(x), F_316(x))
Eq(F_316(x), F_317(x)*F_318(x)*F_49(x))
Eq(F_317(x), -F_279(x) + F_93(x))
Eq(F_318(x), -F_123(x) + F_232(x))
Eq(F_319(x), F_320(x))
Eq(F_320(x), F_28(x)*F_321(x))
Eq(F_321(x), F_322(x) + F_336(x))
Eq(F_322(x), F_26(x)*F_323(x))
Eq(F_323(x), F_324(x))
Eq(F_324(x), F_28(x)*F_325(x))
Eq(F_325(x), F_312(x) + F_326(x))
Eq(F_326(x), F_323(x) + F_327(x))
Eq(F_327(x), F_328(x))
Eq(F_328(x), F_28(x)*F_329(x)*F_49(x))
Eq(F_329(x), F_330(x) + F_4(x))
Eq(F_330(x), F_331(x) + F_332(x))
Eq(F_331(x), F_153(x))
Eq(F_332(x), F_333(x))
Eq(F_333(x), F_28(x)*F_334(x))
Eq(F_334(x), F_202(x) + F_335(x))
Eq(F_335(x), F_18(x)*F_49(x))
Eq(F_336(x), F_337(x))
Eq(F_337(x), F_113(x)*F_317(x)*F_49(x))
Eq(F_338(x), F_18(x) + F_332(x))
Eq(F_339(x), F_340(x)/F_28(x))
Eq(F_340(x), F_341(x))
Eq(F_341(x), -F_26(x) + F_342(x))
Eq(F_342(x), F_343(x) - F_345(x))
Eq(F_343(x), F_344(x)/F_28(x))
Eq(F_344(x), F_18(x))
Eq(F_345(x), F_15(x) + F_297(x))
Eq(F_346(x), F_347(x) + F_348(x))
Eq(F_347(x), F_0(x)*F_273(x))
Eq(F_348(x), F_349(x) + F_351(x))
Eq(F_349(x), F_350(x))
Eq(F_350(x), F_266(x)*F_28(x))
Eq(F_351(x), F_352(x))
Eq(F_352(x), F_28(x)*F_353(x))
Eq(F_353(x), F_354(x) + F_376(x))
Eq(F_354(x), F_273(x)*F_355(x))
Eq(F_355(x), F_356(x) + F_372(x))
Eq(F_356(x), F_357(x))
Eq(F_357(x), F_28(x)*F_358(x))
Eq(F_358(x), F_222(x) + F_359(x))
Eq(F_359(x), F_360(x) + F_74(x))
Eq(F_360(x), F_361(x))
Eq(F_361(x), F_28(x)*F_362(x)*F_49(x))
Eq(F_362(x), F_359(x) + F_363(x))
Eq(F_363(x), -F_358(x) + F_364(x))
Eq(F_364(x), F_365(x) - F_367(x))
Eq(F_365(x), F_366(x)/F_28(x))
Eq(F_366(x), F_87(x))
Eq(F_367(x), F_368(x))
Eq(F_368(x), F_28(x)*F_369(x))
Eq(F_369(x), F_365(x) + F_370(x))
Eq(F_370(x), F_371(x))
Eq(F_371(x), F_261(x)*F_50(x)*F_55(x))
Eq(F_372(x), F_373(x) + F_374(x))
Eq(F_373(x), F_327(x) + F_91(x))
Eq(F_374(x), F_22(x) - F_375(x))
Eq(F_375(x), F_19(x) + F_282(x))
Eq(F_376(x), F_377(x))
Eq(F_377(x), F_263(x)*F_378(x)*F_49(x))
Eq(F_378(x), F_379(x))
Eq(F_379(x), F_28(x)*F_380(x))
Eq(F_380(x), F_381(x)/F_28(x))
Eq(F_381(x), F_382(x))
Eq(F_382(x), F_383(x) - F_385(x))
Eq(F_383(x), F_384(x)/F_28(x))
Eq(F_384(x), F_374(x))
Eq(F_385(x), F_386(x) - F_388(x))
Eq(F_386(x), F_387(x)/F_28(x))
Eq(F_387(x), F_31(x))
Eq(F_388(x), F_389(x))
Eq(F_389(x), F_31(x) + F_390(x))
Eq(F_390(x), F_391(x) + F_392(x))
Eq(F_391(x), F_289(x)*F_49(x))
Eq(F_392(x), F_393(x))
Eq(F_393(x), F_28(x)*F_394(x)*F_49(x))
Eq(F_394(x), F_395(x)/F_28(x))
Eq(F_395(x), F_396(x))
Eq(F_396(x), F_280(x) - F_289(x))
Eq(F_397(x), F_0(x) + F_263(x))
Eq(F_398(x), F_399(x))
Eq(F_399(x), F_28(x)*F_400(x))
Eq(F_400(x), F_401(x)/(F_28(x)*F_49(x)))
Eq(F_401(x), F_402(x))
Eq(F_402(x), F_125(x) + F_403(x))
Eq(F_403(x), F_404(x))
Eq(F_404(x), F_160(x)*F_28(x)*F_405(x))
Eq(F_405(x), F_406(x) + F_409(x))
Eq(F_406(x), F_358(x) + F_407(x))
Eq(F_407(x), F_408(x))
Eq(F_408(x), F_28(x)*F_405(x))
Eq(F_409(x), F_410(x) - F_418(x))
Eq(F_410(x), F_411(x)/F_28(x))
Eq(F_411(x), F_412(x))
Eq(F_412(x), F_413(x) - F_417(x))
Eq(F_413(x), F_414(x)/F_28(x))
Eq(F_414(x), F_415(x))
Eq(F_415(x), F_416(x) + F_81(x))
Eq(F_416(x), F_44(x))
Eq(F_417(x), F_121(x) + F_260(x))
Eq(F_418(x), F_419(x)/F_28(x))
Eq(F_419(x), F_420(x))
Eq(F_420(x), -F_121(x) + F_421(x))
Eq(F_421(x), -F_363(x) + F_422(x))
Eq(F_422(x), F_417(x) + F_423(x))
Eq(F_423(x), F_424(x))
Eq(F_424(x), F_28(x)*F_410(x))
Eq(F_425(x), F_426(x))
Eq(F_426(x), F_28(x)*F_427(x))
Eq(F_427(x), F_112(x) + F_428(x))
Eq(F_428(x), F_142(x) + F_429(x))
Eq(F_429(x), F_113(x)*F_66(x))
Eq(F_430(x), F_431(x))
Eq(F_431(x), F_28(x)*F_432(x))
Eq(F_432(x), F_433(x) + F_440(x))
Eq(F_433(x), F_434(x))
Eq(F_434(x), F_28(x)*F_364(x)*F_435(x))
Eq(F_435(x), F_187(x) + F_436(x))
Eq(F_436(x), F_437(x))
Eq(F_437(x), F_28(x)*F_438(x))
Eq(F_438(x), F_439(x)/F_28(x))
Eq(F_439(x), F_117(x))
Eq(F_440(x), F_441(x))
Eq(F_441(x), F_28(x)*F_442(x))
Eq(F_442(x), F_432(x) + F_443(x))
Eq(F_443(x), F_444(x))
Eq(F_444(x), F_142(x)*F_261(x))
Eq(F_445(x), F_46(x))
Eq(F_446(x), F_2(x)*F_50(x)*F_55(x))
Eq(F_447(x), F_448(x) + F_86(x))
Eq(F_448(x), F_360(x)*F_50(x))
Eq(F_449(x), F_450(x) + F_451(x))
Eq(F_450(x), F_122(x)*F_2(x))
Eq(F_451(x), F_452(x))
Eq(F_452(x), F_28(x)*F_453(x))
Eq(F_453(x), F_454(x) + F_466(x))
Eq(F_454(x), F_455(x) + F_456(x))
Eq(F_455(x), F_2(x)*F_359(x))
Eq(F_456(x), F_457(x))
Eq(F_457(x), F_28(x)*F_458(x))
Eq(F_458(x), F_453(x) + F_459(x))
Eq(F_459(x), F_460(x))
Eq(F_460(x), F_461(x)*F_49(x)*F_50(x))
Eq(F_461(x), F_462(x) + F_464(x))
Eq(F_462(x), F_463(x))
Eq(F_463(x), F_146(x)*F_255(x)*F_28(x))
Eq(F_464(x), F_465(x))
Eq(F_465(x), F_212(x)*F_255(x)*F_28(x))
Eq(F_466(x), F_467(x) + F_468(x))
Eq(F_467(x), F_18(x)*F_359(x))
Eq(F_468(x), F_469(x))
Eq(F_469(x), F_28(x)*F_470(x))
Eq(F_470(x), F_471(x) + F_472(x))
Eq(F_471(x), F_172(x)*F_359(x))
Eq(F_472(x), F_473(x))
Eq(F_473(x), F_474(x)*F_476(x)*F_49(x))
Eq(F_474(x), F_475(x))
Eq(F_475(x), F_255(x)*F_28(x)*F_49(x))
Eq(F_476(x), -F_172(x) + F_205(x))
Eq(F_477(x), F_478(x))
Eq(F_478(x), F_228(x)*F_28(x))
Eq(F_479(x), F_480(x))
Eq(F_480(x), F_28(x)*F_481(x))
Eq(F_481(x), F_482(x) + F_95(x))
Eq(F_482(x), F_483(x) + F_488(x))
Eq(F_483(x), F_484(x))
Eq(F_484(x), F_0(x)*F_485(x))
Eq(F_485(x), F_11(x) + F_486(x))
Eq(F_486(x), F_487(x))
Eq(F_487(x), F_123(x)*F_28(x)*F_49(x)*F_50(x))
Eq(F_488(x), F_489(x))
Eq(F_489(x), F_28(x)*F_490(x))
Eq(F_490(x), F_491(x) + F_508(x))
Eq(F_491(x), F_492(x) - F_498(x))
Eq(F_492(x), F_493(x)/F_28(x))
Eq(F_493(x), F_494(x))
Eq(F_494(x), -F_495(x) + F_93(x))
Eq(F_495(x), F_496(x))
Eq(F_496(x), F_0(x)*F_497(x))
Eq(F_497(x), F_11(x) + F_2(x))
Eq(F_498(x), F_499(x) + F_507(x))
Eq(F_499(x), F_500(x) + F_93(x))
Eq(F_500(x), F_501(x))
Eq(F_501(x), F_28(x)*F_502(x))
Eq(F_502(x), F_503(x)/F_28(x))
Eq(F_503(x), F_504(x))
Eq(F_504(x), F_351(x) + F_505(x))
Eq(F_505(x), -F_341(x) + F_506(x))
Eq(F_506(x), F_339(x) - F_96(x))
Eq(F_507(x), F_2(x)*F_273(x))
Eq(F_508(x), F_509(x))
Eq(F_509(x), F_123(x)*F_28(x)*F_49(x)*F_50(x)*F_510(x))
Eq(F_510(x), F_511(x)/(F_28(x)*F_49(x)))
Eq(F_511(x), F_512(x))
Eq(F_512(x), F_280(x) - F_513(x))
Eq(F_513(x), F_514(x))
Eq(F_514(x), F_0(x)*F_49(x))
Eq(F_515(x), F_516(x) + F_518(x))
Eq(F_516(x), F_517(x))
Eq(F_517(x), F_2(x)*F_289(x))
Eq(F_518(x), F_519(x))
Eq(F_519(x), F_28(x)*F_520(x))
Eq(F_520(x), F_521(x) + F_522(x))
Eq(F_521(x), F_289(x)*F_49(x)*F_50(x))
Eq(F_522(x), F_523(x) + F_530(x))
Eq(F_523(x), F_524(x) + F_529(x))
Eq(F_524(x), F_515(x) + F_525(x))
Eq(F_525(x), F_526(x) + F_527(x))
Eq(F_526(x), F_356(x)*F_5(x))
Eq(F_527(x), F_528(x))
Eq(F_528(x), F_28(x)*F_312(x)*F_397(x)*F_50(x))
Eq(F_529(x), F_289(x)*F_323(x))
Eq(F_530(x), -F_524(x) + F_531(x))
Eq(F_531(x), F_532(x) + F_541(x))
Eq(F_532(x), F_533(x) - F_536(x))
Eq(F_533(x), F_534(x)/F_28(x))
Eq(F_534(x), F_535(x))
Eq(F_535(x), F_30(x) - F_4(x))
Eq(F_536(x), F_537(x) + F_7(x))
Eq(F_537(x), F_538(x) + F_539(x))
Eq(F_538(x), F_0(x)*F_15(x))
Eq(F_539(x), F_540(x))
Eq(F_540(x), F_124(x)*F_356(x)*F_49(x))
Eq(F_541(x), F_542(x) + F_543(x))
Eq(F_542(x), F_356(x)*F_535(x))
Eq(F_543(x), F_544(x))
Eq(F_544(x), F_28(x)*F_397(x)*F_49(x)*F_545(x))
Eq(F_545(x), -F_535(x) + F_546(x))
Eq(F_546(x), F_547(x) - F_549(x))
Eq(F_547(x), F_548(x)/(F_28(x)*F_49(x)))
Eq(F_548(x), F_338(x))
Eq(F_549(x), F_330(x) + F_550(x))
Eq(F_550(x), F_15(x) + F_4(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 2], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 0, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "ignore_parent": false, "include_empty": false, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 2], [2, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[2, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 2
Strategy pack name: insertion_point_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/194/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[29,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[6,x]+F[9,x]
F[9,x] = F[10,x]*F[4,x]
F[10,x] = F[11,x]+F[14,x]+F[9,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[4,x]
F[14,x] = F[15,x]
F[15,x] = F[11,x]*F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[24,x]
F[17,x] = F[11,x]+F[18,x]
F[18,x] = F[12,x]+F[19,x]
F[19,x] = F[20,x]+F[21,x]+F[23,x]
F[20,x] = 0
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[12,x]+F[19,x]
F[23,x] = F[18,x]*F[4,x]
F[24,x] = F[12,x]+F[25,x]
F[25,x] = F[20,x]+F[26,x]+F[27,x]
F[26,x] = F[24,x]*F[4,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[12,x]+F[25,x]
F[29,x] = F[2,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[264,x]+F[33,x]
F[33,x] = F[29,x]+F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[11,x]*F[2,x]
F[36,x] = F[37,x]+F[41,x]
F[37,x] = -F[2,x]+F[38,x]
F[38,x] = -F[0,x]+F[39,x]
F[39,x] = 1/F[4,x]*F[40,x]
F[40,x] = F[2,x]
F[41,x] = F[42,x,1]
F[43,x,k[0]] = F[37,x]+F[42,x,k[0]]
F[44,x,k[0]] = F[263,x,k[0]]+F[43,x,k[0]]
F[45,x,k[0]] = F[118,x,k[0]]+F[44,x,k[0]]
F[46,x,k[0]] = F[45,x,k[0]]*F[54,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[4,x]*F[49,x,k[0]]
F[49,x,k[0]] = F[257,x,k[0]]+F[50,x,k[0]]
F[50,x,k[0]] = F[106,x,k[0]]+F[51,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]+F[56,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]*F[55,x,k[0]]
F[54,x,k[0]] = k[0]*x
F[55,x,k[0]] = F[1,x]+F[52,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[4,x]*F[58,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]+F[63,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]
F[60,x,k[0]] = F[11,x]*F[61,x,k[0]]
F[61,x,k[0]] = F[52,x,k[0]]+F[62,x,k[0]]
F[62,x,k[0]] = F[52,x,k[0]]*F[55,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]+F[94,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]+F[67,x,k[0]]
F[65,x,k[0]] = F[52,x,k[0]]*F[66,x]
F[66,x] = F[7,x]
F[67,x,k[0]] = F[55,x,k[0]]*F[68,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]
F[69,x,k[0]] = F[54,x,k[0]]*F[70,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]+F[72,x,k[0]]
F[71,x,k[0]] = F[12,x]*F[55,x,k[0]]
F[72,x,k[0]] = F[18,x]+F[73,x,k[0]]
F[74,x,k[0]] = F[73,x,k[0]]+F[93,x,k[0]]
F[75,x,k[0]] = F[54,x,k[0]]*F[74,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]
F[77,x,k[0]] = F[4,x]*F[78,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]+F[92,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]+F[83,x,k[0]]
F[80,x,k[0]] = F[76,x,k[0]]+F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]
F[82,x,k[0]] = F[52,x,k[0]]*F[54,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]+F[90,x,k[0]]
F[84,x,k[0]] = F[54,x,k[0]]*F[85,x,k[0]]
F[85,x,k[0]] = F[52,x,k[0]]+F[86,x,k[0]]
F[86,x,k[0]] = F[20,x]+F[87,x,k[0]]+F[88,x,k[0]]
F[87,x,k[0]] = F[4,x]*F[85,x,k[0]]
F[88,x,k[0]] = F[54,x,k[0]]*F[89,x,k[0]]
F[89,x,k[0]] = F[12,x]+F[86,x,k[0]]
F[90,x,k[0]] = F[81,x,k[0]]*F[91,x,k[0]]
F[91,x,k[0]] = F[55,x,k[0]]+F[89,x,k[0]]
F[92,x,k[0]] = F[18,x]*F[81,x,k[0]]
F[93,x,k[0]] = F[12,x]*F[52,x,k[0]]
F[94,x,k[0]] = F[104,x,k[0]]+F[95,x,k[0]]
F[95,x,k[0]] = F[52,x,k[0]]*F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[4,x]*F[98,x]
F[98,x] = F[103,x]+F[99,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[12,x]+F[96,x]
F[101,x] = F[102,x]*F[12,x]
F[102,x] = F[11,x]+F[28,x]
F[103,x] = F[12,x]*F[18,x]
F[104,x,k[0]] = F[105,x,k[0]]*F[55,x,k[0]]
F[105,x,k[0]] = (-F[76,x,1]*k[0]+F[76,x,k[0]])/(-1+k[0])
F[106,x,k[0]] = F[107,x,k[0]]+F[47,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]
F[108,x,k[0]] = F[109,x,k[0]]*F[4,x]
F[109,x,k[0]] = F[110,x,k[0]]+F[130,x,k[0]]
F[110,x,k[0]] = F[111,x,k[0]]+F[115,x,k[0]]
F[111,x,k[0]] = F[106,x,k[0]]+F[112,x,k[0]]
F[112,x,k[0]] = -k[0]*(F[113,x,1]-F[113,x,k[0]])/(-1+k[0])
F[113,x,k[0]] = F[114,x,k[0]]+F[42,x,k[0]]
F[114,x,k[0]] = F[2,x]*F[52,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]*F[52,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]+F[129,x,k[0]]
F[117,x,k[0]] = F[118,x,k[0]]+F[119,x,k[0]]
F[118,x,k[0]] = F[2,x]+F[47,x,k[0]]
F[119,x,k[0]] = F[120,x]+F[124,x,k[0]]
F[120,x] = F[121,x]
F[121,x] = F[122,x]*F[4,x]
F[122,x] = F[123,x]+F[34,x]
F[123,x] = F[120,x]+F[2,x]
F[124,x,k[0]] = F[125,x,k[0]]
F[125,x,k[0]] = F[126,x,k[0]]*F[4,x]
F[126,x,k[0]] = F[115,x,k[0]]+F[127,x,k[0]]
F[127,x,k[0]] = F[112,x,k[0]]+F[128,x,k[0]]
F[128,x,k[0]] = F[124,x,k[0]]+F[47,x,k[0]]
F[129,x,k[0]] = 1/(-1+k[0])*(F[44,x,k[0]]*k[0]-F[44,x,1])
F[130,x,k[0]] = F[131,x,k[0]]+F[225,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]+F[153,x,k[0]]
F[132,x,k[0]] = F[133,x,k[0]]+F[134,x,k[0]]
F[133,x,k[0]] = F[12,x]*F[47,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]
F[135,x,k[0]] = F[136,x,k[0]]*F[4,x]
F[136,x,k[0]] = F[137,x,k[0]]+F[143,x,k[0]]
F[137,x,k[0]] = F[138,x,k[0]]+F[142,x,k[0]]
F[138,x,k[0]] = (-F[139,x,1]*k[0]+F[139,x,k[0]])/(-1+k[0])
F[139,x,k[0]] = F[140,x,k[0]]
F[140,x,k[0]] = F[141,x,k[0]]*F[54,x,k[0]]
F[141,x,k[0]] = F[113,x,k[0]]+F[47,x,k[0]]
F[142,x,k[0]] = -k[0]*(F[124,x,1]-F[124,x,k[0]])/(-1+k[0])
F[143,x,k[0]] = F[144,x,k[0]]+F[146,x,k[0]]
F[144,x,k[0]] = (-F[145,x,1]*k[0]+F[145,x,k[0]])/(-1+k[0])
F[145,x,k[0]] = F[12,x]*F[139,x,k[0]]
F[146,x,k[0]] = -k[0]*(F[147,x,1]-F[147,x,k[0]])/(-1+k[0])
F[147,x,k[0]] = F[148,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]*F[4,x]
F[149,x,k[0]] = F[150,x,k[0]]+F[215,x,k[0]]
F[150,x,k[0]] = F[151,x,k[0]]+F[213,x,k[0]]
F[151,x,k[0]] = F[152,x,k[0]]+F[153,x,k[0]]
F[152,x,k[0]] = F[133,x,k[0]]+F[147,x,k[0]]
F[153,x,k[0]] = F[154,x,k[0]]+F[156,x,k[0]]
F[154,x,k[0]] = F[155,x,k[0]]
F[155,x,k[0]] = F[18,x]*F[2,x]*F[52,x,k[0]]
F[156,x,k[0]] = F[157,x,k[0]]+F[158,x,k[0]]
F[157,x,k[0]] = F[12,x]*F[42,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]
F[159,x,k[0]] = F[160,x,k[0]]*F[4,x]
F[160,x,k[0]] = F[161,x,k[0]]+F[209,x,k[0]]
F[161,x,k[0]] = F[162,x,k[0]]+F[208,x,k[0]]
F[162,x,k[0]] = (-F[163,x,1]*k[0]+F[163,x,k[0]])/(-1+k[0])
F[163,x,k[0]] = F[164,x,k[0]]
F[164,x,k[0]] = F[165,x,k[0]]*F[54,x,k[0]]
F[165,x,k[0]] = F[166,x,k[0]]+F[167,x,k[0]]
F[166,x,k[0]] = F[37,x]*F[52,x,k[0]]
F[168,x,k[0]] = F[167,x,k[0]]+F[172,x]
F[169,x,k[0]] = F[168,x,k[0]]+F[171,x,k[0]]
F[170,x,k[0]] = F[169,x,k[0]]*F[54,x,k[0]]
F[170,x,k[0]] = F[42,x,k[0]]
F[171,x,k[0]] = F[37,x]*F[55,x,k[0]]
F[172,x] = F[173,x]+F[37,x]
F[173,x] = -F[179,x]+F[174,x]
F[174,x] = -F[177,x]+F[175,x]
F[175,x] = 1/F[4,x]*F[176,x]
F[176,x] = F[37,x]
F[177,x] = F[178,x]+F[37,x]
F[178,x] = F[12,x]+F[123,x]
F[179,x] = F[180,x]+F[181,x]
F[180,x] = F[12,x]^2
F[181,x] = F[182,x]+F[37,x]
F[182,x] = F[183,x]
F[183,x] = F[184,x]*F[4,x]
F[184,x] = F[185,x]+F[191,x]
F[185,x] = F[186,x]+F[189,x]
F[186,x] = F[187,x]
F[187,x] = F[188,x]*F[4,x]
F[188,x] = F[12,x]+F[186,x]
F[189,x] = F[190,x,1]
F[190,x,k[0]] = (F[47,x,k[0]]-F[47,x,1])/(-1+k[0])
F[191,x] = F[192,x]+F[194,x]
F[192,x] = F[193,x]
F[193,x] = F[12,x]^3
F[194,x] = F[195,x,1]
F[195,x,k[0]] = (F[196,x,k[0]]-F[196,x,1])/(-1+k[0])
F[196,x,k[0]] = F[197,x,k[0]]
F[197,x,k[0]] = F[198,x,k[0]]*F[4,x]
F[198,x,k[0]] = F[199,x,k[0]]+F[204,x,k[0]]
F[199,x,k[0]] = F[200,x,k[0]]+F[203,x,k[0]]
F[200,x,k[0]] = F[201,x,k[0]]
F[201,x,k[0]] = F[202,x,k[0]]*F[4,x]
F[202,x,k[0]] = F[200,x,k[0]]+F[52,x,k[0]]
F[203,x,k[0]] = -k[0]*(F[47,x,1]-F[47,x,k[0]])/(-1+k[0])
F[204,x,k[0]] = F[205,x,k[0]]+F[207,x,k[0]]
F[205,x,k[0]] = F[206,x,k[0]]
F[206,x,k[0]] = F[12,x]^2*F[52,x,k[0]]
F[207,x,k[0]] = -k[0]*(F[196,x,1]-F[196,x,k[0]])/(-1+k[0])
F[208,x,k[0]] = -k[0]*(F[162,x,1]-F[162,x,k[0]])/(-1+k[0])
F[209,x,k[0]] = F[210,x,k[0]]+F[212,x,k[0]]
F[210,x,k[0]] = (-F[211,x,1]*k[0]+F[211,x,k[0]])/(-1+k[0])
F[211,x,k[0]] = F[12,x]*F[163,x,k[0]]
F[212,x,k[0]] = -k[0]*(F[158,x,1]-F[158,x,k[0]])/(-1+k[0])
F[213,x,k[0]] = F[214,x,k[0]]
F[214,x,k[0]] = F[116,x,k[0]]*F[12,x]*F[52,x,k[0]]
F[215,x,k[0]] = F[12,x]*F[216,x,k[0]]
F[216,x,k[0]] = F[217,x,k[0]]+F[218,x,k[0]]
F[217,x,k[0]] = -k[0]*(F[141,x,1]-F[141,x,k[0]])/(-1+k[0])
F[218,x,k[0]] = F[153,x,k[0]]+F[219,x,k[0]]
F[220,x,k[0]] = F[219,x,k[0]]+F[223,x,k[0]]
F[221,x,k[0]] = F[199,x,k[0]]+F[220,x,k[0]]
F[222,x,k[0]] = F[221,x,k[0]]*F[4,x]
F[222,x,k[0]] = F[196,x,k[0]]
F[223,x,k[0]] = F[224,x,k[0]]
F[224,x,k[0]] = F[19,x]*F[52,x,k[0]]
F[225,x,k[0]] = F[226,x,k[0]]*F[52,x,k[0]]
F[226,x,k[0]] = F[227,x,k[0]]+F[251,x,k[0]]
F[227,x,k[0]] = F[228,x,k[0]]+F[229,x,k[0]]
F[228,x,k[0]] = F[118,x,k[0]]*F[12,x]
F[229,x,k[0]] = F[147,x,k[0]]+F[230,x]
F[230,x] = F[231,x]
F[231,x] = F[232,x]*F[4,x]
F[232,x] = F[233,x]+F[249,x]
F[233,x] = F[234,x]+F[236,x]
F[234,x] = F[230,x]+F[235,x]
F[235,x] = F[12,x]*F[2,x]
F[236,x] = F[237,x]+F[238,x]
F[237,x] = F[18,x]*F[2,x]
F[238,x] = F[239,x]+F[240,x]
F[239,x] = F[12,x]*F[37,x]
F[240,x] = F[241,x]
F[241,x] = F[242,x]*F[4,x]
F[242,x] = F[243,x]+F[245,x]
F[243,x] = F[244,x,1]
F[244,x,k[0]] = (F[42,x,k[0]]*k[0]-F[42,x,1])/(-1+k[0])
F[245,x] = F[246,x]+F[247,x]
F[246,x] = F[12,x]*F[41,x]
F[247,x] = F[240,x]+F[248,x]
F[248,x] = F[158,x,1]
F[249,x] = F[12,x]*F[250,x]
F[250,x] = F[122,x]+F[233,x]
F[251,x,k[0]] = F[252,x,k[0]]+F[254,x,k[0]]
F[252,x,k[0]] = F[253,x,k[0]]
F[253,x,k[0]] = F[18,x]*F[2,x]*F[55,x,k[0]]
F[254,x,k[0]] = F[255,x,k[0]]+F[256,x,k[0]]
F[255,x,k[0]] = F[12,x]*F[43,x,k[0]]
F[256,x,k[0]] = F[158,x,k[0]]+F[240,x]
F[257,x,k[0]] = F[258,x,k[0]]*F[52,x,k[0]]
F[258,x,k[0]] = F[259,x,k[0]]+F[261,x,k[0]]
F[259,x,k[0]] = F[260,x,k[0]]+F[55,x,k[0]]
F[260,x,k[0]] = F[56,x,k[0]]+F[66,x]
F[261,x,k[0]] = F[118,x,k[0]]+F[262,x,k[0]]
F[262,x,k[0]] = F[107,x,k[0]]+F[30,x]
F[263,x,k[0]] = F[2,x]*F[55,x,k[0]]
F[264,x] = F[236,x]+F[265,x]
F[265,x] = F[235,x]+F[266,x]
F[266,x] = F[267,x]
F[267,x] = F[268,x]*F[4,x]
F[268,x] = F[264,x]+F[269,x]
F[269,x] = F[12,x]*F[270,x]
F[270,x] = F[233,x]+F[271,x]
F[271,x] = F[272,x]+F[34,x]
F[272,x] = F[123,x]+F[273,x]
F[273,x] = F[120,x]+F[274,x]
F[274,x] = F[124,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{29}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{6}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)+F_{9}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{24}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right)+F_{19}\! \left(x \right)
F_{23}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{20}\! \left(x \right)+F_{26}\! \left(x \right)+F_{27}\! \left(x \right)
F_{26}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right)+F_{25}\! \left(x \right)
F_{29}\! \left(x \right) = F_{2}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{264}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{29}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{41}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = \frac{F_{40}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{40}\! \left(x \right) = F_{2}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x , 1\right)
F_{43}\! \left(x , y\right) = F_{37}\! \left(x \right)+F_{42}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{263}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{45}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{257}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{55}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = y x
F_{55}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{52}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{55}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{7}\! \left(x \right)
F_{67}\! \left(x , y\right) = F_{55}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{18}\! \left(x \right)+F_{73}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{73}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{74}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{20}\! \left(x \right)+F_{87}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{12}\! \left(x \right)+F_{86}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{81}\! \left(x , y\right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{81}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{103}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{12}\! \left(x \right)+F_{96}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{12}\! \left(x \right)
F_{102}\! \left(x \right) = F_{11}\! \left(x \right)+F_{28}\! \left(x \right)
F_{103}\! \left(x \right) = F_{12}\! \left(x \right) F_{18}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right) F_{55}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = -\frac{F_{76}\! \left(x , 1\right) y -F_{76}\! \left(x , y\right)}{-1+y}
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{130}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{115}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{112}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = -\frac{y \left(F_{113}\! \left(x , 1\right)-F_{113}\! \left(x , y\right)\right)}{-1+y}
F_{113}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{129}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{119}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{47}\! \left(x , y\right)
F_{119}\! \left(x , y\right) = F_{120}\! \left(x \right)+F_{124}\! \left(x , y\right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{4}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{34}\! \left(x \right)
F_{123}\! \left(x \right) = F_{120}\! \left(x \right)+F_{2}\! \left(x \right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = F_{126}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{126}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{127}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{128}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{129}\! \left(x , y\right) = -\frac{-y F_{44}\! \left(x , y\right)+F_{44}\! \left(x , 1\right)}{-1+y}
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)+F_{225}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right)+F_{153}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{134}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{47}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{143}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right)+F_{142}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = -\frac{F_{139}\! \left(x , 1\right) y -F_{139}\! \left(x , y\right)}{-1+y}
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{141}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = -\frac{y \left(F_{124}\! \left(x , 1\right)-F_{124}\! \left(x , y\right)\right)}{-1+y}
F_{143}\! \left(x , y\right) = F_{144}\! \left(x , y\right)+F_{146}\! \left(x , y\right)
F_{144}\! \left(x , y\right) = -\frac{F_{145}\! \left(x , 1\right) y -F_{145}\! \left(x , y\right)}{-1+y}
F_{145}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{139}\! \left(x , y\right)
F_{146}\! \left(x , y\right) = -\frac{y \left(F_{147}\! \left(x , 1\right)-F_{147}\! \left(x , y\right)\right)}{-1+y}
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{215}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right)+F_{213}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{152}\! \left(x , y\right)+F_{153}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{133}\! \left(x , y\right)+F_{147}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right)+F_{156}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{155}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{2}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{157}\! \left(x , y\right)+F_{158}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{42}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right)
F_{159}\! \left(x , y\right) = F_{160}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{209}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = F_{162}\! \left(x , y\right)+F_{208}\! \left(x , y\right)
F_{162}\! \left(x , y\right) = -\frac{F_{163}\! \left(x , 1\right) y -F_{163}\! \left(x , y\right)}{-1+y}
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{167}\! \left(x , y\right)
F_{166}\! \left(x , y\right) = F_{37}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{168}\! \left(x , y\right) = F_{167}\! \left(x , y\right)+F_{172}\! \left(x \right)
F_{169}\! \left(x , y\right) = F_{168}\! \left(x , y\right)+F_{171}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{169}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{171}\! \left(x , y\right) = F_{37}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)+F_{37}\! \left(x \right)
F_{173}\! \left(x \right) = -F_{179}\! \left(x \right)+F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = -F_{177}\! \left(x \right)+F_{175}\! \left(x \right)
F_{175}\! \left(x \right) = \frac{F_{176}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{176}\! \left(x \right) = F_{37}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)+F_{37}\! \left(x \right)
F_{178}\! \left(x \right) = F_{12}\! \left(x \right)+F_{123}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)+F_{181}\! \left(x \right)
F_{180}\! \left(x \right) = F_{12} \left(x \right)^{2}
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)+F_{37}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right) F_{4}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{191}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)+F_{189}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right) F_{4}\! \left(x \right)
F_{188}\! \left(x \right) = F_{12}\! \left(x \right)+F_{186}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x , 1\right)
F_{190}\! \left(x , y\right) = -\frac{F_{47}\! \left(x , 1\right)-F_{47}\! \left(x , y\right)}{-1+y}
F_{191}\! \left(x \right) = F_{192}\! \left(x \right)+F_{194}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)
F_{193}\! \left(x \right) = F_{12} \left(x \right)^{3}
F_{194}\! \left(x \right) = F_{195}\! \left(x , 1\right)
F_{195}\! \left(x , y\right) = -\frac{F_{196}\! \left(x , 1\right)-F_{196}\! \left(x , y\right)}{-1+y}
F_{196}\! \left(x , y\right) = F_{197}\! \left(x , y\right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{198}\! \left(x , y\right) = F_{199}\! \left(x , y\right)+F_{204}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{200}\! \left(x , y\right)+F_{203}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{201}\! \left(x , y\right)
F_{201}\! \left(x , y\right) = F_{202}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{202}\! \left(x , y\right) = F_{200}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{203}\! \left(x , y\right) = -\frac{y \left(F_{47}\! \left(x , 1\right)-F_{47}\! \left(x , y\right)\right)}{-1+y}
F_{204}\! \left(x , y\right) = F_{205}\! \left(x , y\right)+F_{207}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{206}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = F_{12} \left(x \right)^{2} F_{52}\! \left(x , y\right)
F_{207}\! \left(x , y\right) = -\frac{y \left(F_{196}\! \left(x , 1\right)-F_{196}\! \left(x , y\right)\right)}{-1+y}
F_{208}\! \left(x , y\right) = -\frac{y \left(F_{162}\! \left(x , 1\right)-F_{162}\! \left(x , y\right)\right)}{-1+y}
F_{209}\! \left(x , y\right) = F_{210}\! \left(x , y\right)+F_{212}\! \left(x , y\right)
F_{210}\! \left(x , y\right) = -\frac{F_{211}\! \left(x , 1\right) y -F_{211}\! \left(x , y\right)}{-1+y}
F_{211}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{163}\! \left(x , y\right)
F_{212}\! \left(x , y\right) = -\frac{y \left(F_{158}\! \left(x , 1\right)-F_{158}\! \left(x , y\right)\right)}{-1+y}
F_{213}\! \left(x , y\right) = F_{214}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{12}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{216}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = F_{217}\! \left(x , y\right)+F_{218}\! \left(x , y\right)
F_{217}\! \left(x , y\right) = -\frac{y \left(F_{141}\! \left(x , 1\right)-F_{141}\! \left(x , y\right)\right)}{-1+y}
F_{218}\! \left(x , y\right) = F_{153}\! \left(x , y\right)+F_{219}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{219}\! \left(x , y\right)+F_{223}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = F_{199}\! \left(x , y\right)+F_{220}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = F_{221}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{222}\! \left(x , y\right) = F_{196}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{224}\! \left(x , y\right)
F_{224}\! \left(x , y\right) = F_{19}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{226}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = F_{227}\! \left(x , y\right)+F_{251}\! \left(x , y\right)
F_{227}\! \left(x , y\right) = F_{228}\! \left(x , y\right)+F_{229}\! \left(x , y\right)
F_{228}\! \left(x , y\right) = F_{118}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{229}\! \left(x , y\right) = F_{147}\! \left(x , y\right)+F_{230}\! \left(x \right)
F_{230}\! \left(x \right) = F_{231}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right) F_{4}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right)+F_{249}\! \left(x \right)
F_{233}\! \left(x \right) = F_{234}\! \left(x \right)+F_{236}\! \left(x \right)
F_{234}\! \left(x \right) = F_{230}\! \left(x \right)+F_{235}\! \left(x \right)
F_{235}\! \left(x \right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right)
F_{236}\! \left(x \right) = F_{237}\! \left(x \right)+F_{238}\! \left(x \right)
F_{237}\! \left(x \right) = F_{18}\! \left(x \right) F_{2}\! \left(x \right)
F_{238}\! \left(x \right) = F_{239}\! \left(x \right)+F_{240}\! \left(x \right)
F_{239}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{240}\! \left(x \right) = F_{241}\! \left(x \right)
F_{241}\! \left(x \right) = F_{242}\! \left(x \right) F_{4}\! \left(x \right)
F_{242}\! \left(x \right) = F_{243}\! \left(x \right)+F_{245}\! \left(x \right)
F_{243}\! \left(x \right) = F_{244}\! \left(x , 1\right)
F_{244}\! \left(x , y\right) = -\frac{-y F_{42}\! \left(x , y\right)+F_{42}\! \left(x , 1\right)}{-1+y}
F_{245}\! \left(x \right) = F_{246}\! \left(x \right)+F_{247}\! \left(x \right)
F_{246}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{247}\! \left(x \right) = F_{240}\! \left(x \right)+F_{248}\! \left(x \right)
F_{248}\! \left(x \right) = F_{158}\! \left(x , 1\right)
F_{249}\! \left(x \right) = F_{12}\! \left(x \right) F_{250}\! \left(x \right)
F_{250}\! \left(x \right) = F_{122}\! \left(x \right)+F_{233}\! \left(x \right)
F_{251}\! \left(x , y\right) = F_{252}\! \left(x , y\right)+F_{254}\! \left(x , y\right)
F_{252}\! \left(x , y\right) = F_{253}\! \left(x , y\right)
F_{253}\! \left(x , y\right) = F_{18}\! \left(x \right) F_{2}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{254}\! \left(x , y\right) = F_{255}\! \left(x , y\right)+F_{256}\! \left(x , y\right)
F_{255}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{43}\! \left(x , y\right)
F_{256}\! \left(x , y\right) = F_{158}\! \left(x , y\right)+F_{240}\! \left(x \right)
F_{257}\! \left(x , y\right) = F_{258}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{258}\! \left(x , y\right) = F_{259}\! \left(x , y\right)+F_{261}\! \left(x , y\right)
F_{259}\! \left(x , y\right) = F_{260}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{260}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{66}\! \left(x \right)
F_{261}\! \left(x , y\right) = F_{118}\! \left(x , y\right)+F_{262}\! \left(x , y\right)
F_{262}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{263}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{264}\! \left(x \right) = F_{236}\! \left(x \right)+F_{265}\! \left(x \right)
F_{265}\! \left(x \right) = F_{235}\! \left(x \right)+F_{266}\! \left(x \right)
F_{266}\! \left(x \right) = F_{267}\! \left(x \right)
F_{267}\! \left(x \right) = F_{268}\! \left(x \right) F_{4}\! \left(x \right)
F_{268}\! \left(x \right) = F_{264}\! \left(x \right)+F_{269}\! \left(x \right)
F_{269}\! \left(x \right) = F_{12}\! \left(x \right) F_{270}\! \left(x \right)
F_{270}\! \left(x \right) = F_{233}\! \left(x \right)+F_{271}\! \left(x \right)
F_{271}\! \left(x \right) = F_{272}\! \left(x \right)+F_{34}\! \left(x \right)
F_{272}\! \left(x \right) = F_{123}\! \left(x \right)+F_{273}\! \left(x \right)
F_{273}\! \left(x \right) = F_{120}\! \left(x \right)+F_{274}\! \left(x \right)
F_{274}\! \left(x \right) = F_{124}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_29(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_6(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_4(x))
Eq(F_10(x), F_11(x) + F_14(x) + F_9(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_4(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_11(x)*F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_24(x))
Eq(F_17(x), F_11(x) + F_18(x))
Eq(F_18(x), F_12(x) + F_19(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_23(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_12(x) + F_19(x))
Eq(F_23(x), F_18(x)*F_4(x))
Eq(F_24(x), F_12(x) + F_25(x))
Eq(F_25(x), F_20(x) + F_26(x) + F_27(x))
Eq(F_26(x), F_24(x)*F_4(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_12(x) + F_25(x))
Eq(F_29(x), F_2(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_264(x) + F_33(x))
Eq(F_33(x), F_29(x) + F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_11(x)*F_2(x))
Eq(F_36(x), F_37(x) + F_41(x))
Eq(F_37(x), -F_2(x) + F_38(x))
Eq(F_38(x), -F_0(x) + F_39(x))
Eq(F_39(x), F_40(x)/F_4(x))
Eq(F_40(x), F_2(x))
Eq(F_41(x), F_42(x, 1))
Eq(F_43(x, k_0), F_37(x) + F_42(x, k_0))
Eq(F_44(x, k_0), F_263(x, k_0) + F_43(x, k_0))
Eq(F_45(x, k_0), F_118(x, k_0) + F_44(x, k_0))
Eq(F_46(x, k_0), F_45(x, k_0)*F_54(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_4(x)*F_49(x, k_0))
Eq(F_49(x, k_0), F_257(x, k_0) + F_50(x, k_0))
Eq(F_50(x, k_0), F_106(x, k_0) + F_51(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0) + F_56(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0)*F_55(x, k_0))
Eq(F_54(x, k_0), k_0*x)
Eq(F_55(x, k_0), F_1(x) + F_52(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_4(x)*F_58(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0) + F_63(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_60(x, k_0), F_11(x)*F_61(x, k_0))
Eq(F_61(x, k_0), F_52(x, k_0) + F_62(x, k_0))
Eq(F_62(x, k_0), F_52(x, k_0)*F_55(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0) + F_94(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0) + F_67(x, k_0))
Eq(F_65(x, k_0), F_52(x, k_0)*F_66(x))
Eq(F_66(x), F_7(x))
Eq(F_67(x, k_0), F_55(x, k_0)*F_68(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0))
Eq(F_69(x, k_0), F_54(x, k_0)*F_70(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0) + F_72(x, k_0))
Eq(F_71(x, k_0), F_12(x)*F_55(x, k_0))
Eq(F_72(x, k_0), F_18(x) + F_73(x, k_0))
Eq(F_74(x, k_0), F_73(x, k_0) + F_93(x, k_0))
Eq(F_75(x, k_0), F_54(x, k_0)*F_74(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0))
Eq(F_77(x, k_0), F_4(x)*F_78(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0) + F_92(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0) + F_83(x, k_0))
Eq(F_80(x, k_0), F_76(x, k_0) + F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_82(x, k_0), F_52(x, k_0)*F_54(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0) + F_90(x, k_0))
Eq(F_84(x, k_0), F_54(x, k_0)*F_85(x, k_0))
Eq(F_85(x, k_0), F_52(x, k_0) + F_86(x, k_0))
Eq(F_86(x, k_0), F_20(x) + F_87(x, k_0) + F_88(x, k_0))
Eq(F_87(x, k_0), F_4(x)*F_85(x, k_0))
Eq(F_88(x, k_0), F_54(x, k_0)*F_89(x, k_0))
Eq(F_89(x, k_0), F_12(x) + F_86(x, k_0))
Eq(F_90(x, k_0), F_81(x, k_0)*F_91(x, k_0))
Eq(F_91(x, k_0), F_55(x, k_0) + F_89(x, k_0))
Eq(F_92(x, k_0), F_18(x)*F_81(x, k_0))
Eq(F_93(x, k_0), F_12(x)*F_52(x, k_0))
Eq(F_94(x, k_0), F_104(x, k_0) + F_95(x, k_0))
Eq(F_95(x, k_0), F_52(x, k_0)*F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_4(x)*F_98(x))
Eq(F_98(x), F_103(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_12(x) + F_96(x))
Eq(F_101(x), F_102(x)*F_12(x))
Eq(F_102(x), F_11(x) + F_28(x))
Eq(F_103(x), F_12(x)*F_18(x))
Eq(F_104(x, k_0), F_105(x, k_0)*F_55(x, k_0))
Eq(F_105(x, k_0), -F_76(x, 1) - F_76(x, k_0) + (k_0*F_76(x, k_0) - F_76(x, 1))/(k_0 - 1))
Eq(F_106(x, k_0), F_107(x, k_0) + F_47(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0))
Eq(F_108(x, k_0), F_109(x, k_0)*F_4(x))
Eq(F_109(x, k_0), F_110(x, k_0) + F_130(x, k_0))
Eq(F_110(x, k_0), F_111(x, k_0) + F_115(x, k_0))
Eq(F_111(x, k_0), F_106(x, k_0) + F_112(x, k_0))
Eq(F_112(x, k_0), -F_113(x, 1) + (k_0*F_113(x, k_0) - F_113(x, 1))/(k_0 - 1))
Eq(F_113(x, k_0), F_114(x, k_0) + F_42(x, k_0))
Eq(F_114(x, k_0), F_2(x)*F_52(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0)*F_52(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0) + F_129(x, k_0))
Eq(F_117(x, k_0), F_118(x, k_0) + F_119(x, k_0))
Eq(F_118(x, k_0), F_2(x) + F_47(x, k_0))
Eq(F_119(x, k_0), F_120(x) + F_124(x, k_0))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_122(x)*F_4(x))
Eq(F_122(x), F_123(x) + F_34(x))
Eq(F_123(x), F_120(x) + F_2(x))
Eq(F_124(x, k_0), F_125(x, k_0))
Eq(F_125(x, k_0), F_126(x, k_0)*F_4(x))
Eq(F_126(x, k_0), F_115(x, k_0) + F_127(x, k_0))
Eq(F_127(x, k_0), F_112(x, k_0) + F_128(x, k_0))
Eq(F_128(x, k_0), F_124(x, k_0) + F_47(x, k_0))
Eq(F_129(x, k_0), (k_0*F_44(x, k_0) - F_44(x, 1))/(k_0 - 1))
Eq(F_130(x, k_0), F_131(x, k_0) + F_225(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0) + F_153(x, k_0))
Eq(F_132(x, k_0), F_133(x, k_0) + F_134(x, k_0))
Eq(F_133(x, k_0), F_12(x)*F_47(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0))
Eq(F_135(x, k_0), F_136(x, k_0)*F_4(x))
Eq(F_136(x, k_0), F_137(x, k_0) + F_143(x, k_0))
Eq(F_137(x, k_0), F_138(x, k_0) + F_142(x, k_0))
Eq(F_138(x, k_0), -F_139(x, 1) - F_139(x, k_0) + (k_0*F_139(x, k_0) - F_139(x, 1))/(k_0 - 1))
Eq(F_139(x, k_0), F_140(x, k_0))
Eq(F_140(x, k_0), F_141(x, k_0)*F_54(x, k_0))
Eq(F_141(x, k_0), F_113(x, k_0) + F_47(x, k_0))
Eq(F_142(x, k_0), -F_124(x, 1) + (k_0*F_124(x, k_0) - F_124(x, 1))/(k_0 - 1))
Eq(F_143(x, k_0), F_144(x, k_0) + F_146(x, k_0))
Eq(F_144(x, k_0), -F_145(x, 1) - F_145(x, k_0) + (k_0*F_145(x, k_0) - F_145(x, 1))/(k_0 - 1))
Eq(F_145(x, k_0), F_12(x)*F_139(x, k_0))
Eq(F_146(x, k_0), -F_147(x, 1) + (k_0*F_147(x, k_0) - F_147(x, 1))/(k_0 - 1))
Eq(F_147(x, k_0), F_148(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0)*F_4(x))
Eq(F_149(x, k_0), F_150(x, k_0) + F_215(x, k_0))
Eq(F_150(x, k_0), F_151(x, k_0) + F_213(x, k_0))
Eq(F_151(x, k_0), F_152(x, k_0) + F_153(x, k_0))
Eq(F_152(x, k_0), F_133(x, k_0) + F_147(x, k_0))
Eq(F_153(x, k_0), F_154(x, k_0) + F_156(x, k_0))
Eq(F_154(x, k_0), F_155(x, k_0))
Eq(F_155(x, k_0), F_18(x)*F_2(x)*F_52(x, k_0))
Eq(F_156(x, k_0), F_157(x, k_0) + F_158(x, k_0))
Eq(F_157(x, k_0), F_12(x)*F_42(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0))
Eq(F_159(x, k_0), F_160(x, k_0)*F_4(x))
Eq(F_160(x, k_0), F_161(x, k_0) + F_209(x, k_0))
Eq(F_161(x, k_0), F_162(x, k_0) + F_208(x, k_0))
Eq(F_162(x, k_0), -F_163(x, 1) - F_163(x, k_0) + (k_0*F_163(x, k_0) - F_163(x, 1))/(k_0 - 1))
Eq(F_163(x, k_0), F_164(x, k_0))
Eq(F_164(x, k_0), F_165(x, k_0)*F_54(x, k_0))
Eq(F_165(x, k_0), F_166(x, k_0) + F_167(x, k_0))
Eq(F_166(x, k_0), F_37(x)*F_52(x, k_0))
Eq(F_168(x, k_0), F_167(x, k_0) + F_172(x))
Eq(F_169(x, k_0), F_168(x, k_0) + F_171(x, k_0))
Eq(F_170(x, k_0), F_169(x, k_0)*F_54(x, k_0))
Eq(F_170(x, k_0), F_42(x, k_0))
Eq(F_171(x, k_0), F_37(x)*F_55(x, k_0))
Eq(F_172(x), F_173(x) + F_37(x))
Eq(F_173(x), F_174(x) - F_179(x))
Eq(F_174(x), F_175(x) - F_177(x))
Eq(F_175(x), F_176(x)/F_4(x))
Eq(F_176(x), F_37(x))
Eq(F_177(x), F_178(x) + F_37(x))
Eq(F_178(x), F_12(x) + F_123(x))
Eq(F_179(x), F_180(x) + F_181(x))
Eq(F_180(x), F_12(x)**2)
Eq(F_181(x), F_182(x) + F_37(x))
Eq(F_182(x), F_183(x))
Eq(F_183(x), F_184(x)*F_4(x))
Eq(F_184(x), F_185(x) + F_191(x))
Eq(F_185(x), F_186(x) + F_189(x))
Eq(F_186(x), F_187(x))
Eq(F_187(x), F_188(x)*F_4(x))
Eq(F_188(x), F_12(x) + F_186(x))
Eq(F_189(x), F_190(x, 1))
Eq(F_190(x, k_0), -F_47(x, k_0) + (-k_0*F_47(x, k_0) + F_47(x, 1))/(1 - k_0))
Eq(F_191(x), F_192(x) + F_194(x))
Eq(F_192(x), F_193(x))
Eq(F_193(x), F_12(x)**3)
Eq(F_194(x), F_195(x, 1))
Eq(F_195(x, k_0), -F_196(x, k_0) + (-k_0*F_196(x, k_0) + F_196(x, 1))/(1 - k_0))
Eq(F_196(x, k_0), F_197(x, k_0))
Eq(F_197(x, k_0), F_198(x, k_0)*F_4(x))
Eq(F_198(x, k_0), F_199(x, k_0) + F_204(x, k_0))
Eq(F_199(x, k_0), F_200(x, k_0) + F_203(x, k_0))
Eq(F_200(x, k_0), F_201(x, k_0))
Eq(F_201(x, k_0), F_202(x, k_0)*F_4(x))
Eq(F_202(x, k_0), F_200(x, k_0) + F_52(x, k_0))
Eq(F_203(x, k_0), -F_47(x, 1) + (k_0*F_47(x, k_0) - F_47(x, 1))/(k_0 - 1))
Eq(F_204(x, k_0), F_205(x, k_0) + F_207(x, k_0))
Eq(F_205(x, k_0), F_206(x, k_0))
Eq(F_206(x, k_0), F_12(x)**2*F_52(x, k_0))
Eq(F_207(x, k_0), -F_196(x, 1) + (k_0*F_196(x, k_0) - F_196(x, 1))/(k_0 - 1))
Eq(F_208(x, k_0), -F_162(x, 1) + (k_0*F_162(x, k_0) - F_162(x, 1))/(k_0 - 1))
Eq(F_209(x, k_0), F_210(x, k_0) + F_212(x, k_0))
Eq(F_210(x, k_0), -F_211(x, 1) - F_211(x, k_0) + (k_0*F_211(x, k_0) - F_211(x, 1))/(k_0 - 1))
Eq(F_211(x, k_0), F_12(x)*F_163(x, k_0))
Eq(F_212(x, k_0), -F_158(x, 1) + (k_0*F_158(x, k_0) - F_158(x, 1))/(k_0 - 1))
Eq(F_213(x, k_0), F_214(x, k_0))
Eq(F_214(x, k_0), F_116(x, k_0)*F_12(x)*F_52(x, k_0))
Eq(F_215(x, k_0), F_12(x)*F_216(x, k_0))
Eq(F_216(x, k_0), F_217(x, k_0) + F_218(x, k_0))
Eq(F_217(x, k_0), -F_141(x, 1) + (k_0*F_141(x, k_0) - F_141(x, 1))/(k_0 - 1))
Eq(F_218(x, k_0), F_153(x, k_0) + F_219(x, k_0))
Eq(F_220(x, k_0), F_219(x, k_0) + F_223(x, k_0))
Eq(F_221(x, k_0), F_199(x, k_0) + F_220(x, k_0))
Eq(F_222(x, k_0), F_221(x, k_0)*F_4(x))
Eq(F_222(x, k_0), F_196(x, k_0))
Eq(F_223(x, k_0), F_224(x, k_0))
Eq(F_224(x, k_0), F_19(x)*F_52(x, k_0))
Eq(F_225(x, k_0), F_226(x, k_0)*F_52(x, k_0))
Eq(F_226(x, k_0), F_227(x, k_0) + F_251(x, k_0))
Eq(F_227(x, k_0), F_228(x, k_0) + F_229(x, k_0))
Eq(F_228(x, k_0), F_118(x, k_0)*F_12(x))
Eq(F_229(x, k_0), F_147(x, k_0) + F_230(x))
Eq(F_230(x), F_231(x))
Eq(F_231(x), F_232(x)*F_4(x))
Eq(F_232(x), F_233(x) + F_249(x))
Eq(F_233(x), F_234(x) + F_236(x))
Eq(F_234(x), F_230(x) + F_235(x))
Eq(F_235(x), F_12(x)*F_2(x))
Eq(F_236(x), F_237(x) + F_238(x))
Eq(F_237(x), F_18(x)*F_2(x))
Eq(F_238(x), F_239(x) + F_240(x))
Eq(F_239(x), F_12(x)*F_37(x))
Eq(F_240(x), F_241(x))
Eq(F_241(x), F_242(x)*F_4(x))
Eq(F_242(x), F_243(x) + F_245(x))
Eq(F_243(x), F_244(x, 1))
Eq(F_244(x, k_0), (-k_0*F_42(x, k_0) + F_42(x, 1))/(1 - k_0))
Eq(F_245(x), F_246(x) + F_247(x))
Eq(F_246(x), F_12(x)*F_41(x))
Eq(F_247(x), F_240(x) + F_248(x))
Eq(F_248(x), F_158(x, 1))
Eq(F_249(x), F_12(x)*F_250(x))
Eq(F_250(x), F_122(x) + F_233(x))
Eq(F_251(x, k_0), F_252(x, k_0) + F_254(x, k_0))
Eq(F_252(x, k_0), F_253(x, k_0))
Eq(F_253(x, k_0), F_18(x)*F_2(x)*F_55(x, k_0))
Eq(F_254(x, k_0), F_255(x, k_0) + F_256(x, k_0))
Eq(F_255(x, k_0), F_12(x)*F_43(x, k_0))
Eq(F_256(x, k_0), F_158(x, k_0) + F_240(x))
Eq(F_257(x, k_0), F_258(x, k_0)*F_52(x, k_0))
Eq(F_258(x, k_0), F_259(x, k_0) + F_261(x, k_0))
Eq(F_259(x, k_0), F_260(x, k_0) + F_55(x, k_0))
Eq(F_260(x, k_0), F_56(x, k_0) + F_66(x))
Eq(F_261(x, k_0), F_118(x, k_0) + F_262(x, k_0))
Eq(F_262(x, k_0), F_107(x, k_0) + F_30(x))
Eq(F_263(x, k_0), F_2(x)*F_55(x, k_0))
Eq(F_264(x), F_236(x) + F_265(x))
Eq(F_265(x), F_235(x) + F_266(x))
Eq(F_266(x), F_267(x))
Eq(F_267(x), F_268(x)*F_4(x))
Eq(F_268(x), F_264(x) + F_269(x))
Eq(F_269(x), F_12(x)*F_270(x))
Eq(F_270(x), F_233(x) + F_271(x))
Eq(F_271(x), F_272(x) + F_34(x))
Eq(F_272(x), F_123(x) + F_273(x))
Eq(F_273(x), F_120(x) + F_274(x))
Eq(F_274(x), F_124(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "insertion_point_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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"comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "tilings.strategies.fusion.fusion", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 2]]}]]}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": null, "row_idx": 1, "strategy_class": "FusionStrategy", "tracked": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 1], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "tilings.strategies.fusion.fusion", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 1], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": null, "row_idx": 1, "strategy_class": "FusionStrategy", "tracked": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "tilings.strategies.fusion.fusion", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 1], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "FusionRule", "strategy": {"class_module": "tilings.strategies.fusion.fusion", "col_idx": null, "row_idx": 1, "strategy_class": "FusionStrategy", "tracked": true}}]}
Specification 3
Strategy pack name: point_and_row_placements_tracked_fusion
Tree: http://permpal.com/tree/195/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[27,x]*F[3,x]
F[3,x] = F[37,x]+F[4,x]
F[4,x] = F[1,x]+F[5,x]
F[5,x] = F[27,x]*F[6,x]
F[6,x] = F[4,x]+F[7,x]
F[7,x] = F[27,x]*F[8,x]
F[8,x] = F[15,x]+F[7,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x,1]
F[11,x,k[0]] = F[12,x,k[0]]
F[12,x,k[0]] = F[13,x,k[0]]*F[14,x,k[0]]
F[13,x,k[0]] = F[1,x]+F[11,x,k[0]]
F[14,x,k[0]] = k[0]*x
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[27,x]*F[9,x]
F[17,x] = F[18,x]+F[32,x]
F[18,x] = F[19,x]+F[9,x]
F[19,x] = F[20,x]+F[21,x]+F[30,x]
F[20,x] = 0
F[21,x] = F[22,x,1]
F[22,x,k[0]] = F[23,x,k[0]]*F[27,x]
F[23,x,k[0]] = F[24,x,k[0]]+F[9,x]
F[24,x,k[0]] = F[11,x,k[0]]+F[25,x,k[0]]
F[25,x,k[0]] = F[20,x]+F[26,x,k[0]]+F[28,x,k[0]]
F[26,x,k[0]] = F[24,x,k[0]]*F[27,x]
F[27,x] = F[14,x,1]
F[28,x,k[0]] = F[14,x,k[0]]*F[29,x,k[0]]
F[29,x,k[0]] = F[10,x]+F[25,x,k[0]]
F[30,x] = F[31,x,1]
F[31,x,k[0]] = F[14,x,k[0]]*F[29,x,k[0]]
F[32,x] = F[10,x]+F[33,x]
F[33,x] = F[20,x]+F[34,x]+F[35,x]
F[34,x] = F[27,x]*F[32,x]
F[35,x] = F[27,x]*F[36,x]
F[36,x] = F[10,x]+F[33,x]
F[37,x] = F[38,x]
F[38,x] = F[27,x]*F[39,x]
F[39,x] = F[161,x]+F[40,x]
F[40,x] = F[41,x,1]
F[41,x,k[0]] = F[42,x,k[0]]+F[83,x,k[0]]
F[42,x,k[0]] = F[1,x]+F[43,x,k[0]]+F[82,x,k[0]]
F[43,x,k[0]] = F[27,x]*F[44,x,k[0]]
F[44,x,k[0]] = F[42,x,k[0]]+F[45,x,k[0]]
F[45,x,k[0]] = F[20,x]+F[46,x,k[0]]+F[64,x,k[0]]+F[81,x,k[0]]
F[46,x,k[0]] = F[27,x]*F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]+F[53,x,k[0]]
F[48,x,k[0]] = F[13,x,k[0]]+F[49,x,k[0]]
F[49,x,k[0]] = F[10,x]+F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]
F[51,x,k[0]] = F[27,x]*F[52,x,k[0]]
F[52,x,k[0]] = F[11,x,k[0]]+F[50,x,k[0]]
F[53,x,k[0]] = F[29,x,k[0]]+F[54,x,k[0]]
F[54,x,k[0]] = F[55,x]+F[59,x,k[0]]
F[55,x] = F[20,x]+F[56,x]+F[58,x]
F[56,x] = F[27,x]*F[57,x]
F[57,x] = F[10,x]+F[55,x]
F[58,x] = F[19,x]*F[27,x]
F[59,x,k[0]] = 2*F[20,x]+F[60,x,k[0]]+F[62,x,k[0]]
F[60,x,k[0]] = F[27,x]*F[61,x,k[0]]
F[61,x,k[0]] = F[50,x,k[0]]+F[59,x,k[0]]
F[62,x,k[0]] = F[27,x]*F[63,x,k[0]]
F[63,x,k[0]] = F[25,x,k[0]]+F[59,x,k[0]]
F[64,x,k[0]] = F[27,x]*F[65,x,k[0]]
F[65,x,k[0]] = 1/(-1+k[0])*(F[66,x,k[0]]*k[0]-F[66,x,1])
F[66,x,k[0]] = 2*F[20,x]+F[67,x,k[0]]+F[79,x,k[0]]
F[67,x,k[0]] = F[27,x]*F[68,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]+F[71,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[13,x,k[0]]*F[9,x]
F[71,x,k[0]] = F[49,x,k[0]]+F[72,x,k[0]]
F[72,x,k[0]] = F[55,x]+F[73,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]
F[74,x,k[0]] = F[27,x]*F[75,x,k[0]]
F[75,x,k[0]] = F[73,x,k[0]]+F[76,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]
F[77,x,k[0]] = F[14,x,k[0]]*F[78,x,k[0]]
F[78,x,k[0]] = F[10,x]+F[76,x,k[0]]
F[79,x,k[0]] = F[27,x]*F[80,x,k[0]]
F[80,x,k[0]] = F[65,x,k[0]]
F[81,x,k[0]] = F[14,x,k[0]]*F[45,x,k[0]]
F[82,x,k[0]] = F[14,x,k[0]]*F[23,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]
F[84,x,k[0]] = F[27,x]*F[85,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]+F[91,x,k[0]]
F[86,x,k[0]] = F[13,x,k[0]]*F[87,x,k[0]]
F[87,x,k[0]] = F[88,x,1,k[0]]
F[88,x,k[0],k[1]] = F[89,x,k[0],k[1]]+F[90,x,k[0],k[1]]
F[89,x,k[0],k[1]] = (F[42,x,k[0]]*k[0]-F[42,x,k[1]]*k[1])/(-k[1]+k[0])
F[90,x,k[0],k[1]] = (F[83,x,k[0]]*k[0]-F[83,x,k[1]]*k[1])/(-k[1]+k[0])
F[91,x,k[0]] = F[92,x,k[0]]
F[92,x,k[0]] = F[27,x]*F[93,x,k[0]]
F[93,x,k[0]] = F[144,x,k[0]]+F[94,x,k[0]]
F[94,x,k[0]] = F[142,x,k[0]]+F[95,x,k[0]]
F[95,x,k[0]] = F[119,x,k[0]]+F[96,x,k[0]]
F[96,x,k[0]] = 1/(-1+k[0])*(F[97,x,k[0]]*k[0]-F[97,x,1])
F[97,x,k[0]] = F[87,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[27,x]
F[100,x,k[0]] = F[101,x,1,k[0]]
F[101,x,k[0],k[1]] = F[102,x,k[1]]+F[110,x,k[0],k[1]]
F[102,x,k[0]] = F[103,x,1,k[0]]
F[103,x,k[0],k[1]] = F[104,x,k[0],k[1]]+F[105,x,k[0],k[1]]
F[104,x,k[0],k[1]] = (F[87,x,k[0]]*k[0]-F[87,x,k[1]]*k[1])/(-k[1]+k[0])
F[105,x,k[0],k[1]] = F[106,x,k[0],k[1]]
F[106,x,k[0],k[1]] = F[107,x,k[0],k[1]]*F[27,x]
F[107,x,k[0],k[1]] = F[108,x,k[0],k[1]]+F[109,x,k[1]]
F[108,x,k[0],k[1]] = 1/(-1+k[0])*(F[103,x,k[0],k[1]]*k[0]-F[103,x,1,k[1]])
F[109,x,k[0]] = F[110,x,1,k[0]]
F[111,x,k[0],k[1]] = F[110,x,k[0]*k[1],k[1]]
F[111,x,k[0],k[1]] = F[112,x,k[0],k[1]]+F[118,x,k[0],k[1]]+F[20,x]
F[112,x,k[0],k[1]] = F[113,x,k[0],k[1]]*F[27,x]
F[113,x,k[0],k[1]] = F[111,x,k[0],k[1]]+F[114,x,k[0],k[1]]
F[114,x,k[0],k[1]] = F[115,x,k[1]]*F[41,x,k[1]]
F[115,x,k[0]] = F[116,x,k[0]]
F[116,x,k[0]] = F[10,x]*F[117,x]*F[13,x,k[0]]*F[14,x,k[0]]
F[117,x] = F[36,x]+F[9,x]
F[118,x,k[0],k[1]] = F[14,x,k[1]]*F[23,x,k[1]]*F[87,x,k[1]]
F[119,x,k[0]] = F[120,x,k[0]]
F[120,x,k[0]] = F[121,x,k[0]]*F[27,x]
F[121,x,k[0]] = 1/(-1+k[0])*(F[122,x,k[0]]*k[0]-F[122,x,1])
F[122,x,k[0]] = F[123,x,k[0]]+F[134,x,k[0]]
F[123,x,k[0]] = F[124,x,k[0]]*F[9,x]
F[124,x,k[0]] = F[125,x,k[0]]+F[87,x,k[0]]
F[125,x,k[0]] = F[126,x,k[0]]*F[27,x]
F[126,x,k[0]] = F[127,x,k[0]]+F[130,x,k[0]]
F[127,x,k[0]] = F[128,x,1,k[0]]
F[128,x,k[0],k[1]] = F[129,x,k[0],1,k[1]]
F[129,x,k[0],k[1],k[2]] = (F[88,x,k[0],k[1]]*k[1]-F[88,x,k[0],k[2]]*k[2])/(-k[2]+k[1])
F[130,x,k[0]] = F[131,x,1,k[0]]
F[131,x,k[0],k[1]] = F[132,x,k[0],k[1]]*F[27,x]
F[132,x,k[0],k[1]] = 1/(-1+k[1])*(F[133,x,k[0],k[1]]*k[1]-F[133,x,k[0],1])
F[133,x,k[0],k[1]] = F[128,x,k[0],k[1]]+F[131,x,k[0],k[1]]
F[134,x,k[0]] = F[135,x,k[0]]+F[140,x,k[0]]+F[20,x]
F[135,x,k[0]] = F[136,x,k[0]]
F[136,x,k[0]] = F[137,x,k[0]]*F[27,x]
F[137,x,k[0]] = F[122,x,k[0]]+F[138,x,k[0]]
F[138,x,k[0]] = F[139,x,k[0]]
F[139,x,k[0]] = F[117,x]*F[124,x,k[0]]*F[27,x]*F[9,x]
F[140,x,k[0]] = F[141,x,k[0]]
F[141,x,k[0]] = F[19,x]*F[27,x]*F[87,x,k[0]]*F[9,x]
F[142,x,k[0]] = F[143,x,k[0]]
F[143,x,k[0]] = F[100,x,k[0]]*F[11,x,k[0]]
F[144,x,k[0]] = F[145,x,k[0]]+F[158,x,k[0]]
F[145,x,k[0]] = F[146,x,k[0]]+F[150,x,k[0]]+F[157,x,k[0]]+F[20,x]
F[146,x,k[0]] = F[147,x,k[0]]*F[27,x]
F[147,x,k[0]] = F[145,x,k[0]]+F[148,x,k[0]]
F[148,x,k[0]] = F[149,x,k[0]]
F[149,x,k[0]] = F[10,x]*F[117,x]*F[124,x,k[0]]*F[13,x,k[0]]*F[14,x,k[0]]
F[150,x,k[0]] = F[151,x,k[0]]*F[27,x]
F[151,x,k[0]] = F[152,x,k[0]]
F[152,x,k[0]] = F[14,x,k[0]]*F[153,x,k[0]]*F[9,x]
F[153,x,k[0]] = F[154,x,k[0]]+F[156,x,k[0]]
F[154,x,k[0]] = F[155,x,k[0]]
F[155,x,k[0]] = F[126,x,k[0]]*F[13,x,k[0]]
F[156,x,k[0]] = F[53,x,k[0]]*F[87,x,k[0]]
F[157,x,k[0]] = F[118,x,1,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]
F[159,x,k[0]] = F[13,x,k[0]]*F[14,x,k[0]]*F[160,x,k[0]]
F[160,x,k[0]] = k[0]*(F[111,x,1,k[0]]-F[111,x,1/k[0],k[0]])/(-1+k[0])
F[161,x] = F[162,x]
F[162,x] = F[163,x]*F[27,x]
F[163,x] = F[164,x]+F[165,x]
F[164,x] = F[97,x,1]
F[165,x] = F[166,x]
F[166,x] = F[167,x]*F[27,x]
F[167,x] = F[122,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{27}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{37}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{27}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{4}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{27}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{15}\! \left(x \right)+F_{7}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x , 1\right)
F_{11}\! \left(x , y_{0}\right) = F_{12}\! \left(x , y_{0}\right)
F_{12}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right)
F_{13}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}\right)
F_{14}\! \left(x , y_{0}\right) = y_{0} x
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{27}\! \left(x \right) F_{9}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{32}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{9}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{30}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{22}\! \left(x , 1\right)
F_{22}\! \left(x , y_{0}\right) = F_{23}\! \left(x , y_{0}\right) F_{27}\! \left(x \right)
F_{23}\! \left(x , y_{0}\right) = F_{24}\! \left(x , y_{0}\right)+F_{9}\! \left(x \right)
F_{24}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right)+F_{25}\! \left(x , y_{0}\right)
F_{25}\! \left(x , y_{0}\right) = F_{20}\! \left(x \right)+F_{26}\! \left(x , y_{0}\right)+F_{28}\! \left(x , y_{0}\right)
F_{26}\! \left(x , y_{0}\right) = F_{24}\! \left(x , y_{0}\right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{14}\! \left(x , 1\right)
F_{28}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{29}\! \left(x , y_{0}\right)
F_{29}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right)+F_{25}\! \left(x , y_{0}\right)
F_{30}\! \left(x \right) = F_{31}\! \left(x , 1\right)
F_{31}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{29}\! \left(x , y_{0}\right)
F_{32}\! \left(x \right) = F_{10}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{20}\! \left(x \right)+F_{34}\! \left(x \right)+F_{35}\! \left(x \right)
F_{34}\! \left(x \right) = F_{27}\! \left(x \right) F_{32}\! \left(x \right)
F_{35}\! \left(x \right) = F_{27}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{10}\! \left(x \right)+F_{33}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{27}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{161}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x , 1\right)
F_{41}\! \left(x , y_{0}\right) = F_{42}\! \left(x , y_{0}\right)+F_{83}\! \left(x , y_{0}\right)
F_{42}\! \left(x , y_{0}\right) = F_{1}\! \left(x \right)+F_{43}\! \left(x , y_{0}\right)+F_{82}\! \left(x , y_{0}\right)
F_{43}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right) F_{44}\! \left(x , y_{0}\right)
F_{44}\! \left(x , y_{0}\right) = F_{42}\! \left(x , y_{0}\right)+F_{45}\! \left(x , y_{0}\right)
F_{45}\! \left(x , y_{0}\right) = F_{20}\! \left(x \right)+F_{46}\! \left(x , y_{0}\right)+F_{64}\! \left(x , y_{0}\right)+F_{81}\! \left(x , y_{0}\right)
F_{46}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right) F_{47}\! \left(x , y_{0}\right)
F_{47}\! \left(x , y_{0}\right) = F_{48}\! \left(x , y_{0}\right)+F_{53}\! \left(x , y_{0}\right)
F_{48}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right)+F_{49}\! \left(x , y_{0}\right)
F_{49}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right)+F_{50}\! \left(x , y_{0}\right)
F_{50}\! \left(x , y_{0}\right) = F_{51}\! \left(x , y_{0}\right)
F_{51}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right) F_{52}\! \left(x , y_{0}\right)
F_{52}\! \left(x , y_{0}\right) = F_{11}\! \left(x , y_{0}\right)+F_{50}\! \left(x , y_{0}\right)
F_{53}\! \left(x , y_{0}\right) = F_{29}\! \left(x , y_{0}\right)+F_{54}\! \left(x , y_{0}\right)
F_{54}\! \left(x , y_{0}\right) = F_{55}\! \left(x \right)+F_{59}\! \left(x , y_{0}\right)
F_{55}\! \left(x \right) = F_{20}\! \left(x \right)+F_{56}\! \left(x \right)+F_{58}\! \left(x \right)
F_{56}\! \left(x \right) = F_{27}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{10}\! \left(x \right)+F_{55}\! \left(x \right)
F_{58}\! \left(x \right) = F_{19}\! \left(x \right) F_{27}\! \left(x \right)
F_{59}\! \left(x , y_{0}\right) = 2 F_{20}\! \left(x \right)+F_{60}\! \left(x , y_{0}\right)+F_{62}\! \left(x , y_{0}\right)
F_{60}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right) F_{61}\! \left(x , y_{0}\right)
F_{61}\! \left(x , y_{0}\right) = F_{50}\! \left(x , y_{0}\right)+F_{59}\! \left(x , y_{0}\right)
F_{62}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right) F_{63}\! \left(x , y_{0}\right)
F_{63}\! \left(x , y_{0}\right) = F_{25}\! \left(x , y_{0}\right)+F_{59}\! \left(x , y_{0}\right)
F_{64}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right) F_{65}\! \left(x , y_{0}\right)
F_{65}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{66}\! \left(x , y_{0}\right)+F_{66}\! \left(x , 1\right)}{-1+y_{0}}
F_{66}\! \left(x , y_{0}\right) = 2 F_{20}\! \left(x \right)+F_{67}\! \left(x , y_{0}\right)+F_{79}\! \left(x , y_{0}\right)
F_{67}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right) F_{68}\! \left(x , y_{0}\right)
F_{68}\! \left(x , y_{0}\right) = F_{69}\! \left(x , y_{0}\right)+F_{71}\! \left(x , y_{0}\right)
F_{69}\! \left(x , y_{0}\right) = F_{70}\! \left(x , y_{0}\right)
F_{70}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right) F_{9}\! \left(x \right)
F_{71}\! \left(x , y_{0}\right) = F_{49}\! \left(x , y_{0}\right)+F_{72}\! \left(x , y_{0}\right)
F_{72}\! \left(x , y_{0}\right) = F_{55}\! \left(x \right)+F_{73}\! \left(x , y_{0}\right)
F_{73}\! \left(x , y_{0}\right) = F_{74}\! \left(x , y_{0}\right)
F_{74}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right) F_{75}\! \left(x , y_{0}\right)
F_{75}\! \left(x , y_{0}\right) = F_{73}\! \left(x , y_{0}\right)+F_{76}\! \left(x , y_{0}\right)
F_{76}\! \left(x , y_{0}\right) = F_{77}\! \left(x , y_{0}\right)
F_{77}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{78}\! \left(x , y_{0}\right)
F_{78}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right)+F_{76}\! \left(x , y_{0}\right)
F_{79}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right) F_{80}\! \left(x , y_{0}\right)
F_{80}\! \left(x , y_{0}\right) = F_{65}\! \left(x , y_{0}\right)
F_{81}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{45}\! \left(x , y_{0}\right)
F_{82}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{23}\! \left(x , y_{0}\right)
F_{83}\! \left(x , y_{0}\right) = F_{84}\! \left(x , y_{0}\right)
F_{84}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right) F_{85}\! \left(x , y_{0}\right)
F_{85}\! \left(x , y_{0}\right) = F_{86}\! \left(x , y_{0}\right)+F_{91}\! \left(x , y_{0}\right)
F_{86}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right) F_{87}\! \left(x , y_{0}\right)
F_{87}\! \left(x , y_{0}\right) = F_{88}\! \left(x , 1, y_{0}\right)
F_{88}\! \left(x , y_{0}, y_{1}\right) = F_{89}\! \left(x , y_{0}, y_{1}\right)+F_{90}\! \left(x , y_{0}, y_{1}\right)
F_{89}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{42}\! \left(x , y_{0}\right)-y_{1} F_{42}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}
F_{90}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{83}\! \left(x , y_{0}\right)-y_{1} F_{83}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}
F_{91}\! \left(x , y_{0}\right) = F_{92}\! \left(x , y_{0}\right)
F_{92}\! \left(x , y_{0}\right) = F_{27}\! \left(x \right) F_{93}\! \left(x , y_{0}\right)
F_{93}\! \left(x , y_{0}\right) = F_{144}\! \left(x , y_{0}\right)+F_{94}\! \left(x , y_{0}\right)
F_{94}\! \left(x , y_{0}\right) = F_{142}\! \left(x , y_{0}\right)+F_{95}\! \left(x , y_{0}\right)
F_{95}\! \left(x , y_{0}\right) = F_{119}\! \left(x , y_{0}\right)+F_{96}\! \left(x , y_{0}\right)
F_{96}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{97}\! \left(x , y_{0}\right)+F_{97}\! \left(x , 1\right)}{-1+y_{0}}
F_{97}\! \left(x , y_{0}\right) = F_{87}\! \left(x , y_{0}\right)+F_{98}\! \left(x , y_{0}\right)
F_{98}\! \left(x , y_{0}\right) = F_{99}\! \left(x , y_{0}\right)
F_{99}\! \left(x , y_{0}\right) = F_{100}\! \left(x , y_{0}\right) F_{27}\! \left(x \right)
F_{100}\! \left(x , y_{0}\right) = F_{101}\! \left(x , 1, y_{0}\right)
F_{101}\! \left(x , y_{0}, y_{1}\right) = F_{102}\! \left(x , y_{1}\right)+F_{110}\! \left(x , y_{0}, y_{1}\right)
F_{102}\! \left(x , y_{0}\right) = F_{103}\! \left(x , 1, y_{0}\right)
F_{103}\! \left(x , y_{0}, y_{1}\right) = F_{104}\! \left(x , y_{0}, y_{1}\right)+F_{105}\! \left(x , y_{0}, y_{1}\right)
F_{104}\! \left(x , y_{0}, y_{1}\right) = \frac{y_{0} F_{87}\! \left(x , y_{0}\right)-y_{1} F_{87}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}
F_{105}\! \left(x , y_{0}, y_{1}\right) = F_{106}\! \left(x , y_{0}, y_{1}\right)
F_{106}\! \left(x , y_{0}, y_{1}\right) = F_{107}\! \left(x , y_{0}, y_{1}\right) F_{27}\! \left(x \right)
F_{107}\! \left(x , y_{0}, y_{1}\right) = F_{108}\! \left(x , y_{0}, y_{1}\right)+F_{109}\! \left(x , y_{1}\right)
F_{108}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{0} F_{103}\! \left(x , y_{0}, y_{1}\right)+F_{103}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}
F_{109}\! \left(x , y_{0}\right) = F_{110}\! \left(x , 1, y_{0}\right)
F_{111}\! \left(x , y_{0}, y_{1}\right) = F_{110}\! \left(x , y_{0} y_{1}, y_{1}\right)
F_{111}\! \left(x , y_{0}, y_{1}\right) = F_{112}\! \left(x , y_{0}, y_{1}\right)+F_{118}\! \left(x , y_{0}, y_{1}\right)+F_{20}\! \left(x \right)
F_{112}\! \left(x , y_{0}, y_{1}\right) = F_{113}\! \left(x , y_{0}, y_{1}\right) F_{27}\! \left(x \right)
F_{113}\! \left(x , y_{0}, y_{1}\right) = F_{111}\! \left(x , y_{0}, y_{1}\right)+F_{114}\! \left(x , y_{0}, y_{1}\right)
F_{114}\! \left(x , y_{0}, y_{1}\right) = F_{115}\! \left(x , y_{1}\right) F_{41}\! \left(x , y_{1}\right)
F_{115}\! \left(x , y_{0}\right) = F_{116}\! \left(x , y_{0}\right)
F_{116}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{117}\! \left(x \right) F_{13}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right)
F_{117}\! \left(x \right) = F_{36}\! \left(x \right)+F_{9}\! \left(x \right)
F_{118}\! \left(x , y_{0}, y_{1}\right) = F_{14}\! \left(x , y_{1}\right) F_{23}\! \left(x , y_{1}\right) F_{87}\! \left(x , y_{1}\right)
F_{119}\! \left(x , y_{0}\right) = F_{120}\! \left(x , y_{0}\right)
F_{120}\! \left(x , y_{0}\right) = F_{121}\! \left(x , y_{0}\right) F_{27}\! \left(x \right)
F_{121}\! \left(x , y_{0}\right) = -\frac{-y_{0} F_{122}\! \left(x , y_{0}\right)+F_{122}\! \left(x , 1\right)}{-1+y_{0}}
F_{122}\! \left(x , y_{0}\right) = F_{123}\! \left(x , y_{0}\right)+F_{134}\! \left(x , y_{0}\right)
F_{123}\! \left(x , y_{0}\right) = F_{124}\! \left(x , y_{0}\right) F_{9}\! \left(x \right)
F_{124}\! \left(x , y_{0}\right) = F_{125}\! \left(x , y_{0}\right)+F_{87}\! \left(x , y_{0}\right)
F_{125}\! \left(x , y_{0}\right) = F_{126}\! \left(x , y_{0}\right) F_{27}\! \left(x \right)
F_{126}\! \left(x , y_{0}\right) = F_{127}\! \left(x , y_{0}\right)+F_{130}\! \left(x , y_{0}\right)
F_{127}\! \left(x , y_{0}\right) = F_{128}\! \left(x , 1, y_{0}\right)
F_{128}\! \left(x , y_{0}, y_{1}\right) = F_{129}\! \left(x , y_{0}, 1, y_{1}\right)
F_{129}\! \left(x , y_{0}, y_{1}, y_{2}\right) = \frac{y_{1} F_{88}\! \left(x , y_{0}, y_{1}\right)-y_{2} F_{88}\! \left(x , y_{0}, y_{2}\right)}{-y_{2}+y_{1}}
F_{130}\! \left(x , y_{0}\right) = F_{131}\! \left(x , 1, y_{0}\right)
F_{131}\! \left(x , y_{0}, y_{1}\right) = F_{132}\! \left(x , y_{0}, y_{1}\right) F_{27}\! \left(x \right)
F_{132}\! \left(x , y_{0}, y_{1}\right) = -\frac{-y_{1} F_{133}\! \left(x , y_{0}, y_{1}\right)+F_{133}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}
F_{133}\! \left(x , y_{0}, y_{1}\right) = F_{128}\! \left(x , y_{0}, y_{1}\right)+F_{131}\! \left(x , y_{0}, y_{1}\right)
F_{134}\! \left(x , y_{0}\right) = F_{135}\! \left(x , y_{0}\right)+F_{140}\! \left(x , y_{0}\right)+F_{20}\! \left(x \right)
F_{135}\! \left(x , y_{0}\right) = F_{136}\! \left(x , y_{0}\right)
F_{136}\! \left(x , y_{0}\right) = F_{137}\! \left(x , y_{0}\right) F_{27}\! \left(x \right)
F_{137}\! \left(x , y_{0}\right) = F_{122}\! \left(x , y_{0}\right)+F_{138}\! \left(x , y_{0}\right)
F_{138}\! \left(x , y_{0}\right) = F_{139}\! \left(x , y_{0}\right)
F_{139}\! \left(x , y_{0}\right) = F_{117}\! \left(x \right) F_{124}\! \left(x , y_{0}\right) F_{27}\! \left(x \right) F_{9}\! \left(x \right)
F_{140}\! \left(x , y_{0}\right) = F_{141}\! \left(x , y_{0}\right)
F_{141}\! \left(x , y_{0}\right) = F_{19}\! \left(x \right) F_{27}\! \left(x \right) F_{87}\! \left(x , y_{0}\right) F_{9}\! \left(x \right)
F_{142}\! \left(x , y_{0}\right) = F_{143}\! \left(x , y_{0}\right)
F_{143}\! \left(x , y_{0}\right) = F_{100}\! \left(x , y_{0}\right) F_{11}\! \left(x , y_{0}\right)
F_{144}\! \left(x , y_{0}\right) = F_{145}\! \left(x , y_{0}\right)+F_{158}\! \left(x , y_{0}\right)
F_{145}\! \left(x , y_{0}\right) = F_{146}\! \left(x , y_{0}\right)+F_{150}\! \left(x , y_{0}\right)+F_{157}\! \left(x , y_{0}\right)+F_{20}\! \left(x \right)
F_{146}\! \left(x , y_{0}\right) = F_{147}\! \left(x , y_{0}\right) F_{27}\! \left(x \right)
F_{147}\! \left(x , y_{0}\right) = F_{145}\! \left(x , y_{0}\right)+F_{148}\! \left(x , y_{0}\right)
F_{148}\! \left(x , y_{0}\right) = F_{149}\! \left(x , y_{0}\right)
F_{149}\! \left(x , y_{0}\right) = F_{10}\! \left(x \right) F_{117}\! \left(x \right) F_{124}\! \left(x , y_{0}\right) F_{13}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right)
F_{150}\! \left(x , y_{0}\right) = F_{151}\! \left(x , y_{0}\right) F_{27}\! \left(x \right)
F_{151}\! \left(x , y_{0}\right) = F_{152}\! \left(x , y_{0}\right)
F_{152}\! \left(x , y_{0}\right) = F_{14}\! \left(x , y_{0}\right) F_{153}\! \left(x , y_{0}\right) F_{9}\! \left(x \right)
F_{153}\! \left(x , y_{0}\right) = F_{154}\! \left(x , y_{0}\right)+F_{156}\! \left(x , y_{0}\right)
F_{154}\! \left(x , y_{0}\right) = F_{155}\! \left(x , y_{0}\right)
F_{155}\! \left(x , y_{0}\right) = F_{126}\! \left(x , y_{0}\right) F_{13}\! \left(x , y_{0}\right)
F_{156}\! \left(x , y_{0}\right) = F_{53}\! \left(x , y_{0}\right) F_{87}\! \left(x , y_{0}\right)
F_{157}\! \left(x , y_{0}\right) = F_{118}\! \left(x , 1, y_{0}\right)
F_{158}\! \left(x , y_{0}\right) = F_{159}\! \left(x , y_{0}\right)
F_{159}\! \left(x , y_{0}\right) = F_{13}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right) F_{160}\! \left(x , y_{0}\right)
F_{160}\! \left(x , y_{0}\right) = \frac{y_{0} \left(F_{111}\! \left(x , 1, y_{0}\right)-F_{111}\! \left(x , \frac{1}{y_{0}}, y_{0}\right)\right)}{-1+y_{0}}
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right) F_{27}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)+F_{165}\! \left(x \right)
F_{164}\! \left(x \right) = F_{97}\! \left(x , 1\right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right) F_{27}\! \left(x \right)
F_{167}\! \left(x \right) = F_{122}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_27(x)*F_3(x))
Eq(F_3(x), F_37(x) + F_4(x))
Eq(F_4(x), F_1(x) + F_5(x))
Eq(F_5(x), F_27(x)*F_6(x))
Eq(F_6(x), F_4(x) + F_7(x))
Eq(F_7(x), F_27(x)*F_8(x))
Eq(F_8(x), F_15(x) + F_7(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x, 1))
Eq(F_11(x, k_0), F_12(x, k_0))
Eq(F_12(x, k_0), F_13(x, k_0)*F_14(x, k_0))
Eq(F_13(x, k_0), F_1(x) + F_11(x, k_0))
Eq(F_14(x, k_0), k_0*x)
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_27(x)*F_9(x))
Eq(F_17(x), F_18(x) + F_32(x))
Eq(F_18(x), F_19(x) + F_9(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_30(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_22(x, 1))
Eq(F_22(x, k_0), F_23(x, k_0)*F_27(x))
Eq(F_23(x, k_0), F_24(x, k_0) + F_9(x))
Eq(F_24(x, k_0), F_11(x, k_0) + F_25(x, k_0))
Eq(F_25(x, k_0), F_20(x) + F_26(x, k_0) + F_28(x, k_0))
Eq(F_26(x, k_0), F_24(x, k_0)*F_27(x))
Eq(F_27(x), F_14(x, 1))
Eq(F_28(x, k_0), F_14(x, k_0)*F_29(x, k_0))
Eq(F_29(x, k_0), F_10(x) + F_25(x, k_0))
Eq(F_30(x), F_31(x, 1))
Eq(F_31(x, k_0), F_14(x, k_0)*F_29(x, k_0))
Eq(F_32(x), F_10(x) + F_33(x))
Eq(F_33(x), F_20(x) + F_34(x) + F_35(x))
Eq(F_34(x), F_27(x)*F_32(x))
Eq(F_35(x), F_27(x)*F_36(x))
Eq(F_36(x), F_10(x) + F_33(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_27(x)*F_39(x))
Eq(F_39(x), F_161(x) + F_40(x))
Eq(F_40(x), F_41(x, 1))
Eq(F_41(x, k_0), F_42(x, k_0) + F_83(x, k_0))
Eq(F_42(x, k_0), F_1(x) + F_43(x, k_0) + F_82(x, k_0))
Eq(F_43(x, k_0), F_27(x)*F_44(x, k_0))
Eq(F_44(x, k_0), F_42(x, k_0) + F_45(x, k_0))
Eq(F_45(x, k_0), F_20(x) + F_46(x, k_0) + F_64(x, k_0) + F_81(x, k_0))
Eq(F_46(x, k_0), F_27(x)*F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0) + F_53(x, k_0))
Eq(F_48(x, k_0), F_13(x, k_0) + F_49(x, k_0))
Eq(F_49(x, k_0), F_10(x) + F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0))
Eq(F_51(x, k_0), F_27(x)*F_52(x, k_0))
Eq(F_52(x, k_0), F_11(x, k_0) + F_50(x, k_0))
Eq(F_53(x, k_0), F_29(x, k_0) + F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x) + F_59(x, k_0))
Eq(F_55(x), F_20(x) + F_56(x) + F_58(x))
Eq(F_56(x), F_27(x)*F_57(x))
Eq(F_57(x), F_10(x) + F_55(x))
Eq(F_58(x), F_19(x)*F_27(x))
Eq(F_59(x, k_0), 2*F_20(x) + F_60(x, k_0) + F_62(x, k_0))
Eq(F_60(x, k_0), F_27(x)*F_61(x, k_0))
Eq(F_61(x, k_0), F_50(x, k_0) + F_59(x, k_0))
Eq(F_62(x, k_0), F_27(x)*F_63(x, k_0))
Eq(F_63(x, k_0), F_25(x, k_0) + F_59(x, k_0))
Eq(F_64(x, k_0), F_27(x)*F_65(x, k_0))
Eq(F_65(x, k_0), (k_0*F_66(x, k_0) - F_66(x, 1))/(k_0 - 1))
Eq(F_66(x, k_0), 2*F_20(x) + F_67(x, k_0) + F_79(x, k_0))
Eq(F_67(x, k_0), F_27(x)*F_68(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0) + F_71(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_13(x, k_0)*F_9(x))
Eq(F_71(x, k_0), F_49(x, k_0) + F_72(x, k_0))
Eq(F_72(x, k_0), F_55(x) + F_73(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0))
Eq(F_74(x, k_0), F_27(x)*F_75(x, k_0))
Eq(F_75(x, k_0), F_73(x, k_0) + F_76(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0))
Eq(F_77(x, k_0), F_14(x, k_0)*F_78(x, k_0))
Eq(F_78(x, k_0), F_10(x) + F_76(x, k_0))
Eq(F_79(x, k_0), F_27(x)*F_80(x, k_0))
Eq(F_80(x, k_0), F_65(x, k_0))
Eq(F_81(x, k_0), F_14(x, k_0)*F_45(x, k_0))
Eq(F_82(x, k_0), F_14(x, k_0)*F_23(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0))
Eq(F_84(x, k_0), F_27(x)*F_85(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0) + F_91(x, k_0))
Eq(F_86(x, k_0), F_13(x, k_0)*F_87(x, k_0))
Eq(F_87(x, k_0), F_88(x, 1, k_0))
Eq(F_88(x, k_0, k_1), F_89(x, k_0, k_1) + F_90(x, k_0, k_1))
Eq(F_89(x, k_0, k_1), (-k_0*F_42(x, k_0) + k_1*F_42(x, k_1))/(-k_0 + k_1))
Eq(F_90(x, k_0, k_1), (-k_0*F_83(x, k_0) + k_1*F_83(x, k_1))/(-k_0 + k_1))
Eq(F_91(x, k_0), F_92(x, k_0))
Eq(F_92(x, k_0), F_27(x)*F_93(x, k_0))
Eq(F_93(x, k_0), F_144(x, k_0) + F_94(x, k_0))
Eq(F_94(x, k_0), F_142(x, k_0) + F_95(x, k_0))
Eq(F_95(x, k_0), F_119(x, k_0) + F_96(x, k_0))
Eq(F_96(x, k_0), (k_0*F_97(x, k_0) - F_97(x, 1))/(k_0 - 1))
Eq(F_97(x, k_0), F_87(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_27(x))
Eq(F_100(x, k_0), F_101(x, 1, k_0))
Eq(F_101(x, k_0, k_1), F_102(x, k_1) + F_110(x, k_0, k_1))
Eq(F_102(x, k_0), F_103(x, 1, k_0))
Eq(F_103(x, k_0, k_1), F_104(x, k_0, k_1) + F_105(x, k_0, k_1))
Eq(F_104(x, k_0, k_1), (-k_0*F_87(x, k_0) + k_1*F_87(x, k_1))/(-k_0 + k_1))
Eq(F_105(x, k_0, k_1), F_106(x, k_0, k_1))
Eq(F_106(x, k_0, k_1), F_107(x, k_0, k_1)*F_27(x))
Eq(F_107(x, k_0, k_1), F_108(x, k_0, k_1) + F_109(x, k_1))
Eq(F_108(x, k_0, k_1), (k_0*F_103(x, k_0, k_1) - F_103(x, 1, k_1))/(k_0 - 1))
Eq(F_109(x, k_0), F_110(x, 1, k_0))
Eq(F_111(x, k_0, k_1), F_110(x, k_0*k_1, k_1))
Eq(F_111(x, k_0, k_1), F_112(x, k_0, k_1) + F_118(x, k_0, k_1) + F_20(x))
Eq(F_112(x, k_0, k_1), F_113(x, k_0, k_1)*F_27(x))
Eq(F_113(x, k_0, k_1), F_111(x, k_0, k_1) + F_114(x, k_0, k_1))
Eq(F_114(x, k_0, k_1), F_115(x, k_1)*F_41(x, k_1))
Eq(F_115(x, k_0), F_116(x, k_0))
Eq(F_116(x, k_0), F_10(x)*F_117(x)*F_13(x, k_0)*F_14(x, k_0))
Eq(F_117(x), F_36(x) + F_9(x))
Eq(F_118(x, k_0, k_1), F_14(x, k_1)*F_23(x, k_1)*F_87(x, k_1))
Eq(F_119(x, k_0), F_120(x, k_0))
Eq(F_120(x, k_0), F_121(x, k_0)*F_27(x))
Eq(F_121(x, k_0), (k_0*F_122(x, k_0) - F_122(x, 1))/(k_0 - 1))
Eq(F_122(x, k_0), F_123(x, k_0) + F_134(x, k_0))
Eq(F_123(x, k_0), F_124(x, k_0)*F_9(x))
Eq(F_124(x, k_0), F_125(x, k_0) + F_87(x, k_0))
Eq(F_125(x, k_0), F_126(x, k_0)*F_27(x))
Eq(F_126(x, k_0), F_127(x, k_0) + F_130(x, k_0))
Eq(F_127(x, k_0), F_128(x, 1, k_0))
Eq(F_128(x, k_0, k_1), F_129(x, k_0, 1, k_1))
Eq(F_129(x, k_0, k_1, k_2), (-k_1*F_88(x, k_0, k_1) + k_2*F_88(x, k_0, k_2))/(-k_1 + k_2))
Eq(F_130(x, k_0), F_131(x, 1, k_0))
Eq(F_131(x, k_0, k_1), F_132(x, k_0, k_1)*F_27(x))
Eq(F_132(x, k_0, k_1), (k_1*F_133(x, k_0, k_1) - F_133(x, k_0, 1))/(k_1 - 1))
Eq(F_133(x, k_0, k_1), F_128(x, k_0, k_1) + F_131(x, k_0, k_1))
Eq(F_134(x, k_0), F_135(x, k_0) + F_140(x, k_0) + F_20(x))
Eq(F_135(x, k_0), F_136(x, k_0))
Eq(F_136(x, k_0), F_137(x, k_0)*F_27(x))
Eq(F_137(x, k_0), F_122(x, k_0) + F_138(x, k_0))
Eq(F_138(x, k_0), F_139(x, k_0))
Eq(F_139(x, k_0), F_117(x)*F_124(x, k_0)*F_27(x)*F_9(x))
Eq(F_140(x, k_0), F_141(x, k_0))
Eq(F_141(x, k_0), F_19(x)*F_27(x)*F_87(x, k_0)*F_9(x))
Eq(F_142(x, k_0), F_143(x, k_0))
Eq(F_143(x, k_0), F_100(x, k_0)*F_11(x, k_0))
Eq(F_144(x, k_0), F_145(x, k_0) + F_158(x, k_0))
Eq(F_145(x, k_0), F_146(x, k_0) + F_150(x, k_0) + F_157(x, k_0) + F_20(x))
Eq(F_146(x, k_0), F_147(x, k_0)*F_27(x))
Eq(F_147(x, k_0), F_145(x, k_0) + F_148(x, k_0))
Eq(F_148(x, k_0), F_149(x, k_0))
Eq(F_149(x, k_0), F_10(x)*F_117(x)*F_124(x, k_0)*F_13(x, k_0)*F_14(x, k_0))
Eq(F_150(x, k_0), F_151(x, k_0)*F_27(x))
Eq(F_151(x, k_0), F_152(x, k_0))
Eq(F_152(x, k_0), F_14(x, k_0)*F_153(x, k_0)*F_9(x))
Eq(F_153(x, k_0), F_154(x, k_0) + F_156(x, k_0))
Eq(F_154(x, k_0), F_155(x, k_0))
Eq(F_155(x, k_0), F_126(x, k_0)*F_13(x, k_0))
Eq(F_156(x, k_0), F_53(x, k_0)*F_87(x, k_0))
Eq(F_157(x, k_0), F_118(x, 1, k_0))
Eq(F_158(x, k_0), F_159(x, k_0))
Eq(F_159(x, k_0), F_13(x, k_0)*F_14(x, k_0)*F_160(x, k_0))
Eq(F_160(x, k_0), -F_111(x, 1/k_0, k_0) + (k_0*F_111(x, 1, k_0) - F_111(x, 1/k_0, k_0))/(k_0 - 1))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_163(x)*F_27(x))
Eq(F_163(x), F_164(x) + F_165(x))
Eq(F_164(x), F_97(x, 1))
Eq(F_165(x), F_166(x))
Eq(F_166(x), F_167(x)*F_27(x))
Eq(F_167(x), F_122(x, 1))
Pack JSON:
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Specification JSON:
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{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}
Specification 4
Strategy pack name: point_and_row_and_col_placements_tracked_fusion_req_corrob
Tree: http://permpal.com/tree/196/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[0,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[121,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[4,x]
F[12,x] = F[13,x,1]
F[13,x,k[0]] = F[14,x]+F[16,x,k[0]]
F[14,x] = 1/F[4,x]*F[15,x]
F[15,x] = F[6,x]
F[16,x,k[0]] = F[17,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]*F[30,x,k[0]]
F[19,x,k[0]] = F[18,x,k[0]]*F[30,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[21,x,k[0]] = F[14,x]+F[20,x,k[0]]
F[22,x,k[0]] = F[21,x,k[0]]*F[30,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]
F[24,x,k[0]] = F[23,x,k[0]]+F[5,x]
F[24,x,k[0]] = F[25,x,k[0]]+F[31,x,k[0]]
F[25,x,k[0]] = F[0,x]+F[26,x,k[0]]
F[26,x,k[0]] = F[27,x]+F[28,x,k[0]]+F[29,x,k[0]]
F[27,x] = 0
F[28,x,k[0]] = F[23,x,k[0]]*F[4,x]
F[29,x,k[0]] = F[25,x,k[0]]*F[30,x,k[0]]
F[30,x,k[0]] = k[0]*x
F[31,x,k[0]] = F[32,x,k[0]]
F[32,x,k[0]] = F[33,x,k[0]]*F[4,x]
F[33,x,k[0]] = F[120,x,k[0]]+F[34,x,k[0]]
F[34,x,k[0]] = F[35,x,k[0]]+F[83,x,k[0]]
F[36,x,k[0]] = F[35,x,k[0]]+F[80,x,k[0]]
F[36,x,k[0]] = F[37,x,k[0]]+F[41,x,k[0]]+F[61,x,k[0]]+F[62,x,k[0]]
F[37,x,k[0]] = F[0,x]*F[38,x,k[0]]
F[38,x,k[0]] = F[1,x]+F[39,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[30,x,k[0]]*F[38,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]
F[42,x,k[0]] = F[38,x,k[0]]*F[4,x]*F[43,x,k[0]]
F[43,x,k[0]] = 1/(-1+k[0])*(F[44,x,k[0]]*k[0]-F[44,x,1])
F[44,x,k[0]] = F[45,x]+F[54,x,k[0]]
F[45,x] = 1/F[4,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = 1/F[4,x]*F[50,x]
F[50,x] = F[51,x]
F[51,x] = -F[0,x]+F[52,x]
F[52,x] = 1/F[4,x]*F[53,x]
F[53,x] = F[2,x]
F[55,x,k[0]] = F[4,x]*F[54,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[57,x,k[0]] = F[27,x]+F[56,x,k[0]]+F[60,x,k[0]]
F[57,x,k[0]] = F[26,x,k[0]]+F[58,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = F[16,x,k[0]]*F[4,x]
F[60,x,k[0]] = F[26,x,k[0]]
F[61,x,k[0]] = F[31,x,k[0]]
F[62,x,k[0]] = F[30,x,k[0]]*F[38,x,k[0]]*F[63,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]+F[78,x,k[0]]
F[64,x,k[0]] = F[65,x]+F[71,x,k[0]]
F[65,x] = F[1,x]+F[66,x]+F[70,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[5,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[12,x]*F[4,x]
F[70,x] = F[4,x]*F[65,x]
F[71,x,k[0]] = F[72,x,k[0]]
F[72,x,k[0]] = F[30,x,k[0]]*F[73,x,k[0]]
F[73,x,k[0]] = F[65,x]+F[74,x,k[0]]+F[76,x,k[0]]+F[77,x,k[0]]
F[74,x,k[0]] = F[4,x]*F[75,x,k[0]]
F[75,x,k[0]] = 1/(-1+k[0])*(F[21,x,k[0]]*k[0]-F[21,x,1])
F[76,x,k[0]] = F[4,x]*F[73,x,k[0]]
F[77,x,k[0]] = F[30,x,k[0]]*F[73,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]
F[79,x,k[0]] = F[13,x,k[0]]*F[4,x]
F[80,x,k[0]] = F[39,x,k[0]]*F[81,x,k[0]]
F[81,x,k[0]] = F[64,x,k[0]]+F[82,x,k[0]]
F[82,x,k[0]] = 1/(-1+k[0])*(F[78,x,k[0]]*k[0]-F[78,x,1])
F[83,x,k[0]] = F[4,x]*F[84,x,k[0]]
F[84,x,k[0]] = 1/(-1+k[0])*(F[85,x,k[0]]*k[0]-F[85,x,1])
F[85,x,k[0]] = F[102,x,k[0]]+F[86,x]
F[86,x] = F[87,x]+F[92,x]
F[87,x] = F[88,x]*F[91,x]
F[88,x] = F[1,x]+F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[4,x]*F[88,x]
F[91,x] = F[0,x]+F[47,x]
F[92,x] = F[93,x]+F[94,x]
F[93,x] = F[57,x,1]
F[94,x] = F[95,x]
F[95,x] = F[4,x]*F[96,x]
F[96,x] = F[92,x]+F[97,x]
F[97,x] = F[98,x,1]
F[98,x,k[0]] = F[100,x,k[0]]+F[99,x,k[0]]
F[99,x,k[0]] = -k[0]*(F[57,x,1]-F[57,x,k[0]])/(-1+k[0])
F[100,x,k[0]] = F[101,x,k[0]]*F[4,x]
F[101,x,k[0]] = -k[0]*(F[98,x,1]-F[98,x,k[0]])/(-1+k[0])
F[102,x,k[0]] = F[103,x,k[0]]+F[104,x,k[0]]+F[57,x,k[0]]
F[103,x,k[0]] = F[102,x,k[0]]*F[4,x]
F[104,x,k[0]] = F[105,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]*F[4,x]
F[106,x,k[0]] = F[107,x,k[0]]+F[110,x,k[0]]
F[108,x,k[0]] = F[107,x,k[0]]*F[4,x]
F[98,x,k[0]] = F[108,x,k[0]]+F[109,x,k[0]]+F[57,x,k[0]]
F[109,x,k[0]] = F[4,x]*F[98,x,k[0]]
F[111,x,k[0]] = F[110,x,k[0]]+F[114,x,k[0]]
F[112,x,k[0]] = F[111,x,k[0]]*F[4,x]
F[112,x,k[0]] = F[113,x,k[0]]
F[71,x,k[0]] = F[113,x,k[0]]+F[26,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]+F[119,x,k[0]]+F[26,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]*F[4,x]
F[117,x,k[0]] = F[116,x,k[0]]*F[4,x]
F[118,x,k[0]] = F[117,x,k[0]]+F[23,x,k[0]]
F[118,x,k[0]] = -k[0]*(F[23,x,1]-F[23,x,k[0]])/(-1+k[0])
F[119,x,k[0]] = F[114,x,k[0]]*F[4,x]
F[120,x,k[0]] = F[39,x,k[0]]*F[85,x,k[0]]
F[121,x] = F[122,x]
F[122,x] = F[123,x]*F[4,x]
F[123,x] = F[85,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{0}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{121}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{5}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x , 1\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{16}\! \left(x , y\right)
F_{14}\! \left(x \right) = \frac{F_{15}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{15}\! \left(x \right) = F_{6}\! \left(x \right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{20}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{5}\! \left(x \right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{28}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{27}\! \left(x \right) = 0
F_{28}\! \left(x , y\right) = F_{23}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{29}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = y x
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{33}\! \left(x , y\right) = F_{120}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{35}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)+F_{41}\! \left(x , y\right)+F_{61}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{38}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{38}\! \left(x , y\right) F_{4}\! \left(x \right) F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = -\frac{-y F_{44}\! \left(x , y\right)+F_{44}\! \left(x , 1\right)}{-1+y}
F_{44}\! \left(x , y\right) = F_{45}\! \left(x \right)+F_{54}\! \left(x , y\right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = \frac{F_{50}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = \frac{F_{53}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{53}\! \left(x \right) = F_{2}\! \left(x \right)
F_{55}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{54}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{56}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{60}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{38}\! \left(x , y\right) F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x \right)+F_{71}\! \left(x , y\right)
F_{65}\! \left(x \right) = F_{1}\! \left(x \right)+F_{66}\! \left(x \right)+F_{70}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{5}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{65}\! \left(x \right)+F_{74}\! \left(x , y\right)+F_{76}\! \left(x , y\right)+F_{77}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = -\frac{-y F_{21}\! \left(x , y\right)+F_{21}\! \left(x , 1\right)}{-1+y}
F_{76}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{73}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{73}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{80}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = -\frac{-y F_{78}\! \left(x , y\right)+F_{78}\! \left(x , 1\right)}{-1+y}
F_{83}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = -\frac{-y F_{85}\! \left(x , y\right)+F_{85}\! \left(x , 1\right)}{-1+y}
F_{85}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{92}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right) F_{91}\! \left(x \right)
F_{88}\! \left(x \right) = F_{1}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{91}\! \left(x \right) = F_{0}\! \left(x \right)+F_{47}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{94}\! \left(x \right)
F_{93}\! \left(x \right) = F_{57}\! \left(x , 1\right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{92}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x , 1\right)
F_{98}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = -\frac{y \left(F_{57}\! \left(x , 1\right)-F_{57}\! \left(x , y\right)\right)}{-1+y}
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{101}\! \left(x , y\right) = -\frac{y \left(F_{98}\! \left(x , 1\right)-F_{98}\! \left(x , y\right)\right)}{-1+y}
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{104}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{102}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)+F_{110}\! \left(x , y\right)
F_{108}\! \left(x , y\right) = F_{107}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{98}\! \left(x , y\right) = F_{108}\! \left(x , y\right)+F_{109}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{98}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{114}\! \left(x , y\right)
F_{112}\! \left(x , y\right) = F_{111}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right)+F_{119}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{117}\! \left(x , y\right) = F_{116}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{118}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{23}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = -\frac{y \left(F_{23}\! \left(x , 1\right)-F_{23}\! \left(x , y\right)\right)}{-1+y}
F_{119}\! \left(x , y\right) = F_{114}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{120}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{85}\! \left(x , y\right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{4}\! \left(x \right)
F_{123}\! \left(x \right) = F_{85}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_0(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_121(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_4(x))
Eq(F_12(x), F_13(x, 1))
Eq(F_13(x, k_0), F_14(x) + F_16(x, k_0))
Eq(F_14(x), F_15(x)/F_4(x))
Eq(F_15(x), F_6(x))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0)*F_30(x, k_0))
Eq(F_19(x, k_0), F_18(x, k_0)*F_30(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_21(x, k_0), F_14(x) + F_20(x, k_0))
Eq(F_22(x, k_0), F_21(x, k_0)*F_30(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0))
Eq(F_24(x, k_0), F_23(x, k_0) + F_5(x))
Eq(F_24(x, k_0), F_25(x, k_0) + F_31(x, k_0))
Eq(F_25(x, k_0), F_0(x) + F_26(x, k_0))
Eq(F_26(x, k_0), F_27(x) + F_28(x, k_0) + F_29(x, k_0))
Eq(F_27(x), 0)
Eq(F_28(x, k_0), F_23(x, k_0)*F_4(x))
Eq(F_29(x, k_0), F_25(x, k_0)*F_30(x, k_0))
Eq(F_30(x, k_0), k_0*x)
Eq(F_31(x, k_0), F_32(x, k_0))
Eq(F_32(x, k_0), F_33(x, k_0)*F_4(x))
Eq(F_33(x, k_0), F_120(x, k_0) + F_34(x, k_0))
Eq(F_34(x, k_0), F_35(x, k_0) + F_83(x, k_0))
Eq(F_36(x, k_0), F_35(x, k_0) + F_80(x, k_0))
Eq(F_36(x, k_0), F_37(x, k_0) + F_41(x, k_0) + F_61(x, k_0) + F_62(x, k_0))
Eq(F_37(x, k_0), F_0(x)*F_38(x, k_0))
Eq(F_38(x, k_0), F_1(x) + F_39(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_30(x, k_0)*F_38(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0))
Eq(F_42(x, k_0), F_38(x, k_0)*F_4(x)*F_43(x, k_0))
Eq(F_43(x, k_0), (k_0*F_44(x, k_0) - F_44(x, 1))/(k_0 - 1))
Eq(F_44(x, k_0), F_45(x) + F_54(x, k_0))
Eq(F_45(x), F_46(x)/F_4(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x)/F_4(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), -F_0(x) + F_52(x))
Eq(F_52(x), F_53(x)/F_4(x))
Eq(F_53(x), F_2(x))
Eq(F_55(x, k_0), F_4(x)*F_54(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_57(x, k_0), F_27(x) + F_56(x, k_0) + F_60(x, k_0))
Eq(F_57(x, k_0), F_26(x, k_0) + F_58(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), F_16(x, k_0)*F_4(x))
Eq(F_60(x, k_0), F_26(x, k_0))
Eq(F_61(x, k_0), F_31(x, k_0))
Eq(F_62(x, k_0), F_30(x, k_0)*F_38(x, k_0)*F_63(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0) + F_78(x, k_0))
Eq(F_64(x, k_0), F_65(x) + F_71(x, k_0))
Eq(F_65(x), F_1(x) + F_66(x) + F_70(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_5(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_12(x)*F_4(x))
Eq(F_70(x), F_4(x)*F_65(x))
Eq(F_71(x, k_0), F_72(x, k_0))
Eq(F_72(x, k_0), F_30(x, k_0)*F_73(x, k_0))
Eq(F_73(x, k_0), F_65(x) + F_74(x, k_0) + F_76(x, k_0) + F_77(x, k_0))
Eq(F_74(x, k_0), F_4(x)*F_75(x, k_0))
Eq(F_75(x, k_0), (k_0*F_21(x, k_0) - F_21(x, 1))/(k_0 - 1))
Eq(F_76(x, k_0), F_4(x)*F_73(x, k_0))
Eq(F_77(x, k_0), F_30(x, k_0)*F_73(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0))
Eq(F_79(x, k_0), F_13(x, k_0)*F_4(x))
Eq(F_80(x, k_0), F_39(x, k_0)*F_81(x, k_0))
Eq(F_81(x, k_0), F_64(x, k_0) + F_82(x, k_0))
Eq(F_82(x, k_0), (k_0*F_78(x, k_0) - F_78(x, 1))/(k_0 - 1))
Eq(F_83(x, k_0), F_4(x)*F_84(x, k_0))
Eq(F_84(x, k_0), (k_0*F_85(x, k_0) - F_85(x, 1))/(k_0 - 1))
Eq(F_85(x, k_0), F_102(x, k_0) + F_86(x))
Eq(F_86(x), F_87(x) + F_92(x))
Eq(F_87(x), F_88(x)*F_91(x))
Eq(F_88(x), F_1(x) + F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_4(x)*F_88(x))
Eq(F_91(x), F_0(x) + F_47(x))
Eq(F_92(x), F_93(x) + F_94(x))
Eq(F_93(x), F_57(x, 1))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_4(x)*F_96(x))
Eq(F_96(x), F_92(x) + F_97(x))
Eq(F_97(x), F_98(x, 1))
Eq(F_98(x, k_0), F_100(x, k_0) + F_99(x, k_0))
Eq(F_99(x, k_0), -F_57(x, 1) + (k_0*F_57(x, k_0) - F_57(x, 1))/(k_0 - 1))
Eq(F_100(x, k_0), F_101(x, k_0)*F_4(x))
Eq(F_101(x, k_0), -F_98(x, 1) + (k_0*F_98(x, k_0) - F_98(x, 1))/(k_0 - 1))
Eq(F_102(x, k_0), F_103(x, k_0) + F_104(x, k_0) + F_57(x, k_0))
Eq(F_103(x, k_0), F_102(x, k_0)*F_4(x))
Eq(F_104(x, k_0), F_105(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0)*F_4(x))
Eq(F_106(x, k_0), F_107(x, k_0) + F_110(x, k_0))
Eq(F_108(x, k_0), F_107(x, k_0)*F_4(x))
Eq(F_98(x, k_0), F_108(x, k_0) + F_109(x, k_0) + F_57(x, k_0))
Eq(F_109(x, k_0), F_4(x)*F_98(x, k_0))
Eq(F_111(x, k_0), F_110(x, k_0) + F_114(x, k_0))
Eq(F_112(x, k_0), F_111(x, k_0)*F_4(x))
Eq(F_112(x, k_0), F_113(x, k_0))
Eq(F_71(x, k_0), F_113(x, k_0) + F_26(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0) + F_119(x, k_0) + F_26(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0)*F_4(x))
Eq(F_117(x, k_0), F_116(x, k_0)*F_4(x))
Eq(F_118(x, k_0), F_117(x, k_0) + F_23(x, k_0))
Eq(F_118(x, k_0), -F_23(x, 1) + (k_0*F_23(x, k_0) - F_23(x, 1))/(k_0 - 1))
Eq(F_119(x, k_0), F_114(x, k_0)*F_4(x))
Eq(F_120(x, k_0), F_39(x, k_0)*F_85(x, k_0))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x)*F_4(x))
Eq(F_123(x), F_85(x, 1))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}], "iterative": false, "name": "point_and_row_and_col_placements_tracked_fusion_req_corrob", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, "rule_class": "ReverseRule"}, {"class_module": "comb_spec_searcher.strategies.rule", "idx": 0, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 1], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 1], [1, 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[[2, 3], [2, 3]]}, {"patt": [1, 0], "pos": [[2, 3], [4, 3]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[4, 3], [4, 3]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [4, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [2, 0], [4, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 1], [2, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[4, 0], [4, 3], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [4, 0], [4, 3], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 1], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [4, 0], [4, 3], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 0], [4, 0], [4, 3], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[4, 3]]}], [{"patt": [0], "pos": [[3, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}}, "rule_class": "EquivalenceRule"}]}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, "rule_class": "EquivalenceRule"}]}]}
Specification 5
Strategy pack name: insertion_point_placements_tracked_fusion
Tree: http://permpal.com/tree/197/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[29,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[6,x]+F[9,x]
F[9,x] = F[10,x]*F[4,x]
F[10,x] = F[11,x]+F[14,x]+F[9,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[4,x]
F[14,x] = F[15,x]
F[15,x] = F[11,x]*F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[24,x]
F[17,x] = F[11,x]+F[18,x]
F[18,x] = F[12,x]+F[19,x]
F[19,x] = F[20,x]+F[21,x]+F[23,x]
F[20,x] = 0
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[12,x]+F[19,x]
F[23,x] = F[18,x]*F[4,x]
F[24,x] = F[12,x]+F[25,x]
F[25,x] = F[20,x]+F[26,x]+F[28,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[12,x]+F[25,x]
F[28,x] = F[24,x]*F[4,x]
F[29,x] = F[2,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[263,x]+F[33,x]
F[33,x] = F[29,x]+F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[11,x]*F[2,x]
F[36,x] = F[37,x]+F[41,x]
F[37,x] = -F[2,x]+F[38,x]
F[38,x] = -F[0,x]+F[39,x]
F[39,x] = 1/F[4,x]*F[40,x]
F[40,x] = F[2,x]
F[41,x] = F[42,x,1]
F[43,x,k[0]] = F[37,x]+F[42,x,k[0]]
F[44,x,k[0]] = F[262,x,k[0]]+F[43,x,k[0]]
F[45,x,k[0]] = F[117,x,k[0]]+F[44,x,k[0]]
F[46,x,k[0]] = F[45,x,k[0]]*F[54,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]
F[47,x,k[0]] = F[48,x,k[0]]
F[48,x,k[0]] = F[4,x]*F[49,x,k[0]]
F[49,x,k[0]] = F[256,x,k[0]]+F[50,x,k[0]]
F[50,x,k[0]] = F[105,x,k[0]]+F[51,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]+F[56,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]*F[55,x,k[0]]
F[54,x,k[0]] = k[0]*x
F[55,x,k[0]] = F[1,x]+F[52,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[4,x]*F[58,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]+F[63,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]
F[60,x,k[0]] = F[11,x]*F[61,x,k[0]]
F[61,x,k[0]] = F[52,x,k[0]]+F[62,x,k[0]]
F[62,x,k[0]] = F[52,x,k[0]]*F[55,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]+F[94,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]+F[67,x,k[0]]
F[65,x,k[0]] = F[52,x,k[0]]*F[66,x]
F[66,x] = F[7,x]
F[67,x,k[0]] = F[55,x,k[0]]*F[68,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]
F[69,x,k[0]] = F[54,x,k[0]]*F[70,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]+F[72,x,k[0]]
F[71,x,k[0]] = F[12,x]*F[55,x,k[0]]
F[72,x,k[0]] = F[24,x]+F[73,x,k[0]]
F[74,x,k[0]] = F[73,x,k[0]]+F[93,x,k[0]]
F[75,x,k[0]] = F[54,x,k[0]]*F[74,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]
F[77,x,k[0]] = F[4,x]*F[78,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]+F[92,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]+F[83,x,k[0]]
F[80,x,k[0]] = F[76,x,k[0]]+F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]
F[82,x,k[0]] = F[52,x,k[0]]*F[54,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]+F[90,x,k[0]]
F[84,x,k[0]] = F[54,x,k[0]]*F[85,x,k[0]]
F[85,x,k[0]] = F[52,x,k[0]]+F[86,x,k[0]]
F[86,x,k[0]] = F[20,x]+F[87,x,k[0]]+F[88,x,k[0]]
F[87,x,k[0]] = F[4,x]*F[85,x,k[0]]
F[88,x,k[0]] = F[54,x,k[0]]*F[89,x,k[0]]
F[89,x,k[0]] = F[12,x]+F[86,x,k[0]]
F[90,x,k[0]] = F[81,x,k[0]]*F[91,x,k[0]]
F[91,x,k[0]] = F[55,x,k[0]]+F[89,x,k[0]]
F[92,x,k[0]] = F[24,x]*F[81,x,k[0]]
F[93,x,k[0]] = F[12,x]*F[52,x,k[0]]
F[94,x,k[0]] = F[103,x,k[0]]+F[95,x,k[0]]
F[95,x,k[0]] = F[52,x,k[0]]*F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[4,x]*F[98,x]
F[98,x] = F[102,x]+F[99,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[12,x]+F[96,x]
F[101,x] = F[12,x]*F[17,x]
F[102,x] = F[12,x]*F[24,x]
F[103,x,k[0]] = F[104,x,k[0]]*F[55,x,k[0]]
F[104,x,k[0]] = (-F[76,x,1]*k[0]+F[76,x,k[0]])/(-1+k[0])
F[105,x,k[0]] = F[106,x,k[0]]+F[47,x,k[0]]
F[106,x,k[0]] = F[107,x,k[0]]
F[107,x,k[0]] = F[108,x,k[0]]*F[4,x]
F[108,x,k[0]] = F[109,x,k[0]]+F[129,x,k[0]]
F[109,x,k[0]] = F[110,x,k[0]]+F[114,x,k[0]]
F[110,x,k[0]] = F[105,x,k[0]]+F[111,x,k[0]]
F[111,x,k[0]] = -k[0]*(F[112,x,1]-F[112,x,k[0]])/(-1+k[0])
F[112,x,k[0]] = F[113,x,k[0]]+F[42,x,k[0]]
F[113,x,k[0]] = F[2,x]*F[52,x,k[0]]
F[114,x,k[0]] = F[115,x,k[0]]*F[52,x,k[0]]
F[115,x,k[0]] = F[116,x,k[0]]+F[128,x,k[0]]
F[116,x,k[0]] = F[117,x,k[0]]+F[118,x,k[0]]
F[117,x,k[0]] = F[2,x]+F[47,x,k[0]]
F[118,x,k[0]] = F[119,x]+F[123,x,k[0]]
F[119,x] = F[120,x]
F[120,x] = F[121,x]*F[4,x]
F[121,x] = F[122,x]+F[34,x]
F[122,x] = F[119,x]+F[2,x]
F[123,x,k[0]] = F[124,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]*F[4,x]
F[125,x,k[0]] = F[114,x,k[0]]+F[126,x,k[0]]
F[126,x,k[0]] = F[111,x,k[0]]+F[127,x,k[0]]
F[127,x,k[0]] = F[123,x,k[0]]+F[47,x,k[0]]
F[128,x,k[0]] = 1/(-1+k[0])*(F[44,x,k[0]]*k[0]-F[44,x,1])
F[129,x,k[0]] = F[130,x,k[0]]+F[224,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]+F[152,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]+F[133,x,k[0]]
F[132,x,k[0]] = F[12,x]*F[47,x,k[0]]
F[133,x,k[0]] = F[134,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]*F[4,x]
F[135,x,k[0]] = F[136,x,k[0]]+F[142,x,k[0]]
F[136,x,k[0]] = F[137,x,k[0]]+F[141,x,k[0]]
F[137,x,k[0]] = (-F[138,x,1]*k[0]+F[138,x,k[0]])/(-1+k[0])
F[138,x,k[0]] = F[139,x,k[0]]
F[139,x,k[0]] = F[140,x,k[0]]*F[54,x,k[0]]
F[140,x,k[0]] = F[112,x,k[0]]+F[47,x,k[0]]
F[141,x,k[0]] = -k[0]*(F[123,x,1]-F[123,x,k[0]])/(-1+k[0])
F[142,x,k[0]] = F[143,x,k[0]]+F[145,x,k[0]]
F[143,x,k[0]] = (-F[144,x,1]*k[0]+F[144,x,k[0]])/(-1+k[0])
F[144,x,k[0]] = F[12,x]*F[138,x,k[0]]
F[145,x,k[0]] = -k[0]*(F[146,x,1]-F[146,x,k[0]])/(-1+k[0])
F[146,x,k[0]] = F[147,x,k[0]]
F[147,x,k[0]] = F[148,x,k[0]]*F[4,x]
F[148,x,k[0]] = F[149,x,k[0]]+F[214,x,k[0]]
F[149,x,k[0]] = F[150,x,k[0]]+F[212,x,k[0]]
F[150,x,k[0]] = F[151,x,k[0]]+F[152,x,k[0]]
F[151,x,k[0]] = F[132,x,k[0]]+F[146,x,k[0]]
F[152,x,k[0]] = F[153,x,k[0]]+F[155,x,k[0]]
F[153,x,k[0]] = F[154,x,k[0]]
F[154,x,k[0]] = F[2,x]*F[24,x]*F[52,x,k[0]]
F[155,x,k[0]] = F[156,x,k[0]]+F[157,x,k[0]]
F[156,x,k[0]] = F[12,x]*F[42,x,k[0]]
F[157,x,k[0]] = F[158,x,k[0]]
F[158,x,k[0]] = F[159,x,k[0]]*F[4,x]
F[159,x,k[0]] = F[160,x,k[0]]+F[208,x,k[0]]
F[160,x,k[0]] = F[161,x,k[0]]+F[207,x,k[0]]
F[161,x,k[0]] = (-F[162,x,1]*k[0]+F[162,x,k[0]])/(-1+k[0])
F[162,x,k[0]] = F[163,x,k[0]]
F[163,x,k[0]] = F[164,x,k[0]]*F[54,x,k[0]]
F[164,x,k[0]] = F[165,x,k[0]]+F[166,x,k[0]]
F[165,x,k[0]] = F[37,x]*F[52,x,k[0]]
F[167,x,k[0]] = F[166,x,k[0]]+F[171,x]
F[168,x,k[0]] = F[167,x,k[0]]+F[170,x,k[0]]
F[169,x,k[0]] = F[168,x,k[0]]*F[54,x,k[0]]
F[169,x,k[0]] = F[42,x,k[0]]
F[170,x,k[0]] = F[37,x]*F[55,x,k[0]]
F[171,x] = F[172,x]+F[37,x]
F[172,x] = -F[178,x]+F[173,x]
F[173,x] = -F[176,x]+F[174,x]
F[174,x] = 1/F[4,x]*F[175,x]
F[175,x] = F[37,x]
F[176,x] = F[177,x]+F[37,x]
F[177,x] = F[12,x]+F[122,x]
F[178,x] = F[179,x]+F[180,x]
F[179,x] = F[12,x]^2
F[180,x] = F[181,x]+F[37,x]
F[181,x] = F[182,x]
F[182,x] = F[183,x]*F[4,x]
F[183,x] = F[184,x]+F[190,x]
F[184,x] = F[185,x]+F[188,x]
F[185,x] = F[186,x]
F[186,x] = F[187,x]*F[4,x]
F[187,x] = F[12,x]+F[185,x]
F[188,x] = F[189,x,1]
F[189,x,k[0]] = (F[47,x,k[0]]-F[47,x,1])/(-1+k[0])
F[190,x] = F[191,x]+F[193,x]
F[191,x] = F[192,x]
F[192,x] = F[12,x]^3
F[193,x] = F[194,x,1]
F[194,x,k[0]] = (F[195,x,k[0]]-F[195,x,1])/(-1+k[0])
F[195,x,k[0]] = F[196,x,k[0]]
F[196,x,k[0]] = F[197,x,k[0]]*F[4,x]
F[197,x,k[0]] = F[198,x,k[0]]+F[203,x,k[0]]
F[198,x,k[0]] = F[199,x,k[0]]+F[202,x,k[0]]
F[199,x,k[0]] = F[200,x,k[0]]
F[200,x,k[0]] = F[201,x,k[0]]*F[4,x]
F[201,x,k[0]] = F[199,x,k[0]]+F[52,x,k[0]]
F[202,x,k[0]] = -k[0]*(F[47,x,1]-F[47,x,k[0]])/(-1+k[0])
F[203,x,k[0]] = F[204,x,k[0]]+F[206,x,k[0]]
F[204,x,k[0]] = F[205,x,k[0]]
F[205,x,k[0]] = F[12,x]^2*F[52,x,k[0]]
F[206,x,k[0]] = -k[0]*(F[195,x,1]-F[195,x,k[0]])/(-1+k[0])
F[207,x,k[0]] = -k[0]*(F[161,x,1]-F[161,x,k[0]])/(-1+k[0])
F[208,x,k[0]] = F[209,x,k[0]]+F[211,x,k[0]]
F[209,x,k[0]] = (-F[210,x,1]*k[0]+F[210,x,k[0]])/(-1+k[0])
F[210,x,k[0]] = F[12,x]*F[162,x,k[0]]
F[211,x,k[0]] = -k[0]*(F[157,x,1]-F[157,x,k[0]])/(-1+k[0])
F[212,x,k[0]] = F[213,x,k[0]]
F[213,x,k[0]] = F[115,x,k[0]]*F[12,x]*F[52,x,k[0]]
F[214,x,k[0]] = F[12,x]*F[215,x,k[0]]
F[215,x,k[0]] = F[216,x,k[0]]+F[217,x,k[0]]
F[216,x,k[0]] = -k[0]*(F[140,x,1]-F[140,x,k[0]])/(-1+k[0])
F[217,x,k[0]] = F[152,x,k[0]]+F[218,x,k[0]]
F[219,x,k[0]] = F[218,x,k[0]]+F[222,x,k[0]]
F[220,x,k[0]] = F[198,x,k[0]]+F[219,x,k[0]]
F[221,x,k[0]] = F[220,x,k[0]]*F[4,x]
F[221,x,k[0]] = F[195,x,k[0]]
F[222,x,k[0]] = F[223,x,k[0]]
F[223,x,k[0]] = F[25,x]*F[52,x,k[0]]
F[224,x,k[0]] = F[225,x,k[0]]*F[52,x,k[0]]
F[225,x,k[0]] = F[226,x,k[0]]+F[250,x,k[0]]
F[226,x,k[0]] = F[227,x,k[0]]+F[228,x,k[0]]
F[227,x,k[0]] = F[117,x,k[0]]*F[12,x]
F[228,x,k[0]] = F[146,x,k[0]]+F[229,x]
F[229,x] = F[230,x]
F[230,x] = F[231,x]*F[4,x]
F[231,x] = F[232,x]+F[248,x]
F[232,x] = F[233,x]+F[235,x]
F[233,x] = F[229,x]+F[234,x]
F[234,x] = F[12,x]*F[2,x]
F[235,x] = F[236,x]+F[237,x]
F[236,x] = F[2,x]*F[24,x]
F[237,x] = F[238,x]+F[239,x]
F[238,x] = F[12,x]*F[37,x]
F[239,x] = F[240,x]
F[240,x] = F[241,x]*F[4,x]
F[241,x] = F[242,x]+F[244,x]
F[242,x] = F[243,x,1]
F[243,x,k[0]] = (F[42,x,k[0]]*k[0]-F[42,x,1])/(-1+k[0])
F[244,x] = F[245,x]+F[246,x]
F[245,x] = F[12,x]*F[41,x]
F[246,x] = F[239,x]+F[247,x]
F[247,x] = F[157,x,1]
F[248,x] = F[12,x]*F[249,x]
F[249,x] = F[121,x]+F[232,x]
F[250,x,k[0]] = F[251,x,k[0]]+F[253,x,k[0]]
F[251,x,k[0]] = F[252,x,k[0]]
F[252,x,k[0]] = F[2,x]*F[24,x]*F[55,x,k[0]]
F[253,x,k[0]] = F[254,x,k[0]]+F[255,x,k[0]]
F[254,x,k[0]] = F[12,x]*F[43,x,k[0]]
F[255,x,k[0]] = F[157,x,k[0]]+F[239,x]
F[256,x,k[0]] = F[257,x,k[0]]*F[52,x,k[0]]
F[257,x,k[0]] = F[258,x,k[0]]+F[260,x,k[0]]
F[258,x,k[0]] = F[259,x,k[0]]+F[55,x,k[0]]
F[259,x,k[0]] = F[56,x,k[0]]+F[66,x]
F[260,x,k[0]] = F[117,x,k[0]]+F[261,x,k[0]]
F[261,x,k[0]] = F[106,x,k[0]]+F[30,x]
F[262,x,k[0]] = F[2,x]*F[55,x,k[0]]
F[263,x] = F[235,x]+F[264,x]
F[264,x] = F[234,x]+F[265,x]
F[265,x] = F[266,x]
F[266,x] = F[267,x]*F[4,x]
F[267,x] = F[263,x]+F[268,x]
F[268,x] = F[12,x]*F[269,x]
F[269,x] = F[232,x]+F[270,x]
F[270,x] = F[271,x]+F[34,x]
F[271,x] = F[122,x]+F[272,x]
F[272,x] = F[119,x]+F[273,x]
F[273,x] = F[123,x,1]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{29}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{6}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)+F_{9}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{24}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right)+F_{19}\! \left(x \right)
F_{23}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{20}\! \left(x \right)+F_{26}\! \left(x \right)+F_{28}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{12}\! \left(x \right)+F_{25}\! \left(x \right)
F_{28}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{2}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{263}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{29}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{11}\! \left(x \right) F_{2}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{41}\! \left(x \right)
F_{37}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = \frac{F_{40}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{40}\! \left(x \right) = F_{2}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x , 1\right)
F_{43}\! \left(x , y\right) = F_{37}\! \left(x \right)+F_{42}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{262}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{45}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{256}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{55}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = y x
F_{55}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{52}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{55}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{7}\! \left(x \right)
F_{67}\! \left(x , y\right) = F_{55}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{73}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{73}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{74}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{76}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{20}\! \left(x \right)+F_{87}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{85}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{54}\! \left(x , y\right) F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{12}\! \left(x \right)+F_{86}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{81}\! \left(x , y\right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{24}\! \left(x \right) F_{81}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{103}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{52}\! \left(x , y\right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{102}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{12}\! \left(x \right)+F_{96}\! \left(x \right)
F_{101}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{102}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{55}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = -\frac{F_{76}\! \left(x , 1\right) y -F_{76}\! \left(x , y\right)}{-1+y}
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{106}\! \left(x , y\right) = F_{107}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{108}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right)+F_{129}\! \left(x , y\right)
F_{109}\! \left(x , y\right) = F_{110}\! \left(x , y\right)+F_{114}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{111}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = -\frac{y \left(F_{112}\! \left(x , 1\right)-F_{112}\! \left(x , y\right)\right)}{-1+y}
F_{112}\! \left(x , y\right) = F_{113}\! \left(x , y\right)+F_{42}\! \left(x , y\right)
F_{113}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{114}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{115}\! \left(x , y\right) = F_{116}\! \left(x , y\right)+F_{128}\! \left(x , y\right)
F_{116}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{118}\! \left(x , y\right)
F_{117}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{47}\! \left(x , y\right)
F_{118}\! \left(x , y\right) = F_{119}\! \left(x \right)+F_{123}\! \left(x , y\right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{34}\! \left(x \right)
F_{122}\! \left(x \right) = F_{119}\! \left(x \right)+F_{2}\! \left(x \right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{125}\! \left(x , y\right) = F_{114}\! \left(x , y\right)+F_{126}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{127}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{123}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{128}\! \left(x , y\right) = -\frac{-y F_{44}\! \left(x , y\right)+F_{44}\! \left(x , 1\right)}{-1+y}
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{224}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{132}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{47}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = F_{134}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{136}\! \left(x , y\right)+F_{142}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{137}\! \left(x , y\right) = -\frac{F_{138}\! \left(x , 1\right) y -F_{138}\! \left(x , y\right)}{-1+y}
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{140}\! \left(x , y\right) = F_{112}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = -\frac{y \left(F_{123}\! \left(x , 1\right)-F_{123}\! \left(x , y\right)\right)}{-1+y}
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right)+F_{145}\! \left(x , y\right)
F_{143}\! \left(x , y\right) = -\frac{F_{144}\! \left(x , 1\right) y -F_{144}\! \left(x , y\right)}{-1+y}
F_{144}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{138}\! \left(x , y\right)
F_{145}\! \left(x , y\right) = -\frac{y \left(F_{146}\! \left(x , 1\right)-F_{146}\! \left(x , y\right)\right)}{-1+y}
F_{146}\! \left(x , y\right) = F_{147}\! \left(x , y\right)
F_{147}\! \left(x , y\right) = F_{148}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{148}\! \left(x , y\right) = F_{149}\! \left(x , y\right)+F_{214}\! \left(x , y\right)
F_{149}\! \left(x , y\right) = F_{150}\! \left(x , y\right)+F_{212}\! \left(x , y\right)
F_{150}\! \left(x , y\right) = F_{151}\! \left(x , y\right)+F_{152}\! \left(x , y\right)
F_{151}\! \left(x , y\right) = F_{132}\! \left(x , y\right)+F_{146}\! \left(x , y\right)
F_{152}\! \left(x , y\right) = F_{153}\! \left(x , y\right)+F_{155}\! \left(x , y\right)
F_{153}\! \left(x , y\right) = F_{154}\! \left(x , y\right)
F_{154}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{24}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{155}\! \left(x , y\right) = F_{156}\! \left(x , y\right)+F_{157}\! \left(x , y\right)
F_{156}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{42}\! \left(x , y\right)
F_{157}\! \left(x , y\right) = F_{158}\! \left(x , y\right)
F_{158}\! \left(x , y\right) = F_{159}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{159}\! \left(x , y\right) = F_{160}\! \left(x , y\right)+F_{208}\! \left(x , y\right)
F_{160}\! \left(x , y\right) = F_{161}\! \left(x , y\right)+F_{207}\! \left(x , y\right)
F_{161}\! \left(x , y\right) = -\frac{F_{162}\! \left(x , 1\right) y -F_{162}\! \left(x , y\right)}{-1+y}
F_{162}\! \left(x , y\right) = F_{163}\! \left(x , y\right)
F_{163}\! \left(x , y\right) = F_{164}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{164}\! \left(x , y\right) = F_{165}\! \left(x , y\right)+F_{166}\! \left(x , y\right)
F_{165}\! \left(x , y\right) = F_{37}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{167}\! \left(x , y\right) = F_{166}\! \left(x , y\right)+F_{171}\! \left(x \right)
F_{168}\! \left(x , y\right) = F_{167}\! \left(x , y\right)+F_{170}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{168}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{169}\! \left(x , y\right) = F_{42}\! \left(x , y\right)
F_{170}\! \left(x , y\right) = F_{37}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{37}\! \left(x \right)
F_{172}\! \left(x \right) = -F_{178}\! \left(x \right)+F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = -F_{176}\! \left(x \right)+F_{174}\! \left(x \right)
F_{174}\! \left(x \right) = \frac{F_{175}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{175}\! \left(x \right) = F_{37}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)+F_{37}\! \left(x \right)
F_{177}\! \left(x \right) = F_{12}\! \left(x \right)+F_{122}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)+F_{180}\! \left(x \right)
F_{179}\! \left(x \right) = F_{12} \left(x \right)^{2}
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)+F_{37}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right) F_{4}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{190}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{188}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right) F_{4}\! \left(x \right)
F_{187}\! \left(x \right) = F_{12}\! \left(x \right)+F_{185}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x , 1\right)
F_{189}\! \left(x , y\right) = -\frac{F_{47}\! \left(x , 1\right)-F_{47}\! \left(x , y\right)}{-1+y}
F_{190}\! \left(x \right) = F_{191}\! \left(x \right)+F_{193}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{12} \left(x \right)^{3}
F_{193}\! \left(x \right) = F_{194}\! \left(x , 1\right)
F_{194}\! \left(x , y\right) = -\frac{F_{195}\! \left(x , 1\right)-F_{195}\! \left(x , y\right)}{-1+y}
F_{195}\! \left(x , y\right) = F_{196}\! \left(x , y\right)
F_{196}\! \left(x , y\right) = F_{197}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{197}\! \left(x , y\right) = F_{198}\! \left(x , y\right)+F_{203}\! \left(x , y\right)
F_{198}\! \left(x , y\right) = F_{199}\! \left(x , y\right)+F_{202}\! \left(x , y\right)
F_{199}\! \left(x , y\right) = F_{200}\! \left(x , y\right)
F_{200}\! \left(x , y\right) = F_{201}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{201}\! \left(x , y\right) = F_{199}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{202}\! \left(x , y\right) = -\frac{y \left(F_{47}\! \left(x , 1\right)-F_{47}\! \left(x , y\right)\right)}{-1+y}
F_{203}\! \left(x , y\right) = F_{204}\! \left(x , y\right)+F_{206}\! \left(x , y\right)
F_{204}\! \left(x , y\right) = F_{205}\! \left(x , y\right)
F_{205}\! \left(x , y\right) = F_{12} \left(x \right)^{2} F_{52}\! \left(x , y\right)
F_{206}\! \left(x , y\right) = -\frac{y \left(F_{195}\! \left(x , 1\right)-F_{195}\! \left(x , y\right)\right)}{-1+y}
F_{207}\! \left(x , y\right) = -\frac{y \left(F_{161}\! \left(x , 1\right)-F_{161}\! \left(x , y\right)\right)}{-1+y}
F_{208}\! \left(x , y\right) = F_{209}\! \left(x , y\right)+F_{211}\! \left(x , y\right)
F_{209}\! \left(x , y\right) = -\frac{F_{210}\! \left(x , 1\right) y -F_{210}\! \left(x , y\right)}{-1+y}
F_{210}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{162}\! \left(x , y\right)
F_{211}\! \left(x , y\right) = -\frac{y \left(F_{157}\! \left(x , 1\right)-F_{157}\! \left(x , y\right)\right)}{-1+y}
F_{212}\! \left(x , y\right) = F_{213}\! \left(x , y\right)
F_{213}\! \left(x , y\right) = F_{115}\! \left(x , y\right) F_{12}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{214}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{215}\! \left(x , y\right)
F_{215}\! \left(x , y\right) = F_{216}\! \left(x , y\right)+F_{217}\! \left(x , y\right)
F_{216}\! \left(x , y\right) = -\frac{y \left(F_{140}\! \left(x , 1\right)-F_{140}\! \left(x , y\right)\right)}{-1+y}
F_{217}\! \left(x , y\right) = F_{152}\! \left(x , y\right)+F_{218}\! \left(x , y\right)
F_{219}\! \left(x , y\right) = F_{218}\! \left(x , y\right)+F_{222}\! \left(x , y\right)
F_{220}\! \left(x , y\right) = F_{198}\! \left(x , y\right)+F_{219}\! \left(x , y\right)
F_{221}\! \left(x , y\right) = F_{220}\! \left(x , y\right) F_{4}\! \left(x \right)
F_{221}\! \left(x , y\right) = F_{195}\! \left(x , y\right)
F_{222}\! \left(x , y\right) = F_{223}\! \left(x , y\right)
F_{223}\! \left(x , y\right) = F_{25}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{224}\! \left(x , y\right) = F_{225}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{225}\! \left(x , y\right) = F_{226}\! \left(x , y\right)+F_{250}\! \left(x , y\right)
F_{226}\! \left(x , y\right) = F_{227}\! \left(x , y\right)+F_{228}\! \left(x , y\right)
F_{227}\! \left(x , y\right) = F_{117}\! \left(x , y\right) F_{12}\! \left(x \right)
F_{228}\! \left(x , y\right) = F_{146}\! \left(x , y\right)+F_{229}\! \left(x \right)
F_{229}\! \left(x \right) = F_{230}\! \left(x \right)
F_{230}\! \left(x \right) = F_{231}\! \left(x \right) F_{4}\! \left(x \right)
F_{231}\! \left(x \right) = F_{232}\! \left(x \right)+F_{248}\! \left(x \right)
F_{232}\! \left(x \right) = F_{233}\! \left(x \right)+F_{235}\! \left(x \right)
F_{233}\! \left(x \right) = F_{229}\! \left(x \right)+F_{234}\! \left(x \right)
F_{234}\! \left(x \right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right)
F_{235}\! \left(x \right) = F_{236}\! \left(x \right)+F_{237}\! \left(x \right)
F_{236}\! \left(x \right) = F_{2}\! \left(x \right) F_{24}\! \left(x \right)
F_{237}\! \left(x \right) = F_{238}\! \left(x \right)+F_{239}\! \left(x \right)
F_{238}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{239}\! \left(x \right) = F_{240}\! \left(x \right)
F_{240}\! \left(x \right) = F_{241}\! \left(x \right) F_{4}\! \left(x \right)
F_{241}\! \left(x \right) = F_{242}\! \left(x \right)+F_{244}\! \left(x \right)
F_{242}\! \left(x \right) = F_{243}\! \left(x , 1\right)
F_{243}\! \left(x , y\right) = -\frac{-y F_{42}\! \left(x , y\right)+F_{42}\! \left(x , 1\right)}{-1+y}
F_{244}\! \left(x \right) = F_{245}\! \left(x \right)+F_{246}\! \left(x \right)
F_{245}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{246}\! \left(x \right) = F_{239}\! \left(x \right)+F_{247}\! \left(x \right)
F_{247}\! \left(x \right) = F_{157}\! \left(x , 1\right)
F_{248}\! \left(x \right) = F_{12}\! \left(x \right) F_{249}\! \left(x \right)
F_{249}\! \left(x \right) = F_{121}\! \left(x \right)+F_{232}\! \left(x \right)
F_{250}\! \left(x , y\right) = F_{251}\! \left(x , y\right)+F_{253}\! \left(x , y\right)
F_{251}\! \left(x , y\right) = F_{252}\! \left(x , y\right)
F_{252}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{24}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{253}\! \left(x , y\right) = F_{254}\! \left(x , y\right)+F_{255}\! \left(x , y\right)
F_{254}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{43}\! \left(x , y\right)
F_{255}\! \left(x , y\right) = F_{157}\! \left(x , y\right)+F_{239}\! \left(x \right)
F_{256}\! \left(x , y\right) = F_{257}\! \left(x , y\right) F_{52}\! \left(x , y\right)
F_{257}\! \left(x , y\right) = F_{258}\! \left(x , y\right)+F_{260}\! \left(x , y\right)
F_{258}\! \left(x , y\right) = F_{259}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{259}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{66}\! \left(x \right)
F_{260}\! \left(x , y\right) = F_{117}\! \left(x , y\right)+F_{261}\! \left(x , y\right)
F_{261}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{30}\! \left(x \right)
F_{262}\! \left(x , y\right) = F_{2}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{263}\! \left(x \right) = F_{235}\! \left(x \right)+F_{264}\! \left(x \right)
F_{264}\! \left(x \right) = F_{234}\! \left(x \right)+F_{265}\! \left(x \right)
F_{265}\! \left(x \right) = F_{266}\! \left(x \right)
F_{266}\! \left(x \right) = F_{267}\! \left(x \right) F_{4}\! \left(x \right)
F_{267}\! \left(x \right) = F_{263}\! \left(x \right)+F_{268}\! \left(x \right)
F_{268}\! \left(x \right) = F_{12}\! \left(x \right) F_{269}\! \left(x \right)
F_{269}\! \left(x \right) = F_{232}\! \left(x \right)+F_{270}\! \left(x \right)
F_{270}\! \left(x \right) = F_{271}\! \left(x \right)+F_{34}\! \left(x \right)
F_{271}\! \left(x \right) = F_{122}\! \left(x \right)+F_{272}\! \left(x \right)
F_{272}\! \left(x \right) = F_{119}\! \left(x \right)+F_{273}\! \left(x \right)
F_{273}\! \left(x \right) = F_{123}\! \left(x , 1\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_29(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_6(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_4(x))
Eq(F_10(x), F_11(x) + F_14(x) + F_9(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_4(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_11(x)*F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_24(x))
Eq(F_17(x), F_11(x) + F_18(x))
Eq(F_18(x), F_12(x) + F_19(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_23(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_12(x) + F_19(x))
Eq(F_23(x), F_18(x)*F_4(x))
Eq(F_24(x), F_12(x) + F_25(x))
Eq(F_25(x), F_20(x) + F_26(x) + F_28(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_12(x) + F_25(x))
Eq(F_28(x), F_24(x)*F_4(x))
Eq(F_29(x), F_2(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_263(x) + F_33(x))
Eq(F_33(x), F_29(x) + F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_11(x)*F_2(x))
Eq(F_36(x), F_37(x) + F_41(x))
Eq(F_37(x), -F_2(x) + F_38(x))
Eq(F_38(x), -F_0(x) + F_39(x))
Eq(F_39(x), F_40(x)/F_4(x))
Eq(F_40(x), F_2(x))
Eq(F_41(x), F_42(x, 1))
Eq(F_43(x, k_0), F_37(x) + F_42(x, k_0))
Eq(F_44(x, k_0), F_262(x, k_0) + F_43(x, k_0))
Eq(F_45(x, k_0), F_117(x, k_0) + F_44(x, k_0))
Eq(F_46(x, k_0), F_45(x, k_0)*F_54(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0))
Eq(F_47(x, k_0), F_48(x, k_0))
Eq(F_48(x, k_0), F_4(x)*F_49(x, k_0))
Eq(F_49(x, k_0), F_256(x, k_0) + F_50(x, k_0))
Eq(F_50(x, k_0), F_105(x, k_0) + F_51(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0) + F_56(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0)*F_55(x, k_0))
Eq(F_54(x, k_0), k_0*x)
Eq(F_55(x, k_0), F_1(x) + F_52(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_4(x)*F_58(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0) + F_63(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_60(x, k_0), F_11(x)*F_61(x, k_0))
Eq(F_61(x, k_0), F_52(x, k_0) + F_62(x, k_0))
Eq(F_62(x, k_0), F_52(x, k_0)*F_55(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0) + F_94(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0) + F_67(x, k_0))
Eq(F_65(x, k_0), F_52(x, k_0)*F_66(x))
Eq(F_66(x), F_7(x))
Eq(F_67(x, k_0), F_55(x, k_0)*F_68(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0))
Eq(F_69(x, k_0), F_54(x, k_0)*F_70(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0) + F_72(x, k_0))
Eq(F_71(x, k_0), F_12(x)*F_55(x, k_0))
Eq(F_72(x, k_0), F_24(x) + F_73(x, k_0))
Eq(F_74(x, k_0), F_73(x, k_0) + F_93(x, k_0))
Eq(F_75(x, k_0), F_54(x, k_0)*F_74(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0))
Eq(F_77(x, k_0), F_4(x)*F_78(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0) + F_92(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0) + F_83(x, k_0))
Eq(F_80(x, k_0), F_76(x, k_0) + F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_82(x, k_0), F_52(x, k_0)*F_54(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0) + F_90(x, k_0))
Eq(F_84(x, k_0), F_54(x, k_0)*F_85(x, k_0))
Eq(F_85(x, k_0), F_52(x, k_0) + F_86(x, k_0))
Eq(F_86(x, k_0), F_20(x) + F_87(x, k_0) + F_88(x, k_0))
Eq(F_87(x, k_0), F_4(x)*F_85(x, k_0))
Eq(F_88(x, k_0), F_54(x, k_0)*F_89(x, k_0))
Eq(F_89(x, k_0), F_12(x) + F_86(x, k_0))
Eq(F_90(x, k_0), F_81(x, k_0)*F_91(x, k_0))
Eq(F_91(x, k_0), F_55(x, k_0) + F_89(x, k_0))
Eq(F_92(x, k_0), F_24(x)*F_81(x, k_0))
Eq(F_93(x, k_0), F_12(x)*F_52(x, k_0))
Eq(F_94(x, k_0), F_103(x, k_0) + F_95(x, k_0))
Eq(F_95(x, k_0), F_52(x, k_0)*F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_4(x)*F_98(x))
Eq(F_98(x), F_102(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_12(x) + F_96(x))
Eq(F_101(x), F_12(x)*F_17(x))
Eq(F_102(x), F_12(x)*F_24(x))
Eq(F_103(x, k_0), F_104(x, k_0)*F_55(x, k_0))
Eq(F_104(x, k_0), -F_76(x, 1) - F_76(x, k_0) + (k_0*F_76(x, k_0) - F_76(x, 1))/(k_0 - 1))
Eq(F_105(x, k_0), F_106(x, k_0) + F_47(x, k_0))
Eq(F_106(x, k_0), F_107(x, k_0))
Eq(F_107(x, k_0), F_108(x, k_0)*F_4(x))
Eq(F_108(x, k_0), F_109(x, k_0) + F_129(x, k_0))
Eq(F_109(x, k_0), F_110(x, k_0) + F_114(x, k_0))
Eq(F_110(x, k_0), F_105(x, k_0) + F_111(x, k_0))
Eq(F_111(x, k_0), -F_112(x, 1) + (k_0*F_112(x, k_0) - F_112(x, 1))/(k_0 - 1))
Eq(F_112(x, k_0), F_113(x, k_0) + F_42(x, k_0))
Eq(F_113(x, k_0), F_2(x)*F_52(x, k_0))
Eq(F_114(x, k_0), F_115(x, k_0)*F_52(x, k_0))
Eq(F_115(x, k_0), F_116(x, k_0) + F_128(x, k_0))
Eq(F_116(x, k_0), F_117(x, k_0) + F_118(x, k_0))
Eq(F_117(x, k_0), F_2(x) + F_47(x, k_0))
Eq(F_118(x, k_0), F_119(x) + F_123(x, k_0))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x)*F_4(x))
Eq(F_121(x), F_122(x) + F_34(x))
Eq(F_122(x), F_119(x) + F_2(x))
Eq(F_123(x, k_0), F_124(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0)*F_4(x))
Eq(F_125(x, k_0), F_114(x, k_0) + F_126(x, k_0))
Eq(F_126(x, k_0), F_111(x, k_0) + F_127(x, k_0))
Eq(F_127(x, k_0), F_123(x, k_0) + F_47(x, k_0))
Eq(F_128(x, k_0), (k_0*F_44(x, k_0) - F_44(x, 1))/(k_0 - 1))
Eq(F_129(x, k_0), F_130(x, k_0) + F_224(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0) + F_152(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0) + F_133(x, k_0))
Eq(F_132(x, k_0), F_12(x)*F_47(x, k_0))
Eq(F_133(x, k_0), F_134(x, k_0))
Eq(F_134(x, k_0), F_135(x, k_0)*F_4(x))
Eq(F_135(x, k_0), F_136(x, k_0) + F_142(x, k_0))
Eq(F_136(x, k_0), F_137(x, k_0) + F_141(x, k_0))
Eq(F_137(x, k_0), -F_138(x, 1) - F_138(x, k_0) + (k_0*F_138(x, k_0) - F_138(x, 1))/(k_0 - 1))
Eq(F_138(x, k_0), F_139(x, k_0))
Eq(F_139(x, k_0), F_140(x, k_0)*F_54(x, k_0))
Eq(F_140(x, k_0), F_112(x, k_0) + F_47(x, k_0))
Eq(F_141(x, k_0), -F_123(x, 1) + (k_0*F_123(x, k_0) - F_123(x, 1))/(k_0 - 1))
Eq(F_142(x, k_0), F_143(x, k_0) + F_145(x, k_0))
Eq(F_143(x, k_0), -F_144(x, 1) - F_144(x, k_0) + (k_0*F_144(x, k_0) - F_144(x, 1))/(k_0 - 1))
Eq(F_144(x, k_0), F_12(x)*F_138(x, k_0))
Eq(F_145(x, k_0), -F_146(x, 1) + (k_0*F_146(x, k_0) - F_146(x, 1))/(k_0 - 1))
Eq(F_146(x, k_0), F_147(x, k_0))
Eq(F_147(x, k_0), F_148(x, k_0)*F_4(x))
Eq(F_148(x, k_0), F_149(x, k_0) + F_214(x, k_0))
Eq(F_149(x, k_0), F_150(x, k_0) + F_212(x, k_0))
Eq(F_150(x, k_0), F_151(x, k_0) + F_152(x, k_0))
Eq(F_151(x, k_0), F_132(x, k_0) + F_146(x, k_0))
Eq(F_152(x, k_0), F_153(x, k_0) + F_155(x, k_0))
Eq(F_153(x, k_0), F_154(x, k_0))
Eq(F_154(x, k_0), F_2(x)*F_24(x)*F_52(x, k_0))
Eq(F_155(x, k_0), F_156(x, k_0) + F_157(x, k_0))
Eq(F_156(x, k_0), F_12(x)*F_42(x, k_0))
Eq(F_157(x, k_0), F_158(x, k_0))
Eq(F_158(x, k_0), F_159(x, k_0)*F_4(x))
Eq(F_159(x, k_0), F_160(x, k_0) + F_208(x, k_0))
Eq(F_160(x, k_0), F_161(x, k_0) + F_207(x, k_0))
Eq(F_161(x, k_0), -F_162(x, 1) - F_162(x, k_0) + (k_0*F_162(x, k_0) - F_162(x, 1))/(k_0 - 1))
Eq(F_162(x, k_0), F_163(x, k_0))
Eq(F_163(x, k_0), F_164(x, k_0)*F_54(x, k_0))
Eq(F_164(x, k_0), F_165(x, k_0) + F_166(x, k_0))
Eq(F_165(x, k_0), F_37(x)*F_52(x, k_0))
Eq(F_167(x, k_0), F_166(x, k_0) + F_171(x))
Eq(F_168(x, k_0), F_167(x, k_0) + F_170(x, k_0))
Eq(F_169(x, k_0), F_168(x, k_0)*F_54(x, k_0))
Eq(F_169(x, k_0), F_42(x, k_0))
Eq(F_170(x, k_0), F_37(x)*F_55(x, k_0))
Eq(F_171(x), F_172(x) + F_37(x))
Eq(F_172(x), F_173(x) - F_178(x))
Eq(F_173(x), F_174(x) - F_176(x))
Eq(F_174(x), F_175(x)/F_4(x))
Eq(F_175(x), F_37(x))
Eq(F_176(x), F_177(x) + F_37(x))
Eq(F_177(x), F_12(x) + F_122(x))
Eq(F_178(x), F_179(x) + F_180(x))
Eq(F_179(x), F_12(x)**2)
Eq(F_180(x), F_181(x) + F_37(x))
Eq(F_181(x), F_182(x))
Eq(F_182(x), F_183(x)*F_4(x))
Eq(F_183(x), F_184(x) + F_190(x))
Eq(F_184(x), F_185(x) + F_188(x))
Eq(F_185(x), F_186(x))
Eq(F_186(x), F_187(x)*F_4(x))
Eq(F_187(x), F_12(x) + F_185(x))
Eq(F_188(x), F_189(x, 1))
Eq(F_189(x, k_0), -F_47(x, k_0) + (-k_0*F_47(x, k_0) + F_47(x, 1))/(1 - k_0))
Eq(F_190(x), F_191(x) + F_193(x))
Eq(F_191(x), F_192(x))
Eq(F_192(x), F_12(x)**3)
Eq(F_193(x), F_194(x, 1))
Eq(F_194(x, k_0), -F_195(x, k_0) + (-k_0*F_195(x, k_0) + F_195(x, 1))/(1 - k_0))
Eq(F_195(x, k_0), F_196(x, k_0))
Eq(F_196(x, k_0), F_197(x, k_0)*F_4(x))
Eq(F_197(x, k_0), F_198(x, k_0) + F_203(x, k_0))
Eq(F_198(x, k_0), F_199(x, k_0) + F_202(x, k_0))
Eq(F_199(x, k_0), F_200(x, k_0))
Eq(F_200(x, k_0), F_201(x, k_0)*F_4(x))
Eq(F_201(x, k_0), F_199(x, k_0) + F_52(x, k_0))
Eq(F_202(x, k_0), -F_47(x, 1) + (k_0*F_47(x, k_0) - F_47(x, 1))/(k_0 - 1))
Eq(F_203(x, k_0), F_204(x, k_0) + F_206(x, k_0))
Eq(F_204(x, k_0), F_205(x, k_0))
Eq(F_205(x, k_0), F_12(x)**2*F_52(x, k_0))
Eq(F_206(x, k_0), -F_195(x, 1) + (k_0*F_195(x, k_0) - F_195(x, 1))/(k_0 - 1))
Eq(F_207(x, k_0), -F_161(x, 1) + (k_0*F_161(x, k_0) - F_161(x, 1))/(k_0 - 1))
Eq(F_208(x, k_0), F_209(x, k_0) + F_211(x, k_0))
Eq(F_209(x, k_0), -F_210(x, 1) - F_210(x, k_0) + (k_0*F_210(x, k_0) - F_210(x, 1))/(k_0 - 1))
Eq(F_210(x, k_0), F_12(x)*F_162(x, k_0))
Eq(F_211(x, k_0), -F_157(x, 1) + (k_0*F_157(x, k_0) - F_157(x, 1))/(k_0 - 1))
Eq(F_212(x, k_0), F_213(x, k_0))
Eq(F_213(x, k_0), F_115(x, k_0)*F_12(x)*F_52(x, k_0))
Eq(F_214(x, k_0), F_12(x)*F_215(x, k_0))
Eq(F_215(x, k_0), F_216(x, k_0) + F_217(x, k_0))
Eq(F_216(x, k_0), -F_140(x, 1) + (k_0*F_140(x, k_0) - F_140(x, 1))/(k_0 - 1))
Eq(F_217(x, k_0), F_152(x, k_0) + F_218(x, k_0))
Eq(F_219(x, k_0), F_218(x, k_0) + F_222(x, k_0))
Eq(F_220(x, k_0), F_198(x, k_0) + F_219(x, k_0))
Eq(F_221(x, k_0), F_220(x, k_0)*F_4(x))
Eq(F_221(x, k_0), F_195(x, k_0))
Eq(F_222(x, k_0), F_223(x, k_0))
Eq(F_223(x, k_0), F_25(x)*F_52(x, k_0))
Eq(F_224(x, k_0), F_225(x, k_0)*F_52(x, k_0))
Eq(F_225(x, k_0), F_226(x, k_0) + F_250(x, k_0))
Eq(F_226(x, k_0), F_227(x, k_0) + F_228(x, k_0))
Eq(F_227(x, k_0), F_117(x, k_0)*F_12(x))
Eq(F_228(x, k_0), F_146(x, k_0) + F_229(x))
Eq(F_229(x), F_230(x))
Eq(F_230(x), F_231(x)*F_4(x))
Eq(F_231(x), F_232(x) + F_248(x))
Eq(F_232(x), F_233(x) + F_235(x))
Eq(F_233(x), F_229(x) + F_234(x))
Eq(F_234(x), F_12(x)*F_2(x))
Eq(F_235(x), F_236(x) + F_237(x))
Eq(F_236(x), F_2(x)*F_24(x))
Eq(F_237(x), F_238(x) + F_239(x))
Eq(F_238(x), F_12(x)*F_37(x))
Eq(F_239(x), F_240(x))
Eq(F_240(x), F_241(x)*F_4(x))
Eq(F_241(x), F_242(x) + F_244(x))
Eq(F_242(x), F_243(x, 1))
Eq(F_243(x, k_0), (-k_0*F_42(x, k_0) + F_42(x, 1))/(1 - k_0))
Eq(F_244(x), F_245(x) + F_246(x))
Eq(F_245(x), F_12(x)*F_41(x))
Eq(F_246(x), F_239(x) + F_247(x))
Eq(F_247(x), F_157(x, 1))
Eq(F_248(x), F_12(x)*F_249(x))
Eq(F_249(x), F_121(x) + F_232(x))
Eq(F_250(x, k_0), F_251(x, k_0) + F_253(x, k_0))
Eq(F_251(x, k_0), F_252(x, k_0))
Eq(F_252(x, k_0), F_2(x)*F_24(x)*F_55(x, k_0))
Eq(F_253(x, k_0), F_254(x, k_0) + F_255(x, k_0))
Eq(F_254(x, k_0), F_12(x)*F_43(x, k_0))
Eq(F_255(x, k_0), F_157(x, k_0) + F_239(x))
Eq(F_256(x, k_0), F_257(x, k_0)*F_52(x, k_0))
Eq(F_257(x, k_0), F_258(x, k_0) + F_260(x, k_0))
Eq(F_258(x, k_0), F_259(x, k_0) + F_55(x, k_0))
Eq(F_259(x, k_0), F_56(x, k_0) + F_66(x))
Eq(F_260(x, k_0), F_117(x, k_0) + F_261(x, k_0))
Eq(F_261(x, k_0), F_106(x, k_0) + F_30(x))
Eq(F_262(x, k_0), F_2(x)*F_55(x, k_0))
Eq(F_263(x), F_235(x) + F_264(x))
Eq(F_264(x), F_234(x) + F_265(x))
Eq(F_265(x), F_266(x))
Eq(F_266(x), F_267(x)*F_4(x))
Eq(F_267(x), F_263(x) + F_268(x))
Eq(F_268(x), F_12(x)*F_269(x))
Eq(F_269(x), F_232(x) + F_270(x))
Eq(F_270(x), F_271(x) + F_34(x))
Eq(F_271(x), F_122(x) + F_272(x))
Eq(F_272(x), F_119(x) + F_273(x))
Eq(F_273(x), F_123(x, 1))
Pack JSON:
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Specification JSON:
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