01342_01423_01432_02413_10342_10423_10432_20341_20431_30241
Counting sequence:
1, 1, 2, 6, 24, 110, 535, 2690, 13836, 72400, 384086, 2060783, 11163014, 60966409, 335351147, 1856259257, 10332435175, 57801286441, 324808531172, 1832684043137, 10379060215101, 58979237485020, 336192767909860, 1921840552425351, 11015137484899685, 63287839547409837, 364444628846170071, 2103074728272178288, 12159828204009733986, 70435795277835407982, 408697100050070772095, 2375228354516163847907, 13824915745384862985184, 80581288986909936531325, 470310913624852898444713, 2748416086257952099662621, 16080388799798327609488890, 94188884562279144610184748, 552288918400678136450673142, 3241701355123834066427374986, 19045739169154566266798329714, 112000650232368513378925039705, 659207721905538983437411568517, 3883161940433696539603051152143, 22892531411032268957140232381820, 135061615458460302201509274658895, 797417126211407343861674154376732, 4711305577622580553902482954527689, 27853932235604050978563784735069044, 164781888828081017979979979128467648, 975436627587294128261964161823546315, 5777564627240217559030282176450873244, 34240246738533198161026416711744738843, 203032697958514792848257349839335437420, 1204545844059777617291038098554931513432, 7149910871202624810333718878487027241521, 42460979850519761642306761615324568211517, 252280707902554300496851993849894627685032, 1499600772253530772371242456713073982659797, 8917808747839524709809403087322499000880870, 53054859781777107026413657696109297024937799, 315769844116107023111767172783866860104671883, 1880134153096212499066347531775748692755674975, 11198871006699227487931816985245602164124308454, 66730078344873935321784428385251967020906639355, 397764507147106892581631224196127787014139930358, 2371825102522334327143247490748789695290288114888, 14147737268942177271676712803627418082331840510543, 84417921659327753982145738719372749410218440740231, 503873492572784878290634375435252183042906408546737, 3008455379953891392354955239413482331026068928120632, 17967888018056486180385274183369231404789008780123185, 107344113075035373135771771510838422218506254902175663, 641480813466915212175198685728943656049332755335865572, 3834511013131579865804949098742389544852658587510423780, 22927355262895565830496594779891221778883078395800664737, 137123688139218789373633394407542999332279570591196279236, 820318653518125827876123023568317712525110130842766600324, 4908642483213451923307482452474459435688822648690675808830, 29379620039182496001488281118892180398756505638502603212792, 175887208092685726512253648156307651951469223069483075003535, 1053229682828849633113467605456461373281447715945121199689866, 6308269227854031015044960601452176326410028046519665779923980, 37791425558249103155342758735626296989443846423430694317156588, 226448770877423789432699243744316657657809881111560283645932115, 1357182011078055451567999172034005788271094140573268012137965760, 8135711262627106276088524572190978851133638308660663146908953877, 48779821901131714986150883836347773894143507205275168888625665248, 292529830801483993078648518515412511800083303397040676908057411991, 1754621547003535695138692393467743926558782527389836961813559059673, 10526360794538463363895435712055742445028784808118889394330806237247, 63161545357827879648022670041845840673550765161723476652024118864349, 379057602451219271521390449657385991379502241031824490257601818848173, 2275275371115780817195122126681492910649152662850535782870519243602118, 13659581259716682323955024363879327585741397396659026042174999238021201, 82018892180326510654140735783903437215024474240685113637906323981356878, 492563221169121699274938174607252238635917325498171591735756444258829234, 2958558454004667355129230391238475994613968131735363002087551833087422678, 17773255669198377054837113505679599095037510168819237900385091786527073331, 106787665995710747063349503166306046067685189282735293430758301468590463559, 641713426915763485396673981008547630025868482196365780880907628397027156399
Implicit equation for the generating function in Maple syntax:
x*(x^9-9*x^8+30*x^7-45*x^6+32*x^5-22*x^4+27*x^3-13*x^2-6*x+4)*(x-2)^3*F(x)^9+x*(9*x^9-84*x^8+294*x^7-474*x^6+372*x^5-242*x^4+276*x^3-160*x^2-38*x+40)*(x-2)^2*F(x)^8+(x-2)*(36*x^10-348*x^9+1284*x^8-2254*x^7+2029*x^6-1405*x^5+1485*x^4-1009*x^3-10*x^2+184*x-8)*F(x)^7+(84*x^10-842*x^9+3291*x^8-6354*x^7+6689*x^6-5298*x^5+5374*x^4-4076*x^3+720*x^2+472*x-72)*F(x)^6+(126*x^9-1062*x^8+3346*x^7-4998*x^6+4437*x^5-4482*x^4+4625*x^3-1949*x^2-162*x+116)*F(x)^5+(126*x^8-870*x^7+2141*x^6-2488*x^5+2380*x^4-3024*x^3+2182*x^2-364*x-60)*F(x)^4+(84*x^7-460*x^6+857*x^5-853*x^4+1107*x^3-1258*x^2+524*x-40)*F(x)^3+(36*x^6-150*x^5+208*x^4-226*x^3+359*x^2-280*x+64)*F(x)^2+(9*x^5-27*x^4+29*x^3-44*x^2+62*x-28)*F(x)+x^4-2*x^3+2*x^2-4*x+4 = 0
Implicit equation for the generating function in latex syntax:
x \left(x^{9}-9 x^{8}+30 x^{7}-45 x^{6}+32 x^{5}-22 x^{4}+27 x^{3}-13 x^{2}-6 x +4\right) \left(x -2\right)^{3} F \! \left(x \right)^{9}+x \left(9 x^{9}-84 x^{8}+294 x^{7}-474 x^{6}+372 x^{5}-242 x^{4}+276 x^{3}-160 x^{2}-38 x +40\right) \left(x -2\right)^{2} F \! \left(x \right)^{8}+\left(x -2\right) \left(36 x^{10}-348 x^{9}+1284 x^{8}-2254 x^{7}+2029 x^{6}-1405 x^{5}+1485 x^{4}-1009 x^{3}-10 x^{2}+184 x -8\right) F \! \left(x \right)^{7}+\left(84 x^{10}-842 x^{9}+3291 x^{8}-6354 x^{7}+6689 x^{6}-5298 x^{5}+5374 x^{4}-4076 x^{3}+720 x^{2}+472 x -72\right) F \! \left(x \right)^{6}+\left(126 x^{9}-1062 x^{8}+3346 x^{7}-4998 x^{6}+4437 x^{5}-4482 x^{4}+4625 x^{3}-1949 x^{2}-162 x +116\right) F \! \left(x \right)^{5}+\left(126 x^{8}-870 x^{7}+2141 x^{6}-2488 x^{5}+2380 x^{4}-3024 x^{3}+2182 x^{2}-364 x -60\right) F \! \left(x \right)^{4}+\left(84 x^{7}-460 x^{6}+857 x^{5}-853 x^{4}+1107 x^{3}-1258 x^{2}+524 x -40\right) F \! \left(x \right)^{3}+\left(36 x^{6}-150 x^{5}+208 x^{4}-226 x^{3}+359 x^{2}-280 x +64\right) F \! \left(x \right)^{2}+\left(9 x^{5}-27 x^{4}+29 x^{3}-44 x^{2}+62 x -28\right) F \! \left(x \right)+x^{4}-2 x^{3}+2 x^{2}-4 x +4 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 110
a(6) = 535
a(7) = 2690
a(8) = 13836
a(9) = 72400
a(10) = 384086
a(11) = 2060783
a(12) = 11163014
a(13) = 60966409
a(14) = 335351147
a(15) = 1856259257
a(16) = 10332435175
a(17) = 57801286441
a(18) = 324808531172
a(19) = 1832684043137
a(20) = 10379060215101
a(21) = 58979237485020
a(22) = 336192767909860
a(23) = 1921840552425351
a(24) = 11015137484899685
a(25) = 63287839547409837
a(26) = 364444628846170071
a(27) = 2103074728272178288
a(28) = 12159828204009733986
a(29) = 70435795277835407982
a(30) = 408697100050070772095
a(31) = 2375228354516163847907
a(32) = 13824915745384862985184
a(33) = 80581288986909936531325
a(34) = 470310913624852898444713
a(35) = 2748416086257952099662621
a(36) = 16080388799798327609488890
a(37) = 94188884562279144610184748
a(38) = 552288918400678136450673142
a(39) = 3241701355123834066427374986
a(40) = 19045739169154566266798329714
a(41) = 112000650232368513378925039705
a(42) = 659207721905538983437411568517
a(43) = 3883161940433696539603051152143
a(44) = 22892531411032268957140232381820
a(45) = 135061615458460302201509274658895
a(46) = 797417126211407343861674154376732
a(47) = 4711305577622580553902482954527689
a(48) = 27853932235604050978563784735069044
a(49) = 164781888828081017979979979128467648
a(50) = 975436627587294128261964161823546315
a(51) = 5777564627240217559030282176450873244
a(52) = 34240246738533198161026416711744738843
a(53) = 203032697958514792848257349839335437420
a(54) = 1204545844059777617291038098554931513432
a(55) = 7149910871202624810333718878487027241521
a(56) = 42460979850519761642306761615324568211517
a(57) = 252280707902554300496851993849894627685032
a(58) = 1499600772253530772371242456713073982659797
a(59) = 8917808747839524709809403087322499000880870
a(60) = 53054859781777107026413657696109297024937799
a(61) = 315769844116107023111767172783866860104671883
a(62) = 1880134153096212499066347531775748692755674975
a(63) = 11198871006699227487931816985245602164124308454
a(64) = 66730078344873935321784428385251967020906639355
a(65) = 397764507147106892581631224196127787014139930358
a(66) = 2371825102522334327143247490748789695290288114888
a(67) = 14147737268942177271676712803627418082331840510543
a(68) = 84417921659327753982145738719372749410218440740231
a(69) = 503873492572784878290634375435252183042906408546737
a(70) = 3008455379953891392354955239413482331026068928120632
a(71) = 17967888018056486180385274183369231404789008780123185
a(72) = 107344113075035373135771771510838422218506254902175663
a(73) = 641480813466915212175198685728943656049332755335865572
a(74) = 3834511013131579865804949098742389544852658587510423780
a(75) = 22927355262895565830496594779891221778883078395800664737
a(76) = 137123688139218789373633394407542999332279570591196279236
a(77) = 820318653518125827876123023568317712525110130842766600324
a(78) = 4908642483213451923307482452474459435688822648690675808830
a(79) = 29379620039182496001488281118892180398756505638502603212792
a(80) = 175887208092685726512253648156307651951469223069483075003535
a(81) = 1053229682828849633113467605456461373281447715945121199689866
a(82) = 6308269227854031015044960601452176326410028046519665779923980
a(83) = 37791425558249103155342758735626296989443846423430694317156588
a(84) = 226448770877423789432699243744316657657809881111560283645932115
a(85) = 1357182011078055451567999172034005788271094140573268012137965760
a(86) = 8135711262627106276088524572190978851133638308660663146908953877
a(87) = 48779821901131714986150883836347773894143507205275168888625665248
a(88) = 292529830801483993078648518515412511800083303397040676908057411991
a(89) = 1754621547003535695138692393467743926558782527389836961813559059673
a(90) = 10526360794538463363895435712055742445028784808118889394330806237247
a(91) = 63161545357827879648022670041845840673550765161723476652024118864349
a(92) = 379057602451219271521390449657385991379502241031824490257601818848173
a(93) = 2275275371115780817195122126681492910649152662850535782870519243602118
a(94) = 13659581259716682323955024363879327585741397396659026042174999238021201
a(95) = 82018892180326510654140735783903437215024474240685113637906323981356878
a(96) = 492563221169121699274938174607252238635917325498171591735756444258829234
a(97) = 2958558454004667355129230391238475994613968131735363002087551833087422678
a(98) = 17773255669198377054837113505679599095037510168819237900385091786527073331
a(99) = 106787665995710747063349503166306046067685189282735293430758301468590463559
a(100) = 641713426915763485396673981008547630025868482196365780880907628397027156399
a(101) = 3856788091634893343155439438151832599403273449435601409928887236807634915381
a(102) = 23183221250709299955873584676987381892970743531003966133243995022145660146470
a(103) = 139374686195204199885482289341152353122322984346954877877451248418759043356586
a(104) = 838021092798367173002226748015442624755963273636361747433903761463261140734736
a(105) = 5039480400396539336327195331945089657119264705154360489842926117453622737120095
a(106) = 30309251120387353011673235345955723179611990345341357551470526832311137735918654
a(107) = 182314910903028273443053157995816721521998851579967802596320233574810949229569669
a(108) = 1096795461994524725064561323948040695482716288654002457919004384867091659750620834
a(109) = 6599097348865427306108226929891720823179146686082533750106502895458977359666684207
a(110) = 39709813868561936850695250650125631887579472004337201050230545935190330450864312257
a(111) = 238981681512556909035848350274717995418747931089885793085753568011272945205101419855
a(112) = 1438413874499578918189117986767287916684352958252591381616592676053339498968630259416
a(113) = 8658739509008273569897330570997413775061786488362079102698814318567038533806640436923
a(114) = 52128609468087414595744741912150172201324329030825468031503740669360360759469679413678
a(115) = 313868245221676526086307991913572723685961361787074235575623322815700727492249844387032
a(116) = 1890024930981333346789956843503699281974479532005645275682632179813423672257831859206249
a(117) = 11382450340476970860095117076122608920954989422556325339032986772635356431372291800635685
a(118) = 68556913639246607127543133822417160257802567011457840886646743108396632167410296417932173
a(119) = 412964974754320743655970252985456314117068082897990954632489861201691474528933987984252477
a(120) = 2487830984593662625330044736102968081474180535484939649168800991028281984540772956182333171
a(121) = 14989027713367483498791484316177613615041850911381823313704505255602189148400049793806799407
a(122) = 90317155708255382965306050794606369448885872387490616880583778442469076446546704199456132311
a(123) = 544265144225892684774820113873710370697755222535542357524361383651791757493678504899805141883
a(124) = 3280148990640048950987516695008532736116532069085600354053414126819168993944741474081848122926
a(125) = 19770548249813811152692630702106104060348288130604189346576371449780040656654310027170758598614
a(126) = 119175032723413565373598912463617876674060111998786874884677611051469643709161521229759598643890
a(127) = 718443498747175089920116636131919348151868459279149296231183487097684444522943938963660507205450
a(128) = 4331517698030376008067394705123633610999619881351504625348639111339767200229123543669299992690925
a(129) = 26117227934631174398472234117524913807486463793173023442532349753364549571856803779886217380714618
a(130) = 157489995002014976971355268625558212458078887172900534058861499341860767487125387496261579354631871
a(131) = 949767202880838084663755383090937973590143391420210206696318683821208497916693025257472985041062841
a(132) = 5728212181679172265434286964757655643043271831181924578425332444896145240276276015068167707562989769
a(133) = 34550806188054641167232352700131839352794890890683595576147727193912314145362984490346230413185418630
a(134) = 208417355079629569536862893955007292806087908330682999585232761322266706877439302250008273570329439535
a(135) = 1257319462529106867115169008238337051359443686534166030368091226968557264226828853363957583497802086284
a(136) = 7585652239768523696094639146460145186870795378496133244769900717439145333549260183078229213798676578247
a(137) = 45769401447109069116526193757952350589793808850972784608621682537872084691094822250778845094566025861832
a(138) = 276179883972249983625125179895035778886215699507373028580395414259500297553552936469703869821189592486120
a(139) = 1666644070950810772307564565163918500415064351016294286840598178669050732496292403649453604560013665530025
a(140) = 10058360645183173989449130872299076754011329942028220382389152207964243285079511310328224146486685614062465
a(141) = 60707813598615308291929026498990553811104298193614919736909916231366791789214384662423472449351016599324770
a(142) = 366432986268782393788501783547690414956331456762255770153501298197015540874801177400126757273273085871093038
a(143) = 2211956883098224998295955662574826053094860907972838545317566648879551955407512456551926649855032814982190447
a(144) = 13353356118144997107015870870082113794728347585830024021259125182974712308872981817579904286589967173228748577
a(145) = 80618636194041444807788634588982365932752789097262352602006774537739641493694677080862927304044960107223202486
a(146) = 486755958115593517443403200014175166805413947885920434936231030272366095294472116559044070780609719369944226671
a(147) = 2939121226514736387100413956030259471586275795904463190701893315719580889067737221457734828072374830124964625023
a(148) = 17748175124561310747430262889755044479785399571895659855127094813481609804471113374420457923415652050521134224300
a(149) = 107181416326412153143280819899086376671522659413939578268342353423727394274318801015330687483558334651251379520012
a(150) = 647313200500348616620565767499595059863843903091091205219217105389159114994759598195562161112731713084920935909940
a(151) = 3909653188066994119300885424495552719625596406127926376947025567918401772265226289713656583029612833617504351747822
a(152) = 23615134571781534876041561182245278369309860665524027132719909125639942021238352295356466142088601580048316361279451
a(153) = 142649634474147396604296205382353120858157024031231479833564102391095025126070326842556347922809039381196082379354278
a(154) = 861744628560036788458746698786978051559994652764693205543710670532903435129084235362969299949646614671311512755307570
a(155) = 5206115908710362313347495125615956834127359490769251156803397719218716346115645771805567129263586376682547413485082471
a(156) = 31454012604498183511018456495393739490634947448171652305043458901074023673609761499263784231052911177907444300762295646
a(157) = 190048703702046899016154961231149668636339828922689875991270280900243753274511331600225066185040631241093615193619300760
a(158) = 1148365300729540677240084547995990779567949854460260133128939043881202830831760042138384207988028279021893123991776478499
a(159) = 6939388057438820699370836249992105762811395359753120990036653231368509744496366394801665135212648535224268288729445386636
a(160) = 41936089082555194334183434682547786834166959109684429343683919179148059854240820758292702708068407482210552841691463771425
a(161) = 253442823381107508687074349400086194550140163832623789258282659556474579367158163198936788216883197671055624304830024374265
a(162) = 1531782406961520944045785467130315004841474562012618075376954372477104257232875845361352612199028402129873397119758105309331
a(163) = 9258462175879922203113925478455765600126757238035754869546992580587055736800913549742376956010376004585358255833052339948782
a(164) = 55963521551697022103407385681682642671709532736353091999197675553253872206711753426742977284359630598243396705764376464643000
a(165) = 338294795462885212395232703809159491447200163684409042780848799336473146657610058785342083148485987757603431452119888340189322
a(166) = 2045075802673783827485603591659310589314436458147848718885787212913545236694842787143004576458790216588875302263429230328963394
a(167) = 12363659362189833257514437531582805119130559278777985601198353407515636194346651765977093499521761377402054531046726810311957428
a(168) = 74749432329128887514230079398708699913482340584549350578011587792469477722193360149638969000038342595649009650195453058767620512
a(169) = 451951402261222094256534296023085158519331364961146949334683504337920254613569085171763419757144386527899273336491227184446243014
a(170) = 2732739779984043214629234083133307421994114716442392433655135959254695434470947110367486387621874833585378007759910416816222297842
a(171) = 16524459191824726313088725473840442188558100372019740578855941351084288725335069903333433814586372331677457601552975762973612787244
a(172) = 99925977558243705067047112092203106152610506122416630095319434504091585851973830103264807419010833148167937875548777780026106332617
a(173) = 604298441635358686799266850042522520102483767563355009611605898994011253053862210276385123903623415101407289134128069115025138461629
a(174) = 3654653512398436676765403854604058287530805113394164859941318341826252898866237339271380152189335953337747022843201446742283296693052
a(175) = 22103566877016057763009464701211921823570725365920373420867802113127138012185658920047794137168276682899924795781240110484634674052770
a(176) = 133690235889868982672144262063735355251729791959021207884525832668666091380260723210646274832785325895069848920441000755021531296532382
a(177) = 808645087526690826644328304438912728316306424254574824838310785813317167782508811821631845205640541592402770654324162035568929571513084
a(178) = 4891442082135869547972944482949176046028373510771723996197492935598125389471021209315070417220351528398113272562429260350898829340890528
a(179) = 29589412829269715529225703986229830806154572217133574020315503838173746799573342420254743607830605455613029087535281767972443873605425482
a(180) = 179001231857532265650339254865348925431275438188002397186459334235970456950014833988282950338176796774338798455487327567598584073537453190
a(181) = 1082918341845181235125346872242507099927524683300898698462103223324893163190204722321496433333274203765032444276899763444820392505519722442
a(182) = 6551718007097265906545938279731760558583002581783553042253508374952499485734101626827583496323932336446422515176359801054255748136911261344
a(183) = 39640056463401957898223949520499102709205798080648207893148831274033208797193767158449000653464129002837388875017695307702411065752182761120
a(184) = 239846121490614041980835709947598139133423510138372933937152219953297884374909468848141631919221165243644981201565598514215109793934416784774
a(185) = 1451276937207211920615913716015872485834486061607674566977872198422664517843019174003236920138160442685987420139695514066873172127019431252713
a(186) = 8781866682094781756467817805242961070661414052012595072705805175331162764324519695890416924506629550005695918981157015348595416196222090451428
a(187) = 53142518836777917438882758735163858758511937471491146121136572637119415356540355251677327776941110349243939459781989238450375301997219714766535
a(188) = 321599955769813707677388386028655159729367588468418944378971170290798468597029397611152147050289780142319124534289808052136406906918497132618485
a(189) = 1946292813116088304602310479207990895123408657853561302190799496989624229782559453900123586650902746283988994096271154057709224796193336990721249
a(190) = 11779274369582805879668500307037043731039400677332450248342245125290402243645858590126424662721258885690085193685632226132631523764062072622417795
a(191) = 71292996098825158723208560739641173054071748706495827618271396513314153876829406856830310867212101104943547450729938076738883809534416313896112805
a(192) = 431512099410740376116993994429068174849752455868596604428440803612459140336362876436771048244077088758581112495463862041960201663743112014617795692
a(193) = 2611900852604832882908698208008761480674148535359406786680413891860841050138033467115812946020183958197533174620951498143115791313929218468272830803
a(194) = 15810216366646871664084031359817165420325915749845003781179980955280567474587904520735714144529403471571954945237254547180397986582860514156540930412
a(195) = 95705341584963146703873360519589279943412570681232414548095887433393703592980753821519718087290687477356998403760354111997224760159679598178982288852
a(196) = 579364130780186712884430012200298765353787224565977417347815038579383963873307059508672825979198432102470288945337472268814196554522693212584203952701
a(197) = 3507388865623047816451828317949091336805847838367112488772926033940770228720694762268068688120222530707242551358565091655929265519236882537027812529493
a(198) = 21234055689692780180859427884836550628655224973147107207938468529923692517759959185012762543127791019233513898564707023721352996141122905407529469956899
a(199) = 128557830575049168165982121496013237463198325291546744038943877632487246281901763913762903907724544975787564309380833078234421044242759021420848173015762
a(200) = 778359987582281550009245681725051464135826680343229100725091855213731067408800793630354640161157707953752929077397482860393945707782337084342168364137522
a(201) = 4712796542913339039838915409835927181465018465114724915723388686254931566677519688308441407493452238615841724726226141309667872884643348748477116417447135
a(202) = 28535989756009230986633860071657847086035980158050821372423651353297913372421759453729153510499061112755371486000623803746795293434647966755282289973119758
a(203) = 172791785364313826316750904242665226187608986357579580892153027383906087902221733453898505559135257410102323230734550786741788661115334638025363483882453198
a(204) = 1046330752712895404661556661779139155922942869448950334862240926141076343007812521796412690716252554022553523332791900314648726648512463479029851396250725799
a(205) = 6336223390020747207095634032723560014219251442834985568696228497956654693445072595676942168256648838532256004513226726822664909735352779330941218809550838786
a(206) = 38371379418517672764075214250541613821000905774349182472369651520566225950336246310124705408595971512617593214433100906450568296870224460188816019616655696849
a(207) = 232380475244237753170703952000422734558406404529409471894725702021010875452301850138126718331846762604779312561487098044742532082860915835759040074661048190296
a(208) = 1407365834851969514043831523452000839685052153792188979150560340220713637118178574772329257858055741438814068902469174653317992496272666070296788881129871245342
a(209) = 8523723869432811571587264848558168817598869846205220968378620961938458317124462293088582383199814319737635413142661631895830591928027755640317391691795083889360
a(210) = 51625776525128387817298326249280573463493626586673374141302206814335737599171087542109306246943083494013987057022826880958282703489533105699453729177167360084459
a(211) = 312693272890501122604804361612823546698931373088264879106726529346899326307435485787157001893349739564747754895742499779762817880063768851986420407261446779880793
a(212) = 1894022161770118036051691233156439322072119513096901426282844470090303926868553426517157512337128033629846620758017305054635719282172188562055007820597968988316234
a(213) = 11472709967547941698967373310995053847612522268470002479789990549921700111183394031834063586389002066493313164578815737445040755478066389222364282979788428009766184
a(214) = 69496235176067822577882121914051414438428957208405168404232068789567476228850654072306165198923960514331290848843942981272143417646103790765728059893415414494212904
a(215) = 420988966424262928243941849573206816595958494344110323219741925591528080528260925219218421045899299271640146285583203140598759127283619088703917172400970500973046075
a(216) = 2550317141627812657647958789675186248167672652678029703172603549067604720378135658105028754766153260030778248633611696121253770079677493641391250722975231570585297380
a(217) = 15450110060620926422898303556471095382490468962088110268380182436959789735752477515910309446878789491084774890439286156424627215087121135022524213611410135747163946025
a(218) = 93601487100204472991207963599587544633249062001051895521753812447021228774648169315501287783060754243555930480712595334114072984680974250067648056820747229384743698886
a(219) = 567084239547917343238391869185638563377453191145187941039962355296040324877453196044878072689331043243501876985867204843646705823298734982592925992905928344253150508039
a(220) = 3435784687384286057062413264458742940110584055271076172957007418039069708656565497496990492227025294546981912062895302691784860690175135777695564371787099526779268886506
a(221) = 20816979426765991820396843214758101301025783203183264668541661959991945426885082105749346563766708121360327098562378584179832879548755583869582964998289347992328683963849
a(222) = 126131272224223038484900225642541433340771932096181188908671744458279087549354069781256654870777916486543678378184520222942756244380535208503867236193496745553184853290789
a(223) = 764259789469382780302730117676088056655009692880661362227766949405884338206218133946758408884765992633411381632277139499130345304121032168206345741478617920544789599825232
a(224) = 4630973518918038638408895396124483771166822126065514054318780116441273359370156404007999354981075118974379641960304538304353608722206580642769520020142375161525313693340289
a(225) = 28061864414279973137422649993077640042300019479436070695591624082839084973709838110569428965691889486800611713705576281872399333153468506795272214137044006764696083012792471
a(226) = 170048798928562084280315131213433170678789491397185698948458159106644334833607055070525291987461120971538885160140425983929685869012550454268629691816060009997479126526464317
a(227) = 1030488916921135710340061468993680064455205907399111785186004733770883698048350907297654307233995656460426998189410559968492019327802495372341619269190807058227632701424759826
a(228) = 6244902750279450129737713011142875934151577628619362378730382157081568772674937965526496555661352631761576846895332132523524234235682891404319845368720133839155766479043072270
a(229) = 37846046791765277945321181422229449414418431268308086750069825022360588190203313612740342426765383245195828240612085534320912106928246456248537767739720337472005652612662532114
a(230) = 229365314895781382387666597899100987380978559318773829046040247347256940672514148673625819402857151962291718834964220827350569503044083633373828600856538553787970223401682656321
a(231) = 1390103821660049944474296143349784214126434234074241345092027829857884875258101962609256111504874995664841807023780068154784524145977719856400035047097265434740638813086168830252
a(232) = 8425174356134128667837189820347330946817592662182630735419836552984401936840974655613766320033214835089517288940757750290246455082334396868531029260177243802490948582632661538704
a(233) = 51064915651663880346773419809982937096333546218961474979308604344470821387236814846714868747952157051958669373267997520072913452050522106183530316423573537475897645333540052088225
a(234) = 309512575545902888724711045354917584915215786942750407974882907501980475181121159614603121508892441700547184770017568727775254229393573351115491063306568915711307046179226820021426
a(235) = 1876056165851809086305101528350314749770906336753215946224496932957174280416064248350455177622017573369681920219245071868908872878667939673484408737856592450868462376752492733353997
a(236) = 11371693079464928435278382069038352559754166694441093548878705123446915572629714188284828551207835731402949039786975002300800329462789124274288314161607635418939089860639334027534703
a(237) = 68931238247460245386223643926126165532033351354479982416006908783307579309165959279994953208022828613350249461033372290427323612201880644542644512587568453937123248752406226014559426
a(238) = 417848251751163553479364978627321273987563459655676454622440006061470555336084357375787769331296149764854792595814534092934405056407371240969363004896436016885535618671122421765719590
a(239) = 2532984668580169785278552715659264542152090928086097582358958953348840476319864049833273831042364546937408966665154462691458159887477876430472354288074619730999169826453352634700043376
a(240) = 15355285636872299246275663091603619836315781169158393014784930281271676881267561142626231770692842311100114654922784408401544386911412085421913233411989138706917391388876317650948105358
a(241) = 93088173770481848218509328998266840465016082901333955887021477469497091960211164323084596497846037042150475725323454380805242806643107529380902627927040978074500061882617806528091857081
a(242) = 564341905410665894969385675996508572333731043737555778291048470613724637289756302714145120178590096436867230658761056119015823309441736264647455239862822028694346545908073533405696984299
a(243) = 3421378934858524811175170562721415049124047430015092662796281433987921893037944363638421823317923969742760618325064106109550548882528083682265972321994812015661579413627520889445927557624
a(244) = 20742975304503511753905457586819676650618218299894616135544157809983165517023936837037831479634152453848125319720450134774951380733655393998649865869419318606464565833967587137997311008741
a(245) = 125762693391665373746417005163343191547613103413821261328900462264604121111796514369781954810872913687994435234215180947655763742074330604167454775555415283076894711630315803552377026225965
a(246) = 762506283838841938659722207511526624763288880847840786854052999389480693204846941936087574862129607515356781478072719950680970385330944253597896149937915254231935234791273943342131192657190
a(247) = 4623232711930847137985602375173594760938100739397354936601078915686900526556695186194155810065857297076754168388959211490521782611148314692011975491079764084840333783260997591250862471861245
a(248) = 28032299535034741398159667760368086233677467111080385613277972100563761143272922626124545244548928827746741331888243363734737237729796896308424662547976872602074271782152836865725885990298537
a(249) = 169973905691382829950329274680499702199912168689835826033270143544550872771908538443788234944012929095535683587870606554650848935245023776114930913737731955296662505035066904245491438001127744
a(250) = 1030661980764744351909459312046922910691407199754440874640763367865030061288747231508143827124159806796287134156032652386754751285869150006371716695467300319956389571579303693901894964790453613
a(251) = 6249721261531891847591426920605064406565036642786193309724717453284529954666747526298574074475455119989298886081296152478910390798331946022151611454920758227367332403043973260360963416342325289
a(252) = 37897917657127156351266493660240511973434762922113815321529066157431937088300923360987140662277599544651975621476980976861402710352526203533834437384600009737235014909556076050310003559857212830
a(253) = 229816006392410594734529921010435455930429884269765751567775288723917435253141830192363983695851749343095704493497811838840521191238531131766130798205296622349964116540597786279943066751053858609
a(254) = 1393655215866557908581449455432926141172730531478472510297558583260735173072715710938516497616242281496459744856618853329784426195272708372349754945421779748180622835479209402067609470790123713105
a(255) = 8451630104567317379540755588836675605359174034533921867813517857551698810787519666473334561118765532355415612623410475514829251703993511632777574529620550237155758222752279432183104649286112295811
a(256) = 51254925360864435537916466786323727914401060679702619307214407863268380688160380608458179877955396549535899933415806562635171708232875099554704938926661745658937156470525698577287231086819215020070
a(257) = 310842675834239287024634918767815880194224451073794771696893805471399636376728516640168941167891846428095907154957718372399553583426099709338535576219895323409919127657569439484314383221379199130357
a(258) = 1885191638493309936894872622799262874899804521231533557533332936787660772567040722283233892091005722281475279413366552836292259931250865034126431571663244083964546627773245590717615469295524734189527
a(259) = 11433524518697295914325165995526584432321162909044511447465412231724954543221985666362969021014900307200279219990775615675297328457009742537222971554324436968810830984101404551982178616739928699397915
a(260) = 69344884882986455817888471802773648804085465390946656002809565754095330513533093583200791554350231308319920511069895378239418984218173925823126346319800692776983682923460369749649947877376128922094697
a(261) = 420589419244322239549611693630567050761712929790664971380003063547128916481851162875359393867551014917319024095459313760739496581633946534699163330723887709426405828088439255755032559920425016488275733
a(262) = 2551007810543616760519008884311280746624061796678373250783623744112335703083116062088643274467143322122986543901871272501880745482563152319686409135123838066810994158169700655106209603936461837854264760
a(263) = 15473006040560185112675342363811551298875883359863996138705592392609938081715047659756908215325100450842438871569311733407385348780638574830989511053459418018269411141670471191514546496206427223768140056
a(264) = 93852747636090399614172103085358668223030641860952380893983311471306800075773631508194811361800305704567346334197901366027484003040567725926240356594911407224224539258464418225841204450772820122499947870
a(265) = 569283513594653048946984101362034750311814783949869370852388287076415734601406607088579756155511490190576416196527329323246458502283015840848051722567355044009388263159937037884713064870814512519213028369
a(266) = 3453182019350439383119405145731504079765765836475967870680173329050297738001908430038934746630736093441493487381947933353698720366498353155641532780693064091518211915412406419676366677205947148242222910979
a(267) = 20946888179488039846426911665703950625650581747485391036328896354856878124562337139033586664872354730999058487659078597648394282830980366143330164735541323080597172525361060196819567269571563017799447959066
a(268) = 127065798115924355449695748456156241436592492868143605398868636719896504458546289209018519122070989441503560217598869209579427568042386797566445555217172414966822619378884687283690289842128820845209187888648
a(269) = 770809158448500748346890538703677363641808260110416661163867813918304407907177360180828683895699875049335176559168373087013924037514726853872592974663065580989032611112228350481489111051910382927516010162656
a(270) = 4675995017348875315593398199873183824974050803584856742565776676466204890194735833269695399198021744081079761970695807981364644113775956160668070124158151280561136473045500212615789621629051078333523817823959
a(271) = 28366785398599819735583035391987547331335755288982200620260578901555493844070462018964214484299267248468369554866366065701125294857853901332333449410049334354368655684743598446120975345909232439957912318768885
a(272) = 172089768713404584136446610096025300870469540769319540429366678139047710997276476815447831434751100941641834787393238235823221053323876281421295683028022811322185307761099017491050688379041960872446752062955858
a(273) = 1044019855146615340731004744522270530652220440123029926735204269128865871264244660508075537362375268011106897844987444110653064571977945153668531746136965082896258482619026446397667506037528299190278941314482104
a(274) = 6333899684437650768329916895361721520518188813764467552581721802814721473744697229591130334275805726482789896073022440239331489508823456171828716369223818080210707966955668713305367525096589687437082339558034307
a(275) = 38427510986762262783508061016980151692693704881154480120349299616798837724596939753889142718955452551303461175910392494072407769294225303767221594802109112021606995833437837854066735474038818707277585785807587132
a(276) = 233142752400739384191339319399813823299663246008793499876572456916540352149104882369920884189617727093643025046707095658921622583133554225455301300536071723586965561150502645542025587696896820341598254321329896647
a(277) = 1414523315838229449978855098195904456039931164804318147192922230598689603461286809071667999093535662660920416495832354498787740766992922695010948153715095150468664299913899366525315384154740803192893723689841338927
a(278) = 8582360783794051446060390769975280422414804410196690150170229483180024013495801564436642845240084392046085501093582311477510898762033027855219121931950590904218485927772307976230518856652895782986726682727617499200
a(279) = 52072907768148787667545700616851291775094955138779510546957024980944945429494691200604931107643097925741268850952931795392496317952235371586083163323422955122867389006729222607707466547023923788070439960446915760602
a(280) = 315955003078237284011420604368294689605803936640574931841845376280768400110713896032722830575332550435856082944670828384071488713597848194539701653377600347214922549035028439483007190995517760362170641432766973638594
a(281) = 1917109545531778154074439507316930405697781893633617027550972915379189634954774818386392302214648593048372804834482966929559628913848691119006872694781695737294458822164972200094641760200873823745580088333917019282912
a(282) = 11632601466142323294654444102679834687416957689128877153461228537912490040430377546805295385456487339200805603914645517854816008023483434040454048296093561743441989506680773431875891302295303749201498348929064434245234
a(283) = 70585409384451082284825775985306898550752338486752666013454477098035341670150303577494198252586169699558706985078848878889960026680726494062108804980877264564894650907874974902148245268406999301519419380661174509462554
a(284) = 428312883084028294762326069274704195565889932806156806516407174684679862972946750417434301379205781182179823262636142264676254685392231131325148252791381747648433983123386303071216558424785968930199582375728976301662163
a(285) = 2599054530819626969654642860669056515322856040207057719591477318994536678951985350418887242000289294693127966167328705819441841085885732017940178433346478326367642709396167023043918178125268670021274724673689454234911044
a(286) = 15771668615948579639258676847259329068328306666666944298075893165949465761423512066067949795837049980827859066430296988760770555898838697622104303583710416639149660911290116424031711815141182905066046858170016081261104465
a(287) = 95707911069334048159598647833304488065284813113078703008866505989122929456991916423727100253498638801253309526891316829407085287528874285937881712597522321283407699888391490874110274525316578533711028050379495969269131451
a(288) = 580799078110757711048848753180025466487485597886864882153509989068707866708490224390178927001949605187575956832711045300301839428102491194843220981775365916726911744629503899744791223310482132520485361331375040606811876521
a(289) = 3524616189257384112879804750950795954825722556034541918363374315288717720482216089300086408835487122434078173689114164633832324907782256562711259651174357583023559371974346801767210485272867692431435003055671157253449417493
a(290) = 21389740875805278012076607281375909564937607350792107862699170390765919170432310989385764314885363992391499386727533337854545749572089218656668057358416922411169115328694020892227006283693488847400065924879081687221245886968
a(291) = 129809638337091150425265398170236938702364765428278077461279476607142531644460910918179104768707983344171853935909732015321945903850054916394083864907015654432610160620951103979262973077931744501504053362813262217337043421037
a(n+292) = 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/(n+292)/(n+291)/(n+290)/(n+289)/(n+288)/(2*n+585)*a(n+57)-1/23014560426280103113350772162560000000000000000000000000000*(3225326330916237906075309787904156917314948762042735383098292572478026669447790937041801561*n^8+1580392282245331778866084318312162962669139633185033031939778361028994885052001245852789564179*n^7+338794401419257342475230501369266237331483411549337642296798573479168755952779289544814677734719*n^6+41502160477751374760139552949834963585344753558910284892534280964040937720008263393604328673928823*n^5+3177500415319631851370351208655359999862891472545116915506058810196299201250621252928311942849634384*n^4+155696967641356583141531614077906714050197793032214381275243154225351889634464948758350681431685686326*n^3+4768190904217871583924819259708216355413390768880947340086270125576001774543284429200503634691252545136*n^2+83442497017735598991079209834900530887858869265345078563065458394961948924273696219820405965216963343992*n+638846556916458468649391577191637585894355494277795051277559017930710666905610414772322753875102560522560)/(2*n+583)/(2*n+581)/(n+292)/(n+291)/(n+290)/(n+289)/(n+288)/(2*n+585)*a(n+58)+1/92058241705120412453403088650240000000000000000000000000000*(41469073638807455126010470266819627996642406659739137186229866760377013872783721846335660099*n^8+20644167042720629322252378321945680483798314141880268904327213485766037180460525594211314044860*n^7+4496268810707352791766989544566306295957599265556298912337158404344217231929741254737910217804562*n^6+559592814740711247331209071438605671397346413014524696763102223331259492250203250207460764167081820*n^5+43528553966893272917212400104765605213083152436778639041221779804439486655663367714679288810205372671*n^4+2166994511129648923817176483021305986814834589115727644189593816333827650623105975624724119554006757240*n^3+67425188800628009633974726056787367616464341903356095806406486906172673230649812304999662196695149202828*n^2+1198805056387850396081237628427877883477985066710423379182017721383385670832695000695558426472901848650960*n+9325077297918153097883701188840494757604640209180646135003906233532496107189717829826853267043391922647680)/(2*n+583)/(2*n+581)/(n+292)/(n+291)/(n+290)/(n+289)/(n+288)/(2*n+585)*a(n+59)-1/92058241705120412453403088650240000000000000000000000000000*(130417846721049552212072922689403241535278970566892533986757294372513716318059587992398604379*n^8+65940879916431415865603622683468034951094094597364110399391721305474379132638904482484747033900*n^7+14586669721990705387263064568054366106908193731505198977740473325147903079194479455099278942922914*n^6+1843844823912410803074917690961073730476105755317872105902721430850764177803942652953373801409698956*n^5+145672209151276081547933478726400099299875139714680903409141191948690568186085904572941962691435659071*n^4+7365672335723903049386864087660350352745273608429408764103003300215330438585408908901367144422805926120*n^3+232772023110131784630113314600472821175365749676912234833515366860879483269576180554824577189681389883556*n^2+4203520095992152442431027904001768070749478661088011646138513410201906680159572250554848636126935137485184*n+33210460404072820675310229901373867747614030068708309066851652207532674132236812629602839536559223353215360)/(2*n+583)/(2*n+581)/(n+292)/(n+291)/(n+290)/(n+289)/(n+288)/(2*n+585)*a(n+60)-1/23014560426280103113350772162560000000000000000000000000000*(480831878022330935630011698801666174466365036112495514788232808849562824794939356660*n^8+189684153141358872237363060824973289146272173224161738673811687745374002918915732102241*n^7+32735676328702246015087715535643335074048934671681447202282697683348307863035746980986215*n^6+3228103756935134988252504781864650786130018795880254501462024692120241927755140452155733213*n^5+198942321902440926007147373352811781836516613467716213693562503434856645996084652758033013765*n^4+7846210544273862065794874807425410587782565019377455316550779166146274808926722267749321076314*n^3+193395102050857895225399183426002832922066811979588608919601760016476957289000293236390234640680*n^2+2723737773888628174627496084390634381410141379041178137695219720091782294688789474705324019147792*n+16781670524055697047415754488486755994281462024065393905333651930974394873391069743045550044456800)/(2*n+583)/(2*n+581)/(n+292)/(n+291)/(n+290)/(n+289)/(n+288)/(2*n+585)*a(n+46), n >= 292
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 110
a(6) = 535
a(7) = 2690
a(8) = 13836
a(9) = 72400
a(10) = 384086
a(11) = 2060783
a(12) = 11163014
a(13) = 60966409
a(14) = 335351147
a(15) = 1856259257
a(16) = 10332435175
a(17) = 57801286441
a(18) = 324808531172
a(19) = 1832684043137
a(20) = 10379060215101
a(21) = 58979237485020
a(22) = 336192767909860
a(23) = 1921840552425351
a(24) = 11015137484899685
a(25) = 63287839547409837
a(26) = 364444628846170071
a(27) = 2103074728272178288
a(28) = 12159828204009733986
a(29) = 70435795277835407982
a(30) = 408697100050070772095
a(31) = 2375228354516163847907
a(32) = 13824915745384862985184
a(33) = 80581288986909936531325
a(34) = 470310913624852898444713
a(35) = 2748416086257952099662621
a(36) = 16080388799798327609488890
a(37) = 94188884562279144610184748
a(38) = 552288918400678136450673142
a(39) = 3241701355123834066427374986
a(40) = 19045739169154566266798329714
a(41) = 112000650232368513378925039705
a(42) = 659207721905538983437411568517
a(43) = 3883161940433696539603051152143
a(44) = 22892531411032268957140232381820
a(45) = 135061615458460302201509274658895
a(46) = 797417126211407343861674154376732
a(47) = 4711305577622580553902482954527689
a(48) = 27853932235604050978563784735069044
a(49) = 164781888828081017979979979128467648
a(50) = 975436627587294128261964161823546315
a(51) = 5777564627240217559030282176450873244
a(52) = 34240246738533198161026416711744738843
a(53) = 203032697958514792848257349839335437420
a(54) = 1204545844059777617291038098554931513432
a(55) = 7149910871202624810333718878487027241521
a(56) = 42460979850519761642306761615324568211517
a(57) = 252280707902554300496851993849894627685032
a(58) = 1499600772253530772371242456713073982659797
a(59) = 8917808747839524709809403087322499000880870
a(60) = 53054859781777107026413657696109297024937799
a(61) = 315769844116107023111767172783866860104671883
a(62) = 1880134153096212499066347531775748692755674975
a(63) = 11198871006699227487931816985245602164124308454
a(64) = 66730078344873935321784428385251967020906639355
a(65) = 397764507147106892581631224196127787014139930358
a(66) = 2371825102522334327143247490748789695290288114888
a(67) = 14147737268942177271676712803627418082331840510543
a(68) = 84417921659327753982145738719372749410218440740231
a(69) = 503873492572784878290634375435252183042906408546737
a(70) = 3008455379953891392354955239413482331026068928120632
a(71) = 17967888018056486180385274183369231404789008780123185
a(72) = 107344113075035373135771771510838422218506254902175663
a(73) = 641480813466915212175198685728943656049332755335865572
a(74) = 3834511013131579865804949098742389544852658587510423780
a(75) = 22927355262895565830496594779891221778883078395800664737
a(76) = 137123688139218789373633394407542999332279570591196279236
a(77) = 820318653518125827876123023568317712525110130842766600324
a(78) = 4908642483213451923307482452474459435688822648690675808830
a(79) = 29379620039182496001488281118892180398756505638502603212792
a(80) = 175887208092685726512253648156307651951469223069483075003535
a(81) = 1053229682828849633113467605456461373281447715945121199689866
a(82) = 6308269227854031015044960601452176326410028046519665779923980
a(83) = 37791425558249103155342758735626296989443846423430694317156588
a(84) = 226448770877423789432699243744316657657809881111560283645932115
a(85) = 1357182011078055451567999172034005788271094140573268012137965760
a(86) = 8135711262627106276088524572190978851133638308660663146908953877
a(87) = 48779821901131714986150883836347773894143507205275168888625665248
a(88) = 292529830801483993078648518515412511800083303397040676908057411991
a(89) = 1754621547003535695138692393467743926558782527389836961813559059673
a(90) = 10526360794538463363895435712055742445028784808118889394330806237247
a(91) = 63161545357827879648022670041845840673550765161723476652024118864349
a(92) = 379057602451219271521390449657385991379502241031824490257601818848173
a(93) = 2275275371115780817195122126681492910649152662850535782870519243602118
a(94) = 13659581259716682323955024363879327585741397396659026042174999238021201
a(95) = 82018892180326510654140735783903437215024474240685113637906323981356878
a(96) = 492563221169121699274938174607252238635917325498171591735756444258829234
a(97) = 2958558454004667355129230391238475994613968131735363002087551833087422678
a(98) = 17773255669198377054837113505679599095037510168819237900385091786527073331
a(99) = 106787665995710747063349503166306046067685189282735293430758301468590463559
a(100) = 641713426915763485396673981008547630025868482196365780880907628397027156399
a(101) = 3856788091634893343155439438151832599403273449435601409928887236807634915381
a(102) = 23183221250709299955873584676987381892970743531003966133243995022145660146470
a(103) = 139374686195204199885482289341152353122322984346954877877451248418759043356586
a(104) = 838021092798367173002226748015442624755963273636361747433903761463261140734736
a(105) = 5039480400396539336327195331945089657119264705154360489842926117453622737120095
a(106) = 30309251120387353011673235345955723179611990345341357551470526832311137735918654
a(107) = 182314910903028273443053157995816721521998851579967802596320233574810949229569669
a(108) = 1096795461994524725064561323948040695482716288654002457919004384867091659750620834
a(109) = 6599097348865427306108226929891720823179146686082533750106502895458977359666684207
a(110) = 39709813868561936850695250650125631887579472004337201050230545935190330450864312257
a(111) = 238981681512556909035848350274717995418747931089885793085753568011272945205101419855
a(112) = 1438413874499578918189117986767287916684352958252591381616592676053339498968630259416
a(113) = 8658739509008273569897330570997413775061786488362079102698814318567038533806640436923
a(114) = 52128609468087414595744741912150172201324329030825468031503740669360360759469679413678
a(115) = 313868245221676526086307991913572723685961361787074235575623322815700727492249844387032
a(116) = 1890024930981333346789956843503699281974479532005645275682632179813423672257831859206249
a(117) = 11382450340476970860095117076122608920954989422556325339032986772635356431372291800635685
a(118) = 68556913639246607127543133822417160257802567011457840886646743108396632167410296417932173
a(119) = 412964974754320743655970252985456314117068082897990954632489861201691474528933987984252477
a(120) = 2487830984593662625330044736102968081474180535484939649168800991028281984540772956182333171
a(121) = 14989027713367483498791484316177613615041850911381823313704505255602189148400049793806799407
a(122) = 90317155708255382965306050794606369448885872387490616880583778442469076446546704199456132311
a(123) = 544265144225892684774820113873710370697755222535542357524361383651791757493678504899805141883
a(124) = 3280148990640048950987516695008532736116532069085600354053414126819168993944741474081848122926
a(125) = 19770548249813811152692630702106104060348288130604189346576371449780040656654310027170758598614
a(126) = 119175032723413565373598912463617876674060111998786874884677611051469643709161521229759598643890
a(127) = 718443498747175089920116636131919348151868459279149296231183487097684444522943938963660507205450
a(128) = 4331517698030376008067394705123633610999619881351504625348639111339767200229123543669299992690925
a(129) = 26117227934631174398472234117524913807486463793173023442532349753364549571856803779886217380714618
a(130) = 157489995002014976971355268625558212458078887172900534058861499341860767487125387496261579354631871
a(131) = 949767202880838084663755383090937973590143391420210206696318683821208497916693025257472985041062841
a(132) = 5728212181679172265434286964757655643043271831181924578425332444896145240276276015068167707562989769
a(133) = 34550806188054641167232352700131839352794890890683595576147727193912314145362984490346230413185418630
a(134) = 208417355079629569536862893955007292806087908330682999585232761322266706877439302250008273570329439535
a(135) = 1257319462529106867115169008238337051359443686534166030368091226968557264226828853363957583497802086284
a(136) = 7585652239768523696094639146460145186870795378496133244769900717439145333549260183078229213798676578247
a(137) = 45769401447109069116526193757952350589793808850972784608621682537872084691094822250778845094566025861832
a(138) = 276179883972249983625125179895035778886215699507373028580395414259500297553552936469703869821189592486120
a(139) = 1666644070950810772307564565163918500415064351016294286840598178669050732496292403649453604560013665530025
a(140) = 10058360645183173989449130872299076754011329942028220382389152207964243285079511310328224146486685614062465
a(141) = 60707813598615308291929026498990553811104298193614919736909916231366791789214384662423472449351016599324770
a(142) = 366432986268782393788501783547690414956331456762255770153501298197015540874801177400126757273273085871093038
a(143) = 2211956883098224998295955662574826053094860907972838545317566648879551955407512456551926649855032814982190447
a(144) = 13353356118144997107015870870082113794728347585830024021259125182974712308872981817579904286589967173228748577
a(145) = 80618636194041444807788634588982365932752789097262352602006774537739641493694677080862927304044960107223202486
a(146) = 486755958115593517443403200014175166805413947885920434936231030272366095294472116559044070780609719369944226671
a(147) = 2939121226514736387100413956030259471586275795904463190701893315719580889067737221457734828072374830124964625023
a(148) = 17748175124561310747430262889755044479785399571895659855127094813481609804471113374420457923415652050521134224300
a(149) = 107181416326412153143280819899086376671522659413939578268342353423727394274318801015330687483558334651251379520012
a(150) = 647313200500348616620565767499595059863843903091091205219217105389159114994759598195562161112731713084920935909940
a(151) = 3909653188066994119300885424495552719625596406127926376947025567918401772265226289713656583029612833617504351747822
a(152) = 23615134571781534876041561182245278369309860665524027132719909125639942021238352295356466142088601580048316361279451
a(153) = 142649634474147396604296205382353120858157024031231479833564102391095025126070326842556347922809039381196082379354278
a(154) = 861744628560036788458746698786978051559994652764693205543710670532903435129084235362969299949646614671311512755307570
a(155) = 5206115908710362313347495125615956834127359490769251156803397719218716346115645771805567129263586376682547413485082471
a(156) = 31454012604498183511018456495393739490634947448171652305043458901074023673609761499263784231052911177907444300762295646
a(157) = 190048703702046899016154961231149668636339828922689875991270280900243753274511331600225066185040631241093615193619300760
a(158) = 1148365300729540677240084547995990779567949854460260133128939043881202830831760042138384207988028279021893123991776478499
a(159) = 6939388057438820699370836249992105762811395359753120990036653231368509744496366394801665135212648535224268288729445386636
a(160) = 41936089082555194334183434682547786834166959109684429343683919179148059854240820758292702708068407482210552841691463771425
a(161) = 253442823381107508687074349400086194550140163832623789258282659556474579367158163198936788216883197671055624304830024374265
a(162) = 1531782406961520944045785467130315004841474562012618075376954372477104257232875845361352612199028402129873397119758105309331
a(163) = 9258462175879922203113925478455765600126757238035754869546992580587055736800913549742376956010376004585358255833052339948782
a(164) = 55963521551697022103407385681682642671709532736353091999197675553253872206711753426742977284359630598243396705764376464643000
a(165) = 338294795462885212395232703809159491447200163684409042780848799336473146657610058785342083148485987757603431452119888340189322
a(166) = 2045075802673783827485603591659310589314436458147848718885787212913545236694842787143004576458790216588875302263429230328963394
a(167) = 12363659362189833257514437531582805119130559278777985601198353407515636194346651765977093499521761377402054531046726810311957428
a(168) = 74749432329128887514230079398708699913482340584549350578011587792469477722193360149638969000038342595649009650195453058767620512
a(169) = 451951402261222094256534296023085158519331364961146949334683504337920254613569085171763419757144386527899273336491227184446243014
a(170) = 2732739779984043214629234083133307421994114716442392433655135959254695434470947110367486387621874833585378007759910416816222297842
a(171) = 16524459191824726313088725473840442188558100372019740578855941351084288725335069903333433814586372331677457601552975762973612787244
a(172) = 99925977558243705067047112092203106152610506122416630095319434504091585851973830103264807419010833148167937875548777780026106332617
a(173) = 604298441635358686799266850042522520102483767563355009611605898994011253053862210276385123903623415101407289134128069115025138461629
a(174) = 3654653512398436676765403854604058287530805113394164859941318341826252898866237339271380152189335953337747022843201446742283296693052
a(175) = 22103566877016057763009464701211921823570725365920373420867802113127138012185658920047794137168276682899924795781240110484634674052770
a(176) = 133690235889868982672144262063735355251729791959021207884525832668666091380260723210646274832785325895069848920441000755021531296532382
a(177) = 808645087526690826644328304438912728316306424254574824838310785813317167782508811821631845205640541592402770654324162035568929571513084
a(178) = 4891442082135869547972944482949176046028373510771723996197492935598125389471021209315070417220351528398113272562429260350898829340890528
a(179) = 29589412829269715529225703986229830806154572217133574020315503838173746799573342420254743607830605455613029087535281767972443873605425482
a(180) = 179001231857532265650339254865348925431275438188002397186459334235970456950014833988282950338176796774338798455487327567598584073537453190
a(181) = 1082918341845181235125346872242507099927524683300898698462103223324893163190204722321496433333274203765032444276899763444820392505519722442
a(182) = 6551718007097265906545938279731760558583002581783553042253508374952499485734101626827583496323932336446422515176359801054255748136911261344
a(183) = 39640056463401957898223949520499102709205798080648207893148831274033208797193767158449000653464129002837388875017695307702411065752182761120
a(184) = 239846121490614041980835709947598139133423510138372933937152219953297884374909468848141631919221165243644981201565598514215109793934416784774
a(185) = 1451276937207211920615913716015872485834486061607674566977872198422664517843019174003236920138160442685987420139695514066873172127019431252713
a(186) = 8781866682094781756467817805242961070661414052012595072705805175331162764324519695890416924506629550005695918981157015348595416196222090451428
a(187) = 53142518836777917438882758735163858758511937471491146121136572637119415356540355251677327776941110349243939459781989238450375301997219714766535
a(188) = 321599955769813707677388386028655159729367588468418944378971170290798468597029397611152147050289780142319124534289808052136406906918497132618485
a(189) = 1946292813116088304602310479207990895123408657853561302190799496989624229782559453900123586650902746283988994096271154057709224796193336990721249
a(190) = 11779274369582805879668500307037043731039400677332450248342245125290402243645858590126424662721258885690085193685632226132631523764062072622417795
a(191) = 71292996098825158723208560739641173054071748706495827618271396513314153876829406856830310867212101104943547450729938076738883809534416313896112805
a(192) = 431512099410740376116993994429068174849752455868596604428440803612459140336362876436771048244077088758581112495463862041960201663743112014617795692
a(193) = 2611900852604832882908698208008761480674148535359406786680413891860841050138033467115812946020183958197533174620951498143115791313929218468272830803
a(194) = 15810216366646871664084031359817165420325915749845003781179980955280567474587904520735714144529403471571954945237254547180397986582860514156540930412
a(195) = 95705341584963146703873360519589279943412570681232414548095887433393703592980753821519718087290687477356998403760354111997224760159679598178982288852
a(196) = 579364130780186712884430012200298765353787224565977417347815038579383963873307059508672825979198432102470288945337472268814196554522693212584203952701
a(197) = 3507388865623047816451828317949091336805847838367112488772926033940770228720694762268068688120222530707242551358565091655929265519236882537027812529493
a(198) = 21234055689692780180859427884836550628655224973147107207938468529923692517759959185012762543127791019233513898564707023721352996141122905407529469956899
a(199) = 128557830575049168165982121496013237463198325291546744038943877632487246281901763913762903907724544975787564309380833078234421044242759021420848173015762
a(200) = 778359987582281550009245681725051464135826680343229100725091855213731067408800793630354640161157707953752929077397482860393945707782337084342168364137522
a(201) = 4712796542913339039838915409835927181465018465114724915723388686254931566677519688308441407493452238615841724726226141309667872884643348748477116417447135
a(202) = 28535989756009230986633860071657847086035980158050821372423651353297913372421759453729153510499061112755371486000623803746795293434647966755282289973119758
a(203) = 172791785364313826316750904242665226187608986357579580892153027383906087902221733453898505559135257410102323230734550786741788661115334638025363483882453198
a(204) = 1046330752712895404661556661779139155922942869448950334862240926141076343007812521796412690716252554022553523332791900314648726648512463479029851396250725799
a(205) = 6336223390020747207095634032723560014219251442834985568696228497956654693445072595676942168256648838532256004513226726822664909735352779330941218809550838786
a(206) = 38371379418517672764075214250541613821000905774349182472369651520566225950336246310124705408595971512617593214433100906450568296870224460188816019616655696849
a(207) = 232380475244237753170703952000422734558406404529409471894725702021010875452301850138126718331846762604779312561487098044742532082860915835759040074661048190296
a(208) = 1407365834851969514043831523452000839685052153792188979150560340220713637118178574772329257858055741438814068902469174653317992496272666070296788881129871245342
a(209) = 8523723869432811571587264848558168817598869846205220968378620961938458317124462293088582383199814319737635413142661631895830591928027755640317391691795083889360
a(210) = 51625776525128387817298326249280573463493626586673374141302206814335737599171087542109306246943083494013987057022826880958282703489533105699453729177167360084459
a(211) = 312693272890501122604804361612823546698931373088264879106726529346899326307435485787157001893349739564747754895742499779762817880063768851986420407261446779880793
a(212) = 1894022161770118036051691233156439322072119513096901426282844470090303926868553426517157512337128033629846620758017305054635719282172188562055007820597968988316234
a(213) = 11472709967547941698967373310995053847612522268470002479789990549921700111183394031834063586389002066493313164578815737445040755478066389222364282979788428009766184
a(214) = 69496235176067822577882121914051414438428957208405168404232068789567476228850654072306165198923960514331290848843942981272143417646103790765728059893415414494212904
a(215) = 420988966424262928243941849573206816595958494344110323219741925591528080528260925219218421045899299271640146285583203140598759127283619088703917172400970500973046075
a(216) = 2550317141627812657647958789675186248167672652678029703172603549067604720378135658105028754766153260030778248633611696121253770079677493641391250722975231570585297380
a(217) = 15450110060620926422898303556471095382490468962088110268380182436959789735752477515910309446878789491084774890439286156424627215087121135022524213611410135747163946025
a(218) = 93601487100204472991207963599587544633249062001051895521753812447021228774648169315501287783060754243555930480712595334114072984680974250067648056820747229384743698886
a(219) = 567084239547917343238391869185638563377453191145187941039962355296040324877453196044878072689331043243501876985867204843646705823298734982592925992905928344253150508039
a(220) = 3435784687384286057062413264458742940110584055271076172957007418039069708656565497496990492227025294546981912062895302691784860690175135777695564371787099526779268886506
a(221) = 20816979426765991820396843214758101301025783203183264668541661959991945426885082105749346563766708121360327098562378584179832879548755583869582964998289347992328683963849
a(222) = 126131272224223038484900225642541433340771932096181188908671744458279087549354069781256654870777916486543678378184520222942756244380535208503867236193496745553184853290789
a(223) = 764259789469382780302730117676088056655009692880661362227766949405884338206218133946758408884765992633411381632277139499130345304121032168206345741478617920544789599825232
a(224) = 4630973518918038638408895396124483771166822126065514054318780116441273359370156404007999354981075118974379641960304538304353608722206580642769520020142375161525313693340289
a(225) = 28061864414279973137422649993077640042300019479436070695591624082839084973709838110569428965691889486800611713705576281872399333153468506795272214137044006764696083012792471
a(226) = 170048798928562084280315131213433170678789491397185698948458159106644334833607055070525291987461120971538885160140425983929685869012550454268629691816060009997479126526464317
a(227) = 1030488916921135710340061468993680064455205907399111785186004733770883698048350907297654307233995656460426998189410559968492019327802495372341619269190807058227632701424759826
a(228) = 6244902750279450129737713011142875934151577628619362378730382157081568772674937965526496555661352631761576846895332132523524234235682891404319845368720133839155766479043072270
a(229) = 37846046791765277945321181422229449414418431268308086750069825022360588190203313612740342426765383245195828240612085534320912106928246456248537767739720337472005652612662532114
a(230) = 229365314895781382387666597899100987380978559318773829046040247347256940672514148673625819402857151962291718834964220827350569503044083633373828600856538553787970223401682656321
a(231) = 1390103821660049944474296143349784214126434234074241345092027829857884875258101962609256111504874995664841807023780068154784524145977719856400035047097265434740638813086168830252
a(232) = 8425174356134128667837189820347330946817592662182630735419836552984401936840974655613766320033214835089517288940757750290246455082334396868531029260177243802490948582632661538704
a(233) = 51064915651663880346773419809982937096333546218961474979308604344470821387236814846714868747952157051958669373267997520072913452050522106183530316423573537475897645333540052088225
a(234) = 309512575545902888724711045354917584915215786942750407974882907501980475181121159614603121508892441700547184770017568727775254229393573351115491063306568915711307046179226820021426
a(235) = 1876056165851809086305101528350314749770906336753215946224496932957174280416064248350455177622017573369681920219245071868908872878667939673484408737856592450868462376752492733353997
a(236) = 11371693079464928435278382069038352559754166694441093548878705123446915572629714188284828551207835731402949039786975002300800329462789124274288314161607635418939089860639334027534703
a(237) = 68931238247460245386223643926126165532033351354479982416006908783307579309165959279994953208022828613350249461033372290427323612201880644542644512587568453937123248752406226014559426
a(238) = 417848251751163553479364978627321273987563459655676454622440006061470555336084357375787769331296149764854792595814534092934405056407371240969363004896436016885535618671122421765719590
a(239) = 2532984668580169785278552715659264542152090928086097582358958953348840476319864049833273831042364546937408966665154462691458159887477876430472354288074619730999169826453352634700043376
a(240) = 15355285636872299246275663091603619836315781169158393014784930281271676881267561142626231770692842311100114654922784408401544386911412085421913233411989138706917391388876317650948105358
a(241) = 93088173770481848218509328998266840465016082901333955887021477469497091960211164323084596497846037042150475725323454380805242806643107529380902627927040978074500061882617806528091857081
a(242) = 564341905410665894969385675996508572333731043737555778291048470613724637289756302714145120178590096436867230658761056119015823309441736264647455239862822028694346545908073533405696984299
a(243) = 3421378934858524811175170562721415049124047430015092662796281433987921893037944363638421823317923969742760618325064106109550548882528083682265972321994812015661579413627520889445927557624
a(244) = 20742975304503511753905457586819676650618218299894616135544157809983165517023936837037831479634152453848125319720450134774951380733655393998649865869419318606464565833967587137997311008741
a(245) = 125762693391665373746417005163343191547613103413821261328900462264604121111796514369781954810872913687994435234215180947655763742074330604167454775555415283076894711630315803552377026225965
a(246) = 762506283838841938659722207511526624763288880847840786854052999389480693204846941936087574862129607515356781478072719950680970385330944253597896149937915254231935234791273943342131192657190
a(247) = 4623232711930847137985602375173594760938100739397354936601078915686900526556695186194155810065857297076754168388959211490521782611148314692011975491079764084840333783260997591250862471861245
a(248) = 28032299535034741398159667760368086233677467111080385613277972100563761143272922626124545244548928827746741331888243363734737237729796896308424662547976872602074271782152836865725885990298537
a(249) = 169973905691382829950329274680499702199912168689835826033270143544550872771908538443788234944012929095535683587870606554650848935245023776114930913737731955296662505035066904245491438001127744
a(250) = 1030661980764744351909459312046922910691407199754440874640763367865030061288747231508143827124159806796287134156032652386754751285869150006371716695467300319956389571579303693901894964790453613
a(251) = 6249721261531891847591426920605064406565036642786193309724717453284529954666747526298574074475455119989298886081296152478910390798331946022151611454920758227367332403043973260360963416342325289
a(252) = 37897917657127156351266493660240511973434762922113815321529066157431937088300923360987140662277599544651975621476980976861402710352526203533834437384600009737235014909556076050310003559857212830
a(253) = 229816006392410594734529921010435455930429884269765751567775288723917435253141830192363983695851749343095704493497811838840521191238531131766130798205296622349964116540597786279943066751053858609
a(254) = 1393655215866557908581449455432926141172730531478472510297558583260735173072715710938516497616242281496459744856618853329784426195272708372349754945421779748180622835479209402067609470790123713105
a(255) = 8451630104567317379540755588836675605359174034533921867813517857551698810787519666473334561118765532355415612623410475514829251703993511632777574529620550237155758222752279432183104649286112295811
a(256) = 51254925360864435537916466786323727914401060679702619307214407863268380688160380608458179877955396549535899933415806562635171708232875099554704938926661745658937156470525698577287231086819215020070
a(257) = 310842675834239287024634918767815880194224451073794771696893805471399636376728516640168941167891846428095907154957718372399553583426099709338535576219895323409919127657569439484314383221379199130357
a(258) = 1885191638493309936894872622799262874899804521231533557533332936787660772567040722283233892091005722281475279413366552836292259931250865034126431571663244083964546627773245590717615469295524734189527
a(259) = 11433524518697295914325165995526584432321162909044511447465412231724954543221985666362969021014900307200279219990775615675297328457009742537222971554324436968810830984101404551982178616739928699397915
a(260) = 69344884882986455817888471802773648804085465390946656002809565754095330513533093583200791554350231308319920511069895378239418984218173925823126346319800692776983682923460369749649947877376128922094697
a(261) = 420589419244322239549611693630567050761712929790664971380003063547128916481851162875359393867551014917319024095459313760739496581633946534699163330723887709426405828088439255755032559920425016488275733
a(262) = 2551007810543616760519008884311280746624061796678373250783623744112335703083116062088643274467143322122986543901871272501880745482563152319686409135123838066810994158169700655106209603936461837854264760
a(263) = 15473006040560185112675342363811551298875883359863996138705592392609938081715047659756908215325100450842438871569311733407385348780638574830989511053459418018269411141670471191514546496206427223768140056
a(264) = 93852747636090399614172103085358668223030641860952380893983311471306800075773631508194811361800305704567346334197901366027484003040567725926240356594911407224224539258464418225841204450772820122499947870
a(265) = 569283513594653048946984101362034750311814783949869370852388287076415734601406607088579756155511490190576416196527329323246458502283015840848051722567355044009388263159937037884713064870814512519213028369
a(266) = 3453182019350439383119405145731504079765765836475967870680173329050297738001908430038934746630736093441493487381947933353698720366498353155641532780693064091518211915412406419676366677205947148242222910979
a(267) = 20946888179488039846426911665703950625650581747485391036328896354856878124562337139033586664872354730999058487659078597648394282830980366143330164735541323080597172525361060196819567269571563017799447959066
a(268) = 127065798115924355449695748456156241436592492868143605398868636719896504458546289209018519122070989441503560217598869209579427568042386797566445555217172414966822619378884687283690289842128820845209187888648
a(269) = 770809158448500748346890538703677363641808260110416661163867813918304407907177360180828683895699875049335176559168373087013924037514726853872592974663065580989032611112228350481489111051910382927516010162656
a(270) = 4675995017348875315593398199873183824974050803584856742565776676466204890194735833269695399198021744081079761970695807981364644113775956160668070124158151280561136473045500212615789621629051078333523817823959
a(271) = 28366785398599819735583035391987547331335755288982200620260578901555493844070462018964214484299267248468369554866366065701125294857853901332333449410049334354368655684743598446120975345909232439957912318768885
a(272) = 172089768713404584136446610096025300870469540769319540429366678139047710997276476815447831434751100941641834787393238235823221053323876281421295683028022811322185307761099017491050688379041960872446752062955858
a(273) = 1044019855146615340731004744522270530652220440123029926735204269128865871264244660508075537362375268011106897844987444110653064571977945153668531746136965082896258482619026446397667506037528299190278941314482104
a(274) = 6333899684437650768329916895361721520518188813764467552581721802814721473744697229591130334275805726482789896073022440239331489508823456171828716369223818080210707966955668713305367525096589687437082339558034307
a(275) = 38427510986762262783508061016980151692693704881154480120349299616798837724596939753889142718955452551303461175910392494072407769294225303767221594802109112021606995833437837854066735474038818707277585785807587132
a(276) = 233142752400739384191339319399813823299663246008793499876572456916540352149104882369920884189617727093643025046707095658921622583133554225455301300536071723586965561150502645542025587696896820341598254321329896647
a(277) = 1414523315838229449978855098195904456039931164804318147192922230598689603461286809071667999093535662660920416495832354498787740766992922695010948153715095150468664299913899366525315384154740803192893723689841338927
a(278) = 8582360783794051446060390769975280422414804410196690150170229483180024013495801564436642845240084392046085501093582311477510898762033027855219121931950590904218485927772307976230518856652895782986726682727617499200
a(279) = 52072907768148787667545700616851291775094955138779510546957024980944945429494691200604931107643097925741268850952931795392496317952235371586083163323422955122867389006729222607707466547023923788070439960446915760602
a(280) = 315955003078237284011420604368294689605803936640574931841845376280768400110713896032722830575332550435856082944670828384071488713597848194539701653377600347214922549035028439483007190995517760362170641432766973638594
a(281) = 1917109545531778154074439507316930405697781893633617027550972915379189634954774818386392302214648593048372804834482966929559628913848691119006872694781695737294458822164972200094641760200873823745580088333917019282912
a(282) = 11632601466142323294654444102679834687416957689128877153461228537912490040430377546805295385456487339200805603914645517854816008023483434040454048296093561743441989506680773431875891302295303749201498348929064434245234
a(283) = 70585409384451082284825775985306898550752338486752666013454477098035341670150303577494198252586169699558706985078848878889960026680726494062108804980877264564894650907874974902148245268406999301519419380661174509462554
a(284) = 428312883084028294762326069274704195565889932806156806516407174684679862972946750417434301379205781182179823262636142264676254685392231131325148252791381747648433983123386303071216558424785968930199582375728976301662163
a(285) = 2599054530819626969654642860669056515322856040207057719591477318994536678951985350418887242000289294693127966167328705819441841085885732017940178433346478326367642709396167023043918178125268670021274724673689454234911044
a(286) = 15771668615948579639258676847259329068328306666666944298075893165949465761423512066067949795837049980827859066430296988760770555898838697622104303583710416639149660911290116424031711815141182905066046858170016081261104465
a(287) = 95707911069334048159598647833304488065284813113078703008866505989122929456991916423727100253498638801253309526891316829407085287528874285937881712597522321283407699888391490874110274525316578533711028050379495969269131451
a(288) = 580799078110757711048848753180025466487485597886864882153509989068707866708490224390178927001949605187575956832711045300301839428102491194843220981775365916726911744629503899744791223310482132520485361331375040606811876521
a(289) = 3524616189257384112879804750950795954825722556034541918363374315288717720482216089300086408835487122434078173689114164633832324907782256562711259651174357583023559371974346801767210485272867692431435003055671157253449417493
a(290) = 21389740875805278012076607281375909564937607350792107862699170390765919170432310989385764314885363992391499386727533337854545749572089218656668057358416922411169115328694020892227006283693488847400065924879081687221245886968
a(291) = 129809638337091150425265398170236938702364765428278077461279476607142531644460910918179104768707983344171853935909732015321945903850054916394083864907015654432610160620951103979262973077931744501504053362813262217337043421037
a{\left(n + 292 \right)} = \frac{8687079054463150341 \left(n + 4\right) \left(n + 6\right) \left(3 n + 4\right) \left(3 n + 5\right) \left(3 n + 7\right) \left(3 n + 8\right) \left(3 n + 10\right) \left(3 n + 11\right) a{\left(n \right)}}{1275832123205160140800000000000000000000000000 \left(n + 288\right) \left(n + 289\right) \left(n + 290\right) \left(n + 291\right) \left(n + 292\right) \left(2 n + 581\right) \left(2 n + 583\right) \left(2 n + 585\right)} + \frac{\left(11699160269209948246 n^{2} + 6752733085715975878117 n + 974407954012208751543141\right) a{\left(n + 291 \right)}}{62296490390876960 \left(n + 292\right) \left(2 n + 585\right)} - \frac{\left(14670555300002128937564164 n^{4} + 16906170877491245606985703236 n^{3} + 7305900456970436333317776229967 n^{2} + 1403195743380472712445516945528699 n + 101063088539327549347619962353854094\right) a{\left(n + 290 \right)}}{872150865472277440000 \left(n + 291\right) \left(n + 292\right) \left(2 n + 583\right) \left(2 n + 585\right)} + \frac{\left(50408266621700184496105743152 n^{6} + 86981044179121496520278847080592 n^{5} + 62536707432925303631425561915071026 n^{4} + 23979654376411515703138361087847192255 n^{3} + 5172162237015835887631371583536166608548 n^{2} + 594975213716061583091771838909919879854093 n + 28517611907842843275441335713115375243450334\right) a{\left(n + 289 \right)}}{52329051928336646400000 \left(n + 290\right) \left(n + 291\right) \left(n + 292\right) \left(2 n + 581\right) \left(2 n + 583\right) \left(2 n + 585\right)} - \frac{\left(35678140332362953587220684699512 n^{7} + 71603654658114289586385921205750306 n^{6} + 61587217534577900425627661271766036779 n^{5} + 29428808009976670370830227947648506228765 n^{4} + 8437333378736133617896186440681037675303143 n^{3} + 1451403601427270698749455564376365917046617849 n^{2} + 138706839685611371467880595425942613333085740726 n + 5681067773667581722692001085041363979078127135240\right) a{\left(n + 288 \right)}}{1744301730944554880000000 \left(n + 289\right) \left(n + 290\right) \left(n + 291\right) \left(n + 292\right) \left(2 n + 581\right) \left(2 n + 583\right) \left(2 n + 585\right)} - \frac{24431898297807 \left(3 n + 7\right) \left(3 n + 8\right) \left(3 n + 10\right) \left(3 n + 11\right) \left(17002565217 n^{4} + 343030007394 n^{3} + 2567336096623 n^{2} + 8466097887246 n + 10392194536880\right) a{\left(n + 1 \right)}}{51033284928206405632000000000000000000000000000 \left(n + 288\right) \left(n + 289\right) \left(n + 290\right) \left(n + 291\right) \left(n + 292\right) \left(2 n + 581\right) \left(2 n + 583\right) \left(2 n + 585\right)} + \frac{100542791349 \left(3 n + 10\right) \left(3 n + 11\right) \left(4282035990584832 n^{6} + 136378202269859559 n^{5} + 1797435183316349898 n^{4} + 12554718830613458145 n^{3} + 49033885914234545782 n^{2} + 101561881162209410648 n + 87179402990143813440\right) a{\left(n + 2 \right)}}{102066569856412811264000000000000000000000000000 \left(n + 288\right) \left(n + 289\right) \left(n + 290\right) \left(n + 291\right) \left(n + 292\right) \left(2 n + 581\right) \left(2 n + 583\right) \left(2 n + 585\right)} - \frac{1948617 \left(2122096687188469043452371 n^{8} + 91672878915106799099282532 n^{7} + 1709785245132812958239556774 n^{6} + 17959691820344267504080161288 n^{5} + 116007267707258093308028036259 n^{4} + 470739524721078531306885816708 n^{3} + 1168023212281378706660668647076 n^{2} + 1612424742633185571787805092432 n + 941081301481212617989503502080\right) a{\left(n + 3 \right)}}{4082662794256512450560000000000000000000000000000 \left(n + 288\right) \left(n + 289\right) \left(n + 290\right) \left(n + 291\right) \left(n + 292\right) \left(2 n + 581\right) \left(2 n + 583\right) \left(2 n + 585\right)} - \frac{649539 \left(249438168527263396991806347 n^{8} + 20985993097185685901470240149 n^{7} + 677343446573040232846259996331 n^{6} + 11619813451742056109206995923367 n^{5} + 118885766350974289999306232770538 n^{4} + 752895628379631356990896731457516 n^{3} + 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178865785713463606885851700324093873166782414810040236431257420345271091268399570487377679580155098566764358682179110032226537 n^{4} + 23459642600546626793894126325645293556642475286611468204013440714531385101072432101544065203504870040939727383056483371938687916 n^{3} + 1922811108479737052646581996827776591281774152770351261757633984741107473259277651009190288983990625918370545684201617705125441260 n^{2} + 90043850310927840212989626148304016487208022926464289906404689412644469760607525615714524254686396866337548928442718740146322347120 n + 1844543478374877725868395622937117696170802147972413950571083701107480391761096958316961187787234979583157863969096839981448435687680\right) a{\left(n + 163 \right)}}{61372161136746941635602059100160000000000000000000000000000 \left(n + 288\right) \left(n + 289\right) \left(n + 290\right) \left(n + 291\right) \left(n + 292\right) \left(2 n + 581\right) \left(2 n + 583\right) \left(2 n + 585\right)} + \frac{\left(4170452477561515596309268161685298377943607420139617296715228876897173066040300357503617197840110379837908767986311 n^{8} + 5078799959165533723159488848413644127653504779445988723517270123659858383555639004752331903541572873510813781744569916 n^{7} + 2705976964135429554698897639942503476589836768700052016991329007513974937620217249193616596783216609530024757841935199734 n^{6} + 823865306423907615753085439026871334736154898937944412227821219398135753721854816980026953678194492558445100731408454023232 n^{5} + 156774600142150824940161361827228377422044701271880076029015644522113606088730530218922506842645615962661618131331770497023079 n^{4} + 19093373618800693123351388711002656631152119395354246330849473399974696054939773554466815227715504050738993106812745119254596164 n^{3} + 1453373752504653698157278668654552777114496864851797534705570278703079812090299437152697040803269343056625284279373290155813283516 n^{2} + 63218137608647976131125028457097841062977603249717485716963319247341456436254720470249505033453310365309261031980955614620247028768 n + 1203073212946765010490101213785994200466081116984776264176460095686228735385905103708878029283697085174125979273375274814373013048320\right) a{\left(n + 150 \right)}}{92058241705120412453403088650240000000000000000000000000000 \left(n + 288\right) \left(n + 289\right) \left(n + 290\right) \left(n + 291\right) \left(n + 292\right) \left(2 n + 581\right) \left(2 n + 583\right) \left(2 n + 585\right)} + \frac{\left(4281880630462586950846320041373725606129952365245365648205000748892324936335966083472335348745665975396162266385661 n^{8} + 5406512856352417057110157157479369393680258329002376177639598076126372318434365431102965393109160303707185666364980508 n^{7} + 2986556176372184169473255972881442301006647868960375346974427965890219739448850292849273386285303923167783465200160893410 n^{6} + 942711902657163826491869771319904314290844065930332362975287281929008955649939751749907431355183052320818033990472235159184 n^{5} + 185977494829385298902831987450328265122069779909645814459008758034312830385112393229670278606645148271189283187656939746774469 n^{4} + 23480915053378545563010707521097644094295702048827874907445416655094042873906695561217970605097621522331218893710153849860464772 n^{3} + 1852861914084061866987467085544731622190801994213003713934804335545516678684850499841466588426340666588196868721707394937137795740 n^{2} + 83546174964426073383695864935326670597219961317101845957613276231889467362252459482276710943426043449190828101605161324860840615056 n + 1648093290269078292589555288523042779472987139517659381221024773774230438761724307495621571341959966857832873854529736187001940329600\right) a{\left(n + 156 \right)}}{61372161136746941635602059100160000000000000000000000000000 \left(n + 288\right) \left(n + 289\right) \left(n + 290\right) \left(n + 291\right) \left(n + 292\right) \left(2 n + 581\right) \left(2 n + 583\right) \left(2 n + 585\right)} - \frac{\left(4635040720656147012885162679696800335939085433924919809177407246210252935919198573172132955510765844760043260282237 n^{8} + 5679281499365923204901877714285100745310342575778310574807473859797851777022642156894510886519128656357452118534356764 n^{7} + 3044505380076464108965144247993001526329805472130293095681354360034321860931611416695743608021943829670101880391966254694 n^{6} + 932626374901727070026456345977023303944139435071269089360652038979995930711751752937992340370363568602712628059970460386084 n^{5} + 178560126851644771583686503512889246464431102974408365652700093122409313705434253188469202993007464930527692014246948191023033 n^{4} + 21879996610866589819717136790409916324605776051778732395539408085737354398069840836912301909012990292676812230841629957378364656 n^{3} + 1675699689210441484227459054137800181186291591996020055776929382894220078339199049360936219065581655091065428591980721057535643236 n^{2} + 73335352403729170542451363957474452485386001560007901748619614112547479937660419397251728708461516199468662342967462230881813215056 n + 1404155078881396587787689959698089544047147386623326638475419858999010017732009276229651948300358731160811929099883096336082272524800\right) a{\left(n + 151 \right)}}{92058241705120412453403088650240000000000000000000000000000 \left(n + 288\right) \left(n + 289\right) \left(n + 290\right) \left(n + 291\right) \left(n + 292\right) \left(2 n + 581\right) \left(2 n + 583\right) \left(2 n + 585\right)} + \frac{\left(5083496756556227407537465149632644542392697040255557467723599377379280441973247901507093906613930688559872988243851 n^{8} + 6266856518559014765270957966532178037462915118184624765601681435021071763505208665270892309367945509857383114853153160 n^{7} + 3380014915681172912146959726368467393409977700313740279998259250696093270764230054583681001061038473780472109046633164738 n^{6} + 1041725379538440750131382097752314940487988465049963612047228757289143232489154427354597972266767372513441541788808411875132 n^{5} + 200665122228904751654505095149801975774224868573597998987443739138294873449640843239178966677323450672789283974192178952499639 n^{4} + 24738576138845669416132715215276077593249294439102568762907725056635994036188914936744528464780268408012378286470491620895734620 n^{3} + 1906171063408503551199675329997983746555959262566780938712743515313243874839664488429941404017037448350596222353537679387758025532 n^{2} + 83929667311135511407668034445478945097852633733942568774613675618399714272049731065372062009654242850691980975629079454225667471648 n + 1616783381766905522515125364665219332062063060780138800725332266628386271637189787179970724400937550586815808854106734964316133169280\right) a{\left(n + 152 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48831018028040785572576783083739774941216238477389949896046526836879620425360256533490127529839640274660036418485279801799620564 n^{3} + 4050220076851939683494166514564425761190818036212039840499806723847436258065763783591031225390629122385261076869629850132384797676 n^{2} + 191899823037921923832296717702920922656303176625212078436076215678656029384386128891313885831635479620758230195388199082194379919120 n + 3976445610852502684656810978918444103404991377289812914843021429281937837257202194427590768179441667203521551107087096958803597248640\right) a{\left(n + 166 \right)}}{184116483410240824906806177300480000000000000000000000000000 \left(n + 288\right) \left(n + 289\right) \left(n + 290\right) \left(n + 291\right) \left(n + 292\right) \left(2 n + 581\right) \left(2 n + 583\right) \left(2 n + 585\right)} - \frac{\left(11002752740242518635859212456677720448631138635464440074777542835806849365580507061056982837752027872760057018621237 n^{8} + 13646433831779742803456420817842058001365260554983789268631607605205493018216292694456605724858401610133440854619561316 n^{7} + 7404853950458603962810921813515787905649200832063134708466871733740595843683242881932683169187511216138358522821944771130 n^{6} + 2296029313642757948111544860507725748677008897018204714665742519060866438541393943120181890303953044599126844335013500345912 n^{5} + 444959241576136635896847653474216062417936715979075940521011756392628510966935297514917285009493914291900890682464777990335173 n^{4} + 55188049699295118071933976821262694471193106478424645320076026534121354532191543368386930852520067979115685212389166420049537524 n^{3} + 4278111405147922411176679560661783298860774536034519320259039081444376340847731170454739783363253176411242365506785088918638186060 n^{2} + 189506213108126489972622529137469528717715725898843452290847001781364596532047540813438770522097847389706412662838467651981912854768 n + 3672614882951416530237218624121969697339135429599089944754331145538473172319723302766464067944465315536003807040340654811920317036160\right) a{\left(n + 153 \right)}}{184116483410240824906806177300480000000000000000000000000000 \left(n + 288\right) \left(n + 289\right) \left(n + 290\right) \left(n + 291\right) \left(n + 292\right) \left(2 n + 581\right) \left(2 n + 583\right) \left(2 n + 585\right)} + \frac{\left(11747380875524845648540587991641095156397579546625518741601472525940387906832853412244669196669760536600531557272793 n^{8} + 14657850329368854346322635443358936092786503898817806123750846947758272461242257092063024221590558063858478284135977764 n^{7} + 8001593985867923762205925509825958004515042396133351913163346804913427836537579428985634360957004283695048677612911664114 n^{6} + 2495995743066614269227197778339593889508321117613954019847457648750089617220754168980502716664823528410643301911326664070408 n^{5} + 486620651712029987579163665661774906008529800313479448947388811832823707910775711240637668563133935087829264699965099422231257 n^{4} + 60717899528520449909076223739879613137735099906978641553781833600389051552350865077729774377489865776521432362973623542119552036 n^{3} + 4735029228480020848710361387687570678116950671118304066061601129768151317494161746793213993686201826797962760982927484333446869916 n^{2} + 211003861163708119295473584896737725308393049673555227140102817266069488371540153194298449257712199254216678718864130570868077752432 n + 4113733986931117591257894277888862709713015279979068082724441442652119412665370665860905603445769496566047137878378670400373726338560\right) a{\left(n + 154 \right)}}{184116483410240824906806177300480000000000000000000000000000 \left(n + 288\right) \left(n + 289\right) \left(n + 290\right) \left(n + 291\right) \left(n + 292\right) \left(2 n + 581\right) \left(2 n + 583\right) \left(2 n + 585\right)} - \frac{\left(12285247506208904540842549262481123866874444390230896374186819564433697356586664073157686186512874509874514700610889 n^{8} + 15956314252834916072336571731030908318050827475374567692252462967981504039334506778860057848229492160728039772801148172 n^{7} + 9066186293139842679514420318229546046446668127400718561780516802424918739669939157222227759185875985249095590649585264114 n^{6} + 2943363154757758335710716382813107777403928481865691404904242898143239109275899646092140533583064181647506288743598359745000 n^{5} + 597183936399378469043836465344811045119652569095105825807321447348090822802332264290066957365971301970945187364462137278945001 n^{4} + 77538466363362686114876984436275197120061666325799271370307068745887024365000645168857227625328787780311890562023119278532219068 n^{3} + 6291742441402296039160981478868131902897406331463143310419925160732150312184183650703158618926251238360150573330939515237394383516 n^{2} + 291709773932893016987552527028993285982597778561323642333691534417284450417329115779109430215539923656994215265827376713218105896080 n + 5916612894227263880229204376314584299050636837891569512836838501236377631069717956300928921271720478165036396451059142271947547190400\right) a{\left(n + 161 \right)}}{184116483410240824906806177300480000000000000000000000000000 \left(n + 288\right) \left(n + 289\right) \left(n + 290\right) \left(n + 291\right) \left(n + 292\right) \left(2 n + 581\right) \left(2 n + 583\right) \left(2 n + 585\right)} - \frac{\left(12371081398938350105116912667929119990359283042192213867750774670816776599335617966911156947397742829972393368750109 n^{8} + 15528384642463548614952814197425492591362707275423381586259901123551483487549017857921505197788849008359524008210992220 n^{7} + 8527446352532563491733341597344597180456775528669716560483555987171512772575821124243573524221604751774771073744481610250 n^{6} + 2675900213380374234115187785179557852268473366867574286206726451663446700088380774288523491183388695666359173660691667042120 n^{5} + 524804190807978541530639533963730025713958719622617095416355371921774628150495538782815865360352393321795628384122712830648781 n^{4} + 65872064024216015907170068708705008993540173682731174571478789951068051148181181975106366186723797918630507681910777494108545740 n^{3} + 5167518659298102901263661643219013412382403039504352081053119554816504576922501491807213458304933990733689390528536560660458127820 n^{2} + 231644356023536432319258751090120110401477389822665050357413830850564375851039981489709932444300384961882724251750195976408031502800 n + 4542934992677811874700179594732049744441409118724784234708422030384374337306416209674747145635205945650037359801275678193820686313600\right) a{\left(n + 155 \right)}}{184116483410240824906806177300480000000000000000000000000000 \left(n + 288\right) \left(n + 289\right) \left(n + 290\right) \left(n + 291\right) \left(n + 292\right) \left(2 n + 581\right) \left(2 n + 583\right) \left(2 n + 585\right)} + \frac{\left(12824715820845790595357740996146888701158034494522858237655007207823982228998663049035908148673506803074790077387033 n^{8} + 16566880348620982732890149300926203863971070691988091884977425642735279594562893990165344467044315222119068205740872756 n^{7} + 9362345605464548765359966888604702473128796982525072726026715777586748960580211285818872227272257382474027777718590210642 n^{6} + 3023176069330249036503546822439701859592701877801902034505634079741761622660256051599215213341790156613756205912403390974824 n^{5} + 610091662078615706580472594775650990001255988996199828198663316722737463156764271474407760862848406400081354384598973693540057 n^{4} + 78791526707396383510120898343390824089558178413278032211021920982080701910318027025630628112126613325012202489733870928319857844 n^{3} + 6359407884397005276968875205591918322440167371713785762841279382026850834244300806005536099968236661436501575643115124627301896828 n^{2} + 293284027520901615880708135640236695758290343176332062614887284897677591699501417559669988608840255451724603455096245282706186658416 n + 5917124120001186211855984801664455081967854305069348222028712648993151871497221860581211056469995844766403593755243420468797294752640\right) a{\left(n + 160 \right)}}{184116483410240824906806177300480000000000000000000000000000 \left(n + 288\right) \left(n + 289\right) \left(n + 290\right) \left(n + 291\right) \left(n + 292\right) \left(2 n + 581\right) \left(2 n + 583\right) \left(2 n + 585\right)}, \quad n \geq 292
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24755/
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[22,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]+F[66,x]
F[11,x] = F[12,x]+F[13,x]
F[12,x] = x*(1+F[12,x])^2*(x*F[12,x]+1)
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[4,x]*F[63,x]
F[15,x] = 1/F[2,x]*F[16,x]
F[16,x] = -F[20,x]+F[17,x]
F[17,x] = 1/F[4,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = -F[12,x]+F[6,x]
F[20,x] = F[21,x]+F[58,x]
F[21,x] = -F[22,x]+F[17,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]*F[9,x]
F[24,x] = F[25,x]+F[27,x]
F[25,x] = 1/F[4,x]*F[26,x]
F[26,x] = F[2,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[30,x]+F[53,x]
F[30,x] = F[31,x]+F[51,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[12,x]+F[5,x]
F[33,x] = F[19,x]+F[34,x]
F[34,x] = -F[50,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]+F[45,x]
F[38,x] = F[25,x]*F[39,x]
F[39,x] = F[40,x]+F[6,x]
F[40,x] = F[2,x]+F[41,x]
F[41,x] = F[1,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[4,x]*F[41,x]*F[44,x]
F[44,x] = F[1,x]+F[4,x]
F[45,x] = F[46,x]*F[5,x]
F[46,x] = F[47,x]
F[47,x] = F[2,x]+F[48,x]
F[48,x] = -F[2,x]+F[49,x]
F[49,x] = -F[0,x]+F[25,x]
F[50,x] = F[2,x]*F[42,x]
F[51,x] = F[52,x]
F[52,x] = F[24,x]*F[31,x]*F[4,x]
F[53,x] = -F[56,x]+F[54,x]
F[54,x] = 1/F[4,x]*F[55,x]
F[55,x] = F[48,x]
F[56,x] = F[57,x]
F[57,x] = F[24,x]*F[4,x]*F[5,x]
F[58,x] = F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[15,x]*F[27,x]
F[62,x] = F[21,x]*F[24,x]
F[63,x] = F[2,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[31,x]*F[4,x]
F[66,x] = F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[15,x]*F[6,x]
F[70,x] = F[71,x]
F[71,x] = F[72,x]^2*F[73,x]
F[72,x] = 1+x^2*F[72,x]^3+(-x^2+x)*F[72,x]^2
F[73,x] = -F[74,x]+F[31,x]
F[74,x] = F[6,x]+F[75,x]
F[75,x] = F[0,x]+F[64,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_{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_{22}\! \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_{66}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{13}\! \left(x \right)
F_{12}\! \left(x \right) = x^{2} F_{12} \left(x \right)^{3}+2 x^{2} F_{12} \left(x \right)^{2}+x^{2} F_{12}\! \left(x \right)+x F_{12} \left(x \right)^{2}+2 x F_{12}\! \left(x \right)+x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{2}\! \left(x \right)}
F_{16}\! \left(x \right) = -F_{20}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{12}\! \left(x \right)+F_{6}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{58}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{17}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{27}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{26}\! \left(x \right) = F_{2}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{53}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{51}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right)+F_{5}\! \left(x \right)
F_{33}\! \left(x \right) = F_{19}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{50}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{45}\! \left(x \right)
F_{38}\! \left(x \right) = F_{25}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{6}\! \left(x \right)
F_{40}\! \left(x \right) = F_{2}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{1}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right) F_{5}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{2}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{25}\! \left(x \right)
F_{50}\! \left(x \right) = F_{2}\! \left(x \right) F_{42}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{24}\! \left(x \right) F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{56}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{48}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{15}\! \left(x \right) F_{27}\! \left(x \right)
F_{62}\! \left(x \right) = F_{21}\! \left(x \right) F_{24}\! \left(x \right)
F_{63}\! \left(x \right) = F_{2}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{15}\! \left(x \right) F_{6}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72} \left(x \right)^{2} F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = x^{2} F_{72} \left(x \right)^{3}-x^{2} F_{72} \left(x \right)^{2}+x F_{72} \left(x \right)^{2}+1
F_{73}\! \left(x \right) = -F_{74}\! \left(x \right)+F_{31}\! \left(x \right)
F_{74}\! \left(x \right) = F_{6}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{0}\! \left(x \right)+F_{64}\! \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_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_22(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x) + F_66(x))
Eq(F_11(x), F_12(x) + F_13(x))
Eq(F_12(x), x**2*(F_12(x) + 1)**3 - x*(x - 1)*(F_12(x) + 1)**2)
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_4(x)*F_63(x))
Eq(F_15(x), F_16(x)/F_2(x))
Eq(F_16(x), F_17(x) - F_20(x))
Eq(F_17(x), F_18(x)/F_4(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), -F_12(x) + F_6(x))
Eq(F_20(x), F_21(x) + F_58(x))
Eq(F_21(x), F_17(x) - F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_4(x)*F_9(x))
Eq(F_24(x), F_25(x) + F_27(x))
Eq(F_25(x), F_26(x)/F_4(x))
Eq(F_26(x), F_2(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_30(x) + F_53(x))
Eq(F_30(x), F_31(x) + F_51(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_12(x) + F_5(x))
Eq(F_33(x), F_19(x) + F_34(x))
Eq(F_34(x), F_35(x) - F_50(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x) + F_45(x))
Eq(F_38(x), F_25(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_6(x))
Eq(F_40(x), F_2(x) + F_41(x))
Eq(F_41(x), F_1(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_4(x)*F_41(x)*F_44(x))
Eq(F_44(x), F_1(x) + F_4(x))
Eq(F_45(x), F_46(x)*F_5(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_2(x) + F_48(x))
Eq(F_48(x), -F_2(x) + F_49(x))
Eq(F_49(x), -F_0(x) + F_25(x))
Eq(F_50(x), F_2(x)*F_42(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_24(x)*F_31(x)*F_4(x))
Eq(F_53(x), F_54(x) - F_56(x))
Eq(F_54(x), F_55(x)/F_4(x))
Eq(F_55(x), F_48(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_24(x)*F_4(x)*F_5(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_15(x)*F_27(x))
Eq(F_62(x), F_21(x)*F_24(x))
Eq(F_63(x), F_2(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_31(x)*F_4(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_15(x)*F_6(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_72(x)**2*F_73(x))
Eq(F_72(x), x**2*F_72(x)**3 - x*(x - 1)*F_72(x)**2 + 1)
Eq(F_73(x), F_31(x) - F_74(x))
Eq(F_74(x), F_6(x) + F_75(x))
Eq(F_75(x), F_0(x) + F_64(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 4, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 4, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": 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{"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 3]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 3]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"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": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"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, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"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": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 4, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 4, 1]], "symmetry": false}}]}
Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24774/
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[24,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]+F[70,x]
F[11,x] = F[12,x]+F[13,x]
F[12,x] = x*(1+F[12,x])^2*(x*F[12,x]+1)
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[4,x]*F[69,x]
F[15,x] = 1/F[2,x]*F[16,x]
F[16,x] = -F[22,x]+F[17,x]
F[17,x] = 1/F[4,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = -F[2,x]+F[20,x]
F[20,x] = -F[21,x]+F[5,x]
F[21,x] = 1+x^2*F[21,x]^3+(-x^2+x)*F[21,x]^2
F[22,x] = F[23,x]+F[64,x]
F[23,x] = -F[24,x]+F[17,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[4,x]*F[9,x]
F[26,x] = F[27,x]+F[29,x]
F[27,x] = 1/F[4,x]*F[28,x]
F[28,x] = F[2,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[58,x]
F[32,x] = F[33,x]+F[56,x]
F[33,x] = F[34,x]+F[37,x]
F[34,x] = F[35,x]+F[5,x]
F[35,x] = F[36,x]
F[36,x] = F[33,x]*F[4,x]
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[0,x]*F[12,x]
F[39,x] = -F[35,x]+F[40,x]
F[40,x] = F[20,x]+F[41,x]
F[41,x] = -F[55,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[45,x]+F[52,x]
F[45,x] = F[27,x]*F[46,x]
F[46,x] = F[20,x]+F[47,x]
F[47,x] = F[12,x]+F[48,x]
F[48,x] = F[1,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[4,x]*F[48,x]*F[51,x]
F[51,x] = F[1,x]+F[4,x]
F[52,x] = F[5,x]*F[53,x]
F[53,x] = F[54,x]
F[54,x] = -F[0,x]+F[27,x]
F[55,x] = F[2,x]*F[47,x]
F[56,x] = F[57,x]
F[57,x] = F[26,x]*F[33,x]*F[4,x]
F[58,x] = -F[62,x]+F[59,x]
F[59,x] = 1/F[4,x]*F[60,x]
F[60,x] = F[61,x]
F[61,x] = -F[2,x]+F[54,x]
F[62,x] = F[63,x]
F[63,x] = F[26,x]*F[4,x]*F[5,x]
F[64,x] = F[65,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[67,x]+F[68,x]
F[67,x] = F[15,x]*F[29,x]
F[68,x] = F[23,x]*F[26,x]
F[69,x] = F[2,x]+F[35,x]
F[70,x] = F[71,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[73,x]+F[74,x]
F[73,x] = F[15,x]*F[6,x]
F[74,x] = F[75,x]
F[75,x] = F[21,x]^2*F[37,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_{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_{24}\! \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_{70}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{13}\! \left(x \right)
F_{12}\! \left(x \right) = x^{2} F_{12} \left(x \right)^{3}+2 x^{2} F_{12} \left(x \right)^{2}+x^{2} F_{12}\! \left(x \right)+x F_{12} \left(x \right)^{2}+2 x F_{12}\! \left(x \right)+x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{2}\! \left(x \right)}
F_{16}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{21}\! \left(x \right)+F_{5}\! \left(x \right)
F_{21}\! \left(x \right) = x^{2} F_{21} \left(x \right)^{3}-x^{2} F_{21} \left(x \right)^{2}+x F_{21} \left(x \right)^{2}+1
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{64}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{17}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{29}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{2}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \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_{58}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{56}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{5}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{0}\! \left(x \right) F_{12}\! \left(x \right)
F_{39}\! \left(x \right) = -F_{35}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{20}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = -F_{55}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{52}\! \left(x \right)
F_{45}\! \left(x \right) = F_{27}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{20}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{1}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{52}\! \left(x \right) = F_{5}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{27}\! \left(x \right)
F_{55}\! \left(x \right) = F_{2}\! \left(x \right) F_{47}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{26}\! \left(x \right) F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = \frac{F_{60}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{54}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{15}\! \left(x \right) F_{29}\! \left(x \right)
F_{68}\! \left(x \right) = F_{23}\! \left(x \right) F_{26}\! \left(x \right)
F_{69}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{74}\! \left(x \right)
F_{73}\! \left(x \right) = F_{15}\! \left(x \right) F_{6}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{21} \left(x \right)^{2} F_{37}\! \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_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_24(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x) + F_70(x))
Eq(F_11(x), F_12(x) + F_13(x))
Eq(F_12(x), x**2*(F_12(x) + 1)**3 - x*(x - 1)*(F_12(x) + 1)**2)
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_4(x)*F_69(x))
Eq(F_15(x), F_16(x)/F_2(x))
Eq(F_16(x), F_17(x) - F_22(x))
Eq(F_17(x), F_18(x)/F_4(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), -F_2(x) + F_20(x))
Eq(F_20(x), -F_21(x) + F_5(x))
Eq(F_21(x), x**2*F_21(x)**3 - x*(x - 1)*F_21(x)**2 + 1)
Eq(F_22(x), F_23(x) + F_64(x))
Eq(F_23(x), F_17(x) - F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_4(x)*F_9(x))
Eq(F_26(x), F_27(x) + F_29(x))
Eq(F_27(x), F_28(x)/F_4(x))
Eq(F_28(x), F_2(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_58(x))
Eq(F_32(x), F_33(x) + F_56(x))
Eq(F_33(x), F_34(x) + F_37(x))
Eq(F_34(x), F_35(x) + F_5(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_33(x)*F_4(x))
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_0(x)*F_12(x))
Eq(F_39(x), -F_35(x) + F_40(x))
Eq(F_40(x), F_20(x) + F_41(x))
Eq(F_41(x), F_42(x) - F_55(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_52(x))
Eq(F_45(x), F_27(x)*F_46(x))
Eq(F_46(x), F_20(x) + F_47(x))
Eq(F_47(x), F_12(x) + F_48(x))
Eq(F_48(x), F_1(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_4(x)*F_48(x)*F_51(x))
Eq(F_51(x), F_1(x) + F_4(x))
Eq(F_52(x), F_5(x)*F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), -F_0(x) + F_27(x))
Eq(F_55(x), F_2(x)*F_47(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_26(x)*F_33(x)*F_4(x))
Eq(F_58(x), F_59(x) - F_62(x))
Eq(F_59(x), F_60(x)/F_4(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), -F_2(x) + F_54(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_26(x)*F_4(x)*F_5(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_68(x))
Eq(F_67(x), F_15(x)*F_29(x))
Eq(F_68(x), F_23(x)*F_26(x))
Eq(F_69(x), F_2(x) + F_35(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_74(x))
Eq(F_73(x), F_15(x)*F_6(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_21(x)**2*F_37(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 4, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 4, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 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Specification 3
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25106/
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[24,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]+F[70,x]
F[11,x] = F[12,x]+F[13,x]
F[12,x] = x*(1+F[12,x])^2*(x*F[12,x]+1)
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[4,x]*F[69,x]
F[15,x] = 1/F[2,x]*F[16,x]
F[16,x] = -F[22,x]+F[17,x]
F[17,x] = 1/F[4,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = -F[2,x]+F[20,x]
F[20,x] = -F[21,x]+F[5,x]
F[21,x] = 1+x^2*F[21,x]^3+(-x^2+x)*F[21,x]^2
F[22,x] = F[23,x]+F[64,x]
F[23,x] = -F[24,x]+F[17,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[4,x]*F[9,x]
F[26,x] = F[27,x]+F[29,x]
F[27,x] = 1/F[4,x]*F[28,x]
F[28,x] = F[2,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[58,x]
F[32,x] = F[33,x]+F[56,x]
F[33,x] = F[34,x]+F[37,x]
F[34,x] = F[35,x]+F[5,x]
F[35,x] = F[36,x]
F[36,x] = F[33,x]*F[4,x]
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[0,x]*F[12,x]
F[39,x] = -F[35,x]+F[40,x]
F[40,x] = F[20,x]+F[41,x]
F[41,x] = -F[55,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[45,x]+F[52,x]
F[45,x] = F[27,x]*F[46,x]
F[46,x] = F[20,x]+F[47,x]
F[47,x] = F[12,x]+F[48,x]
F[48,x] = F[1,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[4,x]*F[48,x]*F[51,x]
F[51,x] = F[1,x]+F[4,x]
F[52,x] = F[5,x]*F[53,x]
F[53,x] = F[54,x]
F[54,x] = -F[0,x]+F[27,x]
F[55,x] = F[2,x]*F[47,x]
F[56,x] = F[57,x]
F[57,x] = F[26,x]*F[33,x]*F[4,x]
F[58,x] = -F[62,x]+F[59,x]
F[59,x] = 1/F[4,x]*F[60,x]
F[60,x] = F[61,x]
F[61,x] = -F[2,x]+F[54,x]
F[62,x] = F[63,x]
F[63,x] = F[26,x]*F[4,x]*F[5,x]
F[64,x] = F[65,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[67,x]+F[68,x]
F[67,x] = F[15,x]*F[29,x]
F[68,x] = F[23,x]*F[26,x]
F[69,x] = F[2,x]+F[35,x]
F[70,x] = F[71,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[73,x]+F[74,x]
F[73,x] = F[15,x]*F[6,x]
F[74,x] = F[75,x]
F[75,x] = F[21,x]^2*F[37,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_{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_{24}\! \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_{70}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{13}\! \left(x \right)
F_{12}\! \left(x \right) = x^{2} F_{12} \left(x \right)^{3}+2 x^{2} F_{12} \left(x \right)^{2}+x^{2} F_{12}\! \left(x \right)+x F_{12} \left(x \right)^{2}+2 x F_{12}\! \left(x \right)+x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{2}\! \left(x \right)}
F_{16}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{21}\! \left(x \right)+F_{5}\! \left(x \right)
F_{21}\! \left(x \right) = x^{2} F_{21} \left(x \right)^{3}-x^{2} F_{21} \left(x \right)^{2}+x F_{21} \left(x \right)^{2}+1
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{64}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{17}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{29}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{2}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \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_{58}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{56}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{5}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{0}\! \left(x \right) F_{12}\! \left(x \right)
F_{39}\! \left(x \right) = -F_{35}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{20}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = -F_{55}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{52}\! \left(x \right)
F_{45}\! \left(x \right) = F_{27}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{20}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{1}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{52}\! \left(x \right) = F_{5}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{27}\! \left(x \right)
F_{55}\! \left(x \right) = F_{2}\! \left(x \right) F_{47}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{26}\! \left(x \right) F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = \frac{F_{60}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{54}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{15}\! \left(x \right) F_{29}\! \left(x \right)
F_{68}\! \left(x \right) = F_{23}\! \left(x \right) F_{26}\! \left(x \right)
F_{69}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{74}\! \left(x \right)
F_{73}\! \left(x \right) = F_{15}\! \left(x \right) F_{6}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{21} \left(x \right)^{2} F_{37}\! \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_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_24(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x) + F_70(x))
Eq(F_11(x), F_12(x) + F_13(x))
Eq(F_12(x), x**2*(F_12(x) + 1)**3 - x*(x - 1)*(F_12(x) + 1)**2)
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_4(x)*F_69(x))
Eq(F_15(x), F_16(x)/F_2(x))
Eq(F_16(x), F_17(x) - F_22(x))
Eq(F_17(x), F_18(x)/F_4(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), -F_2(x) + F_20(x))
Eq(F_20(x), -F_21(x) + F_5(x))
Eq(F_21(x), x**2*F_21(x)**3 - x*(x - 1)*F_21(x)**2 + 1)
Eq(F_22(x), F_23(x) + F_64(x))
Eq(F_23(x), F_17(x) - F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_4(x)*F_9(x))
Eq(F_26(x), F_27(x) + F_29(x))
Eq(F_27(x), F_28(x)/F_4(x))
Eq(F_28(x), F_2(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_58(x))
Eq(F_32(x), F_33(x) + F_56(x))
Eq(F_33(x), F_34(x) + F_37(x))
Eq(F_34(x), F_35(x) + F_5(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_33(x)*F_4(x))
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_0(x)*F_12(x))
Eq(F_39(x), -F_35(x) + F_40(x))
Eq(F_40(x), F_20(x) + F_41(x))
Eq(F_41(x), F_42(x) - F_55(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_52(x))
Eq(F_45(x), F_27(x)*F_46(x))
Eq(F_46(x), F_20(x) + F_47(x))
Eq(F_47(x), F_12(x) + F_48(x))
Eq(F_48(x), F_1(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_4(x)*F_48(x)*F_51(x))
Eq(F_51(x), F_1(x) + F_4(x))
Eq(F_52(x), F_5(x)*F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), -F_0(x) + F_27(x))
Eq(F_55(x), F_2(x)*F_47(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_26(x)*F_33(x)*F_4(x))
Eq(F_58(x), F_59(x) - F_62(x))
Eq(F_59(x), F_60(x)/F_4(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), -F_2(x) + F_54(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_26(x)*F_4(x)*F_5(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_68(x))
Eq(F_67(x), F_15(x)*F_29(x))
Eq(F_68(x), F_23(x)*F_26(x))
Eq(F_69(x), F_2(x) + F_35(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_74(x))
Eq(F_73(x), F_15(x)*F_6(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_21(x)**2*F_37(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "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", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": 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"pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 3], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"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, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"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": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 4, 1]], "symmetry": true}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 4, 1]], "symmetry": true}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25139/
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[22,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]+F[66,x]
F[11,x] = F[12,x]+F[13,x]
F[12,x] = x*(1+F[12,x])^2*(x*F[12,x]+1)
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[4,x]*F[63,x]
F[15,x] = 1/F[2,x]*F[16,x]
F[16,x] = -F[20,x]+F[17,x]
F[17,x] = 1/F[4,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = -F[12,x]+F[6,x]
F[20,x] = F[21,x]+F[58,x]
F[21,x] = -F[22,x]+F[17,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]*F[9,x]
F[24,x] = F[25,x]+F[27,x]
F[25,x] = 1/F[4,x]*F[26,x]
F[26,x] = F[2,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[30,x]+F[53,x]
F[30,x] = F[31,x]+F[51,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[12,x]+F[5,x]
F[33,x] = F[19,x]+F[34,x]
F[34,x] = -F[50,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]+F[45,x]
F[38,x] = F[25,x]*F[39,x]
F[39,x] = F[40,x]+F[6,x]
F[40,x] = F[2,x]+F[41,x]
F[41,x] = F[1,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[4,x]*F[41,x]*F[44,x]
F[44,x] = F[1,x]+F[4,x]
F[45,x] = F[46,x]*F[5,x]
F[46,x] = F[47,x]
F[47,x] = F[2,x]+F[48,x]
F[48,x] = -F[2,x]+F[49,x]
F[49,x] = -F[0,x]+F[25,x]
F[50,x] = F[2,x]*F[42,x]
F[51,x] = F[52,x]
F[52,x] = F[24,x]*F[31,x]*F[4,x]
F[53,x] = -F[56,x]+F[54,x]
F[54,x] = 1/F[4,x]*F[55,x]
F[55,x] = F[48,x]
F[56,x] = F[57,x]
F[57,x] = F[24,x]*F[4,x]*F[5,x]
F[58,x] = F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[15,x]*F[27,x]
F[62,x] = F[21,x]*F[24,x]
F[63,x] = F[2,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[31,x]*F[4,x]
F[66,x] = F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[15,x]*F[6,x]
F[70,x] = F[71,x]
F[71,x] = F[72,x]^2*F[73,x]
F[72,x] = 1+x^2*F[72,x]^3+(-x^2+x)*F[72,x]^2
F[73,x] = -F[74,x]+F[31,x]
F[74,x] = F[6,x]+F[75,x]
F[75,x] = F[0,x]+F[64,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_{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_{22}\! \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_{66}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{13}\! \left(x \right)
F_{12}\! \left(x \right) = x^{2} F_{12} \left(x \right)^{3}+2 x^{2} F_{12} \left(x \right)^{2}+x^{2} F_{12}\! \left(x \right)+x F_{12} \left(x \right)^{2}+2 x F_{12}\! \left(x \right)+x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{2}\! \left(x \right)}
F_{16}\! \left(x \right) = -F_{20}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{12}\! \left(x \right)+F_{6}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{58}\! \left(x \right)
F_{21}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{17}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{27}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{26}\! \left(x \right) = F_{2}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{53}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{51}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right)+F_{5}\! \left(x \right)
F_{33}\! \left(x \right) = F_{19}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = -F_{50}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{45}\! \left(x \right)
F_{38}\! \left(x \right) = F_{25}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{6}\! \left(x \right)
F_{40}\! \left(x \right) = F_{2}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{1}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right) F_{5}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{2}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{25}\! \left(x \right)
F_{50}\! \left(x \right) = F_{2}\! \left(x \right) F_{42}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{24}\! \left(x \right) F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{53}\! \left(x \right) = -F_{56}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = \frac{F_{55}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{55}\! \left(x \right) = F_{48}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{15}\! \left(x \right) F_{27}\! \left(x \right)
F_{62}\! \left(x \right) = F_{21}\! \left(x \right) F_{24}\! \left(x \right)
F_{63}\! \left(x \right) = F_{2}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{15}\! \left(x \right) F_{6}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72} \left(x \right)^{2} F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = x^{2} F_{72} \left(x \right)^{3}-x^{2} F_{72} \left(x \right)^{2}+x F_{72} \left(x \right)^{2}+1
F_{73}\! \left(x \right) = -F_{74}\! \left(x \right)+F_{31}\! \left(x \right)
F_{74}\! \left(x \right) = F_{6}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{0}\! \left(x \right)+F_{64}\! \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_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_22(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x) + F_66(x))
Eq(F_11(x), F_12(x) + F_13(x))
Eq(F_12(x), x**2*(F_12(x) + 1)**3 - x*(x - 1)*(F_12(x) + 1)**2)
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_4(x)*F_63(x))
Eq(F_15(x), F_16(x)/F_2(x))
Eq(F_16(x), F_17(x) - F_20(x))
Eq(F_17(x), F_18(x)/F_4(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), -F_12(x) + F_6(x))
Eq(F_20(x), F_21(x) + F_58(x))
Eq(F_21(x), F_17(x) - F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_4(x)*F_9(x))
Eq(F_24(x), F_25(x) + F_27(x))
Eq(F_25(x), F_26(x)/F_4(x))
Eq(F_26(x), F_2(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_30(x) + F_53(x))
Eq(F_30(x), F_31(x) + F_51(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_12(x) + F_5(x))
Eq(F_33(x), F_19(x) + F_34(x))
Eq(F_34(x), F_35(x) - F_50(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x) + F_45(x))
Eq(F_38(x), F_25(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_6(x))
Eq(F_40(x), F_2(x) + F_41(x))
Eq(F_41(x), F_1(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_4(x)*F_41(x)*F_44(x))
Eq(F_44(x), F_1(x) + F_4(x))
Eq(F_45(x), F_46(x)*F_5(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_2(x) + F_48(x))
Eq(F_48(x), -F_2(x) + F_49(x))
Eq(F_49(x), -F_0(x) + F_25(x))
Eq(F_50(x), F_2(x)*F_42(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_24(x)*F_31(x)*F_4(x))
Eq(F_53(x), F_54(x) - F_56(x))
Eq(F_54(x), F_55(x)/F_4(x))
Eq(F_55(x), F_48(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_24(x)*F_4(x)*F_5(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_15(x)*F_27(x))
Eq(F_62(x), F_21(x)*F_24(x))
Eq(F_63(x), F_2(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_31(x)*F_4(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_15(x)*F_6(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_72(x)**2*F_73(x))
Eq(F_72(x), x**2*F_72(x)**3 - x*(x - 1)*F_72(x)**2 + 1)
Eq(F_73(x), F_31(x) - F_74(x))
Eq(F_74(x), F_6(x) + F_75(x))
Eq(F_75(x), F_0(x) + F_64(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 4, 1]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 4, 1]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, 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"assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "EquivalencePathRule", "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "children": [{"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": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[0, 0]]}], "indices": [0], "direction": 0, "own_col": true, "own_row": true, "include_empty": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"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": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"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, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"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": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 4, 1]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [0, 2, 4, 1, 3], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [2, 0, 3, 4, 1], [2, 0, 4, 3, 1], [3, 0, 2, 4, 1]], "symmetry": false}}]}
Specification 5
Strategy pack name: point_placements_tracked_fusion_tracked_component_fusion_symmetries
Tree: http://permpal.com/tree/25731/
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[24,x]+F[9,x]
F[9,x] = F[10,x]+F[5,x]
F[10,x] = F[11,x]+F[70,x]
F[11,x] = F[12,x]+F[13,x]
F[12,x] = x*(1+F[12,x])^2*(x*F[12,x]+1)
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[4,x]*F[69,x]
F[15,x] = 1/F[2,x]*F[16,x]
F[16,x] = -F[22,x]+F[17,x]
F[17,x] = 1/F[4,x]*F[18,x]
F[18,x] = F[19,x]
F[19,x] = -F[2,x]+F[20,x]
F[20,x] = -F[21,x]+F[5,x]
F[21,x] = 1+x^2*F[21,x]^3+(-x^2+x)*F[21,x]^2
F[22,x] = F[23,x]+F[64,x]
F[23,x] = -F[24,x]+F[17,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[4,x]*F[9,x]
F[26,x] = F[27,x]+F[29,x]
F[27,x] = 1/F[4,x]*F[28,x]
F[28,x] = F[2,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[58,x]
F[32,x] = F[33,x]+F[56,x]
F[33,x] = F[34,x]+F[37,x]
F[34,x] = F[35,x]+F[5,x]
F[35,x] = F[36,x]
F[36,x] = F[33,x]*F[4,x]
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[0,x]*F[12,x]
F[39,x] = -F[35,x]+F[40,x]
F[40,x] = F[20,x]+F[41,x]
F[41,x] = -F[55,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[45,x]+F[52,x]
F[45,x] = F[27,x]*F[46,x]
F[46,x] = F[20,x]+F[47,x]
F[47,x] = F[12,x]+F[48,x]
F[48,x] = F[1,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[4,x]*F[48,x]*F[51,x]
F[51,x] = F[1,x]+F[4,x]
F[52,x] = F[5,x]*F[53,x]
F[53,x] = F[54,x]
F[54,x] = -F[0,x]+F[27,x]
F[55,x] = F[2,x]*F[47,x]
F[56,x] = F[57,x]
F[57,x] = F[26,x]*F[33,x]*F[4,x]
F[58,x] = -F[62,x]+F[59,x]
F[59,x] = 1/F[4,x]*F[60,x]
F[60,x] = F[61,x]
F[61,x] = -F[2,x]+F[54,x]
F[62,x] = F[63,x]
F[63,x] = F[26,x]*F[4,x]*F[5,x]
F[64,x] = F[65,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[67,x]+F[68,x]
F[67,x] = F[15,x]*F[29,x]
F[68,x] = F[23,x]*F[26,x]
F[69,x] = F[2,x]+F[35,x]
F[70,x] = F[71,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[73,x]+F[74,x]
F[73,x] = F[15,x]*F[6,x]
F[74,x] = F[75,x]
F[75,x] = F[21,x]^2*F[37,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_{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_{24}\! \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_{70}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{13}\! \left(x \right)
F_{12}\! \left(x \right) = x^{2} F_{12} \left(x \right)^{3}+2 x^{2} F_{12} \left(x \right)^{2}+x^{2} F_{12}\! \left(x \right)+x F_{12} \left(x \right)^{2}+2 x F_{12}\! \left(x \right)+x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{2}\! \left(x \right)}
F_{16}\! \left(x \right) = -F_{22}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = \frac{F_{18}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{21}\! \left(x \right)+F_{5}\! \left(x \right)
F_{21}\! \left(x \right) = x^{2} F_{21} \left(x \right)^{3}-x^{2} F_{21} \left(x \right)^{2}+x F_{21} \left(x \right)^{2}+1
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{64}\! \left(x \right)
F_{23}\! \left(x \right) = -F_{24}\! \left(x \right)+F_{17}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{29}\! \left(x \right)
F_{27}\! \left(x \right) = \frac{F_{28}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{28}\! \left(x \right) = F_{2}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \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_{58}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{56}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{5}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{0}\! \left(x \right) F_{12}\! \left(x \right)
F_{39}\! \left(x \right) = -F_{35}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{20}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = -F_{55}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{52}\! \left(x \right)
F_{45}\! \left(x \right) = F_{27}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{20}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{1}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{52}\! \left(x \right) = F_{5}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{27}\! \left(x \right)
F_{55}\! \left(x \right) = F_{2}\! \left(x \right) F_{47}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{26}\! \left(x \right) F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{58}\! \left(x \right) = -F_{62}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = \frac{F_{60}\! \left(x \right)}{F_{4}\! \left(x \right)}
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{54}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{15}\! \left(x \right) F_{29}\! \left(x \right)
F_{68}\! \left(x \right) = F_{23}\! \left(x \right) F_{26}\! \left(x \right)
F_{69}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{74}\! \left(x \right)
F_{73}\! \left(x \right) = F_{15}\! \left(x \right) F_{6}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{21} \left(x \right)^{2} F_{37}\! \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_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_24(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_5(x))
Eq(F_10(x), F_11(x) + F_70(x))
Eq(F_11(x), F_12(x) + F_13(x))
Eq(F_12(x), x**2*(F_12(x) + 1)**3 - x*(x - 1)*(F_12(x) + 1)**2)
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_4(x)*F_69(x))
Eq(F_15(x), F_16(x)/F_2(x))
Eq(F_16(x), F_17(x) - F_22(x))
Eq(F_17(x), F_18(x)/F_4(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), -F_2(x) + F_20(x))
Eq(F_20(x), -F_21(x) + F_5(x))
Eq(F_21(x), x**2*F_21(x)**3 - x*(x - 1)*F_21(x)**2 + 1)
Eq(F_22(x), F_23(x) + F_64(x))
Eq(F_23(x), F_17(x) - F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_4(x)*F_9(x))
Eq(F_26(x), F_27(x) + F_29(x))
Eq(F_27(x), F_28(x)/F_4(x))
Eq(F_28(x), F_2(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_58(x))
Eq(F_32(x), F_33(x) + F_56(x))
Eq(F_33(x), F_34(x) + F_37(x))
Eq(F_34(x), F_35(x) + F_5(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_33(x)*F_4(x))
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_0(x)*F_12(x))
Eq(F_39(x), -F_35(x) + F_40(x))
Eq(F_40(x), F_20(x) + F_41(x))
Eq(F_41(x), F_42(x) - F_55(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_52(x))
Eq(F_45(x), F_27(x)*F_46(x))
Eq(F_46(x), F_20(x) + F_47(x))
Eq(F_47(x), F_12(x) + F_48(x))
Eq(F_48(x), F_1(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_4(x)*F_48(x)*F_51(x))
Eq(F_51(x), F_1(x) + F_4(x))
Eq(F_52(x), F_5(x)*F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), -F_0(x) + F_27(x))
Eq(F_55(x), F_2(x)*F_47(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_26(x)*F_33(x)*F_4(x))
Eq(F_58(x), F_59(x) - F_62(x))
Eq(F_59(x), F_60(x)/F_4(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), -F_2(x) + F_54(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_26(x)*F_4(x)*F_5(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_68(x))
Eq(F_67(x), F_15(x)*F_29(x))
Eq(F_68(x), F_23(x)*F_26(x))
Eq(F_69(x), F_2(x) + F_35(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_74(x))
Eq(F_73(x), F_15(x)*F_6(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_21(x)**2*F_37(x))
Pack JSON:
{"name": "point_placements_tracked_fusion_tracked_component_fusion_symmetries", "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", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"class_module": "tilings.strategies.fusion.component", "strategy_class": "ComponentFusionFactory", "tracked": true, "isolation_level": null}, {"class_module": "tilings.strategies.detect_components", "strategy_class": "DetectComponentsStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": true, "workable": true}, {"class_module": "tilings.strategies.monotone_sliding", "strategy_class": "MonotoneSlidingFactory"}, {"class_module": "tilings.strategies.point_jumping", "strategy_class": "AssumptionAndPointJumpingFactory"}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "ComponentVerificationStrategy", "ignore_parent": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}], [{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "FusableRowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [{"class_module": "tilings.strategies.symmetry", "strategy_class": "SymmetriesFactory", "basis": null}], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "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]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]]}}, "idx": 0}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "ReverseRule", "original_rule": {"class_module": 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