01243_02143_02413_10243_12043_12403_20143_20413_21043_21403_24013_24103

Counting sequence:
1, 1, 2, 6, 24, 108, 512, 2496, 12382, 62168, 314934, 1606572, 8242198, 42486590, 219906314, 1142305670, 5952728554, 31110248532, 163017382982, 856278856638, 4507847650308, 23780918456208, 125699810227774, 665633681038582, 3530890580627812, 18760299474128026, 99830649520649556, 532012700429583354, 2839110073142390558, 15171033738149132116, 81169626757907654142, 434802427240363209198, 2331775287493225494206, 12518594084100965203324, 67278719914141869126678, 361937516669295400361282, 1948968269930130709791556, 10504462452172836071858162, 56666237806384217946649492, 305943261859775912496646300, 1653136407652662916581527996, 8939513228544237945489689480, 48377481953652978800571275258, 261989785974132841948206202862, 1419793929572571512825714024276, 7699364219090799125639611473390, 41779410753457759399953250455404, 226849320916018280684211112586068, 1232453978834042112255899648613720, 6699660408802115768008375341921526, 36439713781294494989205696435882596, 198302809611690368448174843920989988, 1079708619133359649686289111536135460, 5881667617318336974719204774572637086, 32055559852968981307825316359535271022, 174786679945710056736777031696590696274, 953473862425541469211548192715423245224, 5203534683963308976585395122806026246552, 28410004831301089002438838805497134855784, 155174948290996402625506032406486349950126, 847898497157319301088991787567493921369334, 4634819446562959921465529763643908716155460, 25344483439048920651617164536021813566620594, 138640756509660316406784011503406776251102650, 758666019800455898894649181755436185393776398, 4152963953842347348773744745263238467792828452, 22740984719754352405174804203399674031858147358, 124566103637732311039126428263011950345375244694, 682536844567246389589877312054852782088049392936, 3740969611339586736385345225070491921446223747866, 20510229589258180807480555108733770121061845427836, 112481647149131036766375073433856979932047545901152, 617041385702582885604335191818253237575097638651940, 3385830436509172065458191011400105448102329071918506, 18583663202334515544672305234027981498020035619123768, 102025727105138124468280880189869297389744227730387236, 560270135196768784092577296755045142330775356735626124, 3077456382221083298039198629794055819861730385484727472, 16907926573972718519314186446267070972396808436878051428, 92915948623576826987216935566397134925942295714007124604, 510727431138142145301602643837468379561293718337837455788, 2807920061546951991952464529311359104242038110226226751776, 15440972265344428680180342416642355567108078700101641811098, 84929131864567548285395181232402532005994312366029941652994, 467227860918016936492791941216589308494964424418547512178464, 2570920949805897940902105089217690837665251132032656135619602, 14149290610888287040900652080498457617299440447712383474611292, 77886939008259661862346071066211196539632607397853761150654560, 428821715110557048013544061444523326130773577902442676339003008, 2361398399391291700323498805052717197863278009945787205314239406, 13005899011759990452273248338443413893878679738372497181742637040, 71645417882123683522124971960378536900102920528647246724726223616, 394740564222477252310548879857294601655255025513043592076831585120, 2175248140357780664907542886270198312202255039288358577221255704708, 11988863925493528852371774943538237204721129568305920621414187612480, 66087290194149736941527483726939211973475257515478434339749376930932, 364356989304500435046570857865441677323840632582573169052109004702012, 2009111837333771928158576309555751927989040762151599957923889517931150, 11080200273229253366944253129217662294367972522989335070250198437050340, 61116191234042631986998809283994835597867319721561667523421028543310064, 337154411357607412625021649796766575258021599518953868308507271144721292

Implicit equation for the generating function in Maple syntax:
x^2*F(x)^8+2*x^2*(x-4)*F(x)^7+(4*x^5-8*x^4+6*x^3+10*x^2+8*x-1)*F(x)^6+(8*x^6-18*x^5+20*x^4-42*x^3+36*x^2-46*x+6)*F(x)^5+(4*x^7+7*x^6-62*x^5+128*x^4-34*x^3-87*x^2+106*x-15)*F(x)^4+(80*x^5-276*x^4+242*x^3+28*x^2-124*x+20)*F(x)^3+(4*x^6-12*x^5+145*x^4-258*x^3+68*x^2+76*x-15)*F(x)^2+2*(x-1)*(2*x^4-3*x^3+40*x^2+8*x-3)*F(x)+x^4-2*x^3+16*x^2+2*x-1 = 0

Implicit equation for the generating function in latex syntax:
x^{2} F \! \left(x \right)^{8}+2 x^{2} \left(x -4\right) F \! \left(x \right)^{7}+\left(4 x^{5}-8 x^{4}+6 x^{3}+10 x^{2}+8 x -1\right) F \! \left(x \right)^{6}+\left(8 x^{6}-18 x^{5}+20 x^{4}-42 x^{3}+36 x^{2}-46 x +6\right) F \! \left(x \right)^{5}+\left(4 x^{7}+7 x^{6}-62 x^{5}+128 x^{4}-34 x^{3}-87 x^{2}+106 x -15\right) F \! \left(x \right)^{4}+\left(80 x^{5}-276 x^{4}+242 x^{3}+28 x^{2}-124 x +20\right) F \! \left(x \right)^{3}+\left(4 x^{6}-12 x^{5}+145 x^{4}-258 x^{3}+68 x^{2}+76 x -15\right) F \! \left(x \right)^{2}+2 \left(x -1\right) \left(2 x^{4}-3 x^{3}+40 x^{2}+8 x -3\right) F \! \left(x \right)+x^{4}-2 x^{3}+16 x^{2}+2 x -1 = 0

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 108
a(6) = 512
a(7) = 2496
a(8) = 12382
a(9) = 62168
a(10) = 314934
a(11) = 1606572
a(12) = 8242198
a(13) = 42486590
a(14) = 219906314
a(15) = 1142305670
a(16) = 5952728554
a(17) = 31110248532
a(18) = 163017382982
a(19) = 856278856638
a(20) = 4507847650308
a(21) = 23780918456208
a(22) = 125699810227774
a(23) = 665633681038582
a(24) = 3530890580627812
a(25) = 18760299474128026
a(26) = 99830649520649556
a(27) = 532012700429583354
a(28) = 2839110073142390558
a(29) = 15171033738149132116
a(30) = 81169626757907654142
a(31) = 434802427240363209198
a(32) = 2331775287493225494206
a(33) = 12518594084100965203324
a(34) = 67278719914141869126678
a(35) = 361937516669295400361282
a(36) = 1948968269930130709791556
a(37) = 10504462452172836071858162
a(38) = 56666237806384217946649492
a(39) = 305943261859775912496646300
a(40) = 1653136407652662916581527996
a(41) = 8939513228544237945489689480
a(42) = 48377481953652978800571275258
a(43) = 261989785974132841948206202862
a(44) = 1419793929572571512825714024276
a(45) = 7699364219090799125639611473390
a(46) = 41779410753457759399953250455404
a(47) = 226849320916018280684211112586068
a(48) = 1232453978834042112255899648613720
a(49) = 6699660408802115768008375341921526
a(50) = 36439713781294494989205696435882596
a(51) = 198302809611690368448174843920989988
a(52) = 1079708619133359649686289111536135460
a(53) = 5881667617318336974719204774572637086
a(54) = 32055559852968981307825316359535271022
a(55) = 174786679945710056736777031696590696274
a(56) = 953473862425541469211548192715423245224
a(57) = 5203534683963308976585395122806026246552
a(58) = 28410004831301089002438838805497134855784
a(59) = 155174948290996402625506032406486349950126
a(60) = 847898497157319301088991787567493921369334
a(61) = 4634819446562959921465529763643908716155460
a(62) = 25344483439048920651617164536021813566620594
a(63) = 138640756509660316406784011503406776251102650
a(64) = 758666019800455898894649181755436185393776398
a(65) = 4152963953842347348773744745263238467792828452
a(66) = 22740984719754352405174804203399674031858147358
a(67) = 124566103637732311039126428263011950345375244694
a(68) = 682536844567246389589877312054852782088049392936
a(69) = 3740969611339586736385345225070491921446223747866
a(70) = 20510229589258180807480555108733770121061845427836
a(71) = 112481647149131036766375073433856979932047545901152
a(72) = 617041385702582885604335191818253237575097638651940
a(73) = 3385830436509172065458191011400105448102329071918506
a(74) = 18583663202334515544672305234027981498020035619123768
a(75) = 102025727105138124468280880189869297389744227730387236
a(76) = 560270135196768784092577296755045142330775356735626124
a(77) = 3077456382221083298039198629794055819861730385484727472
a(78) = 16907926573972718519314186446267070972396808436878051428
a(79) = 92915948623576826987216935566397134925942295714007124604
a(80) = 510727431138142145301602643837468379561293718337837455788
a(81) = 2807920061546951991952464529311359104242038110226226751776
a(82) = 15440972265344428680180342416642355567108078700101641811098
a(83) = 84929131864567548285395181232402532005994312366029941652994
a(84) = 467227860918016936492791941216589308494964424418547512178464
a(85) = 2570920949805897940902105089217690837665251132032656135619602
a(86) = 14149290610888287040900652080498457617299440447712383474611292
a(87) = 77886939008259661862346071066211196539632607397853761150654560
a(88) = 428821715110557048013544061444523326130773577902442676339003008
a(89) = 2361398399391291700323498805052717197863278009945787205314239406
a(90) = 13005899011759990452273248338443413893878679738372497181742637040
a(91) = 71645417882123683522124971960378536900102920528647246724726223616
a(92) = 394740564222477252310548879857294601655255025513043592076831585120
a(93) = 2175248140357780664907542886270198312202255039288358577221255704708
a(94) = 11988863925493528852371774943538237204721129568305920621414187612480
a(95) = 66087290194149736941527483726939211973475257515478434339749376930932
a(96) = 364356989304500435046570857865441677323840632582573169052109004702012
a(97) = 2009111837333771928158576309555751927989040762151599957923889517931150
a(98) = 11080200273229253366944253129217662294367972522989335070250198437050340
a(99) = 61116191234042631986998809283994835597867319721561667523421028543310064
a(100) = 337154411357607412625021649796766575258021599518953868308507271144721292
a(101) = 1860218951087313366781077854415765211701321976213816879646885945608683264
a(102) = 10265041970821065769868218401389042232839383098858038817134197432241019740
a(103) = 56652316094623213313456643071132920456910950848357494884546237976178933416
a(104) = 312704223198846767941584365598947113000880422669880443980658510164132299952
a(105) = 1726266543089994010734078893145819920789384172293722265098864566027807532174
a(106) = 9531009760288515817023558330259465518700402650587187625159518387117759895438
a(107) = 52629092613852267872403663382643236299437755256519467357020796198959091685522
a(108) = 290648268196636744601422255663081110617493149263079806844620949454103506887484
a(109) = 1605326945427730818743527030711689592620627373124596928035046788459915737200658
a(110) = 8867724366727647689040590075641227098188210211493282784069892798862207654637064
a(111) = 48990612765586445454174804384466545623109784436014930067562111820312068798938868
a(112) = 270685280080698671470384487298030578327135450677049815877679879780155768207609708
a(113) = 1495776131990083686063644380144809286857035651928871414951768078122746697743485412
a(n+114) = 3/144200*(177455295588*n^6+116464729763796*n^5+31847171928163447*n^4+4644386058140216245*n^3+380969821120207946677*n^2+16666096343132008203559*n+303772401984444018485328)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+111)+1/2575*(991682*n^3+331699297*n^2+36976209505*n+1373744326466)/(n+115)/(n+113)/(2*n+227)*a(n+113)-2/18025*n*(n-1)*(2*n+3)*(2*n+1)*(2*n-1)*(2*n-3)*(n+1)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n)-1/36050*n*(2*n+3)*(2*n+1)*(2*n-1)*(n+1)*(1342*n^2+7579*n+10546)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+1)+1/72100*(2*n+3)*(2*n+1)*(n+1)*(542944*n^4+6923824*n^3+31722071*n^2+62042543*n+43895040)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+2)-1/604818636800*(281595187866345549094538697249055792836373518841*n^7+96617173147628910276458714563829887050082554579671*n^6+14206593285967821803156464277953903313762593162452061*n^5+1160477387274332617370503436204565036338821619151816365*n^4+56874633209437210039116946950716926631933598571057674874*n^3+1672384218347481330833596103630876896132564412138941762484*n^2+27319052191489276372713262727538790473074593002116551974024*n+191250856375632357460969885879216756387603348072558896855840)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+50)+1/302409318400*(164129410123961967380727034627086371637630506459*n^7+57308218847271733597133747481100134654487820645906*n^6+8575514470005892838246268966086226023940551652034202*n^5+712888349418748323201525274377863339184548214075448010*n^4+35557049474813717385557292272134832955351301580299447271*n^3+1064079005895655986770455006773378535404494938990684364324*n^2+17690633155580312454564843315459551690140928270020708666548*n+126046597571621618729309910456254347557721049944589226124080)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+51)+1/604818636800*(94106042186013230503606831514649522929574181061*n^7+30389539176680431557660601378275109479442805677969*n^6+4205373249656559981664655178497836163024987766350975*n^5+323267622170930471277657174160869156103451036003051875*n^4+14908019050423607862843383277537343751318024153076469844*n^3+412455206921895594986402051915463259642966266708045876436*n^2+6338814231911639100498355378986503254139392770753176743440*n+41745372451273107079508296993238866664813309407277589960480)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+47)-1/151204659200*(37058137659285016608985369473661090774226848452*n^7+12222071545317157624425200890037927608045679247791*n^6+1727389134903374785475490288880227529852772720647647*n^5+135619893786729213836725607262127395076263198354445205*n^4+6388040340528420657564931642053397796480075540759885433*n^3+180518758472226924270903567895377277623015401128093115444*n^2+2833760170324407164517654494863401849001599427880396497788*n+19062725503885162295875155614247901706282069344959381723120)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+48)+1/604818636800*(214397462582502645158753244355946100849599634205*n^7+72160016801962828998998755206989065468054524478969*n^6+10408042955773663712003801207406380345601832527388159*n^5+833952081274200500384786890210988064194378983387211275*n^4+40090019077937500612848049133511176142322768862905091740*n^3+1156257033633854545126927509815673701304047174532784593556*n^2+18525567618641650237032111049626657942616098776090739002016*n+127198852411390743973306957328676599110331801266746488785920)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+49)-1/604818636800*(55154673054395802786342209741080472056490828639*n^7+17428381639844556128298664334864299913918878167329*n^6+2359917762152893307613877368970885573104134510332715*n^5+177502656811030472804132360542033348606287581062435295*n^4+8009466249950370732027870571848721377502881979492213166*n^3+216816218715298893422487007807500188238815133732942120296*n^2+3260200924179095117285593846741947308314380731433448579920*n+21006598592097832825683863030131633793846600455180940364960)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+46)-1/604818636800*(15011652772226086634542142730757033663191004347*n^7+4534468599282737104755143504123155432680245912156*n^6+586917391351422921047180927361636969386710183956786*n^5+42197133052030006927591468826699876995067058618495740*n^4+1819979083523336859575028220125976971826234392805682223*n^3+47089664984153450852544285750541858923815076653128828664*n^2+676760482045553101076291377357192432364286124472214894324*n+4167622719360294398157749671747758927546266029812166024800)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+44)+1/151204659200*(7477453940593778248729212766249906257513380123*n^7+2310745578073477126639840078474753083021790699023*n^6+305990915314844854251251291575941676143751160762210*n^5+22507426334860969055507016300498778746042022795719210*n^4+993176290788788613236394164217913903193460153156148577*n^3+26291086338829006146685190902274794609790590126442643207*n^2+38658683565494395803291739909641340858514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9349056878664097*n^5+1117194960915153220134489035610085*n^4+111844217118297138840588441237229847*n^3+6717643299156299155949646203539939855*n^2+224138212254628786080738948369895813698*n+3204841902052122914387935369531473299880)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+100)+1/4614400*(7045381350703186539102808*n^7+4957463716274363602400791608*n^6+1494957844626068845054956314587*n^5+250447692180218410557381563866095*n^4+25173732024141080807973816090151807*n^3+1518171031928348295192713871709088337*n^2+50864245590810070216412751636538089438*n+730329910973407101019833708563790432360)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+101)-1/2307200*(581172923720863969886610*n^7+411799418381361355077307540*n^6+125049902411821576494403086366*n^5+21096118527177237089708020144825*n^4+2135340329894851235489998372517670*n^3+129681197878839745438768779480524215*n^2+4375307218559986126568023057335233094*n+63264118353669816932603419293131413200)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+102)+1/2307200*(77434454999216988557582*n^7+55309004238282785245738672*n^6+16930674892245284707608863015*n^5+2879213287909309290976687103005*n^4+293777355814746744232851262454093*n^3+17984887624562192247166900961080963*n^2+611671625309597672402602954410152910*n+8915503493250593147527621577420937840)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+103)-1/1153600*(4286553190058272378384*n^7+3087814466885815922336648*n^6+953256980397374528626480618*n^5+163489139159321734159821577745*n^4+16823320232811369739293836261236*n^3+1038672008967164584342539690834647*n^2+35625856943592528973646518083633762*n+523682577665335518432659280252029520)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+104)-1/604818636800*(40848439746428368535590861834287351*n^7+6302459378831153241367993820481017818*n^6+413369437851950456911568455922602397292*n^5+14915188372257130331222736083180076071980*n^4+319017257057909509459338460299135637563069*n^3+4031949410663739121691438702756568828983722*n^2+27752588308770002728538724148324182152234448*n+79689148521780611700661021190143063997958720)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+24)+1/2419274547200*(1095280203343421461378438383748612519*n^7+173811823291325312925614129116253031779*n^6+11727489946070306492753863131527145802561*n^5+435376251662329895952350579077620074514665*n^4+9582603641586608678759056740262986979916176*n^3+124643885798168252051622041384311067323243196*n^2+883044173092497051832815623748380522617063824*n+2609810971106315683357155369236353377158851200)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+25)-1/1209637273600*(2668409199997381366067145274031251444*n^7+437221737769582484432078402472939745437*n^6+30458130144588051620114877822376033506385*n^5+1167420049143946208370038427016160395122915*n^4+26528360576634250024550459507065368267258271*n^3+356271050958986929584410853620318591897040888*n^2+2606285648134507551220014959403877851697755300*n+7955677774148553387002783816971418235498428880)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+26)+1/604818636800*(4605451486496995920907200134474504681*n^7+771705878661999107666177638875731288545*n^6+54880764674700078606745248200346654825053*n^5+2142531275528891820290419551281608683529225*n^4+49439762883523704699625486812089894849912594*n^3+671373388016748461244547427274791144377213930*n^2+4934823887184765705754482720230959264365373452*n+14981903010273296390163768930963149391087966960)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+27)-1/1209637273600*(268091721835041293760227088406031*n^7+29716219647426177373179184172009931*n^6+1304243329018267883581115608285507841*n^5+27211112086794315770144928125459369505*n^4+213287973761203306481279104436016514544*n^3-1473038562723903620069423914310453415276*n^2-37059893954641951333567579858607440972416*n-184558606794442973810146991520401564385600)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+21)+1/604818636800*(164636284945955547226264254034320*n^7+10996338360395130131307570875734805*n^6-113802610529113226334008945414412429*n^5-31166318425088491218639446569989734605*n^4-1199665700038298553371752383767294921535*n^3-21610462914474335005545890128962442446160*n^2-193725280697380348896891706370800202522076*n-698234166364808129506919715447052395012000)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+22)+1/302409318400*(1790076189080935471890839403774178*n^7+280029758990644851672745038656718581*n^6+18585784464150579470843058027552404485*n^5+677910272212734342367262972780335543805*n^4+14658281002856664473265235578075698577577*n^3+187562714628393496385933793451526719941374*n^2+1311643737788190293654856590567399403957480*n+3852272839998156602135375840501913387919200)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+23)-1/10300*(697127332*n^5+384886948984*n^4+84993768143363*n^3+9383910176288672*n^2+517992512179247721*n+11436575801983768728)/(n+112)/(n+113)/(n+115)/(2*n+225)/(2*n+227)*a(n+112)-1/288400*(2*n+3)*(195269104*n^6+4287981912*n^5+37951520566*n^4+173723726451*n^3+434662943887*n^2+564503845914*n+297640212240)/(n+110)/(2*n+227)/(2*n+225)/(n+115)/(n+113)/(n+112)/(n+111)*a(n+3), n >= 114

Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 108
a(6) = 512
a(7) = 2496
a(8) = 12382
a(9) = 62168
a(10) = 314934
a(11) = 1606572
a(12) = 8242198
a(13) = 42486590
a(14) = 219906314
a(15) = 1142305670
a(16) = 5952728554
a(17) = 31110248532
a(18) = 163017382982
a(19) = 856278856638
a(20) = 4507847650308
a(21) = 23780918456208
a(22) = 125699810227774
a(23) = 665633681038582
a(24) = 3530890580627812
a(25) = 18760299474128026
a(26) = 99830649520649556
a(27) = 532012700429583354
a(28) = 2839110073142390558
a(29) = 15171033738149132116
a(30) = 81169626757907654142
a(31) = 434802427240363209198
a(32) = 2331775287493225494206
a(33) = 12518594084100965203324
a(34) = 67278719914141869126678
a(35) = 361937516669295400361282
a(36) = 1948968269930130709791556
a(37) = 10504462452172836071858162
a(38) = 56666237806384217946649492
a(39) = 305943261859775912496646300
a(40) = 1653136407652662916581527996
a(41) = 8939513228544237945489689480
a(42) = 48377481953652978800571275258
a(43) = 261989785974132841948206202862
a(44) = 1419793929572571512825714024276
a(45) = 7699364219090799125639611473390
a(46) = 41779410753457759399953250455404
a(47) = 226849320916018280684211112586068
a(48) = 1232453978834042112255899648613720
a(49) = 6699660408802115768008375341921526
a(50) = 36439713781294494989205696435882596
a(51) = 198302809611690368448174843920989988
a(52) = 1079708619133359649686289111536135460
a(53) = 5881667617318336974719204774572637086
a(54) = 32055559852968981307825316359535271022
a(55) = 174786679945710056736777031696590696274
a(56) = 953473862425541469211548192715423245224
a(57) = 5203534683963308976585395122806026246552
a(58) = 28410004831301089002438838805497134855784
a(59) = 155174948290996402625506032406486349950126
a(60) = 847898497157319301088991787567493921369334
a(61) = 4634819446562959921465529763643908716155460
a(62) = 25344483439048920651617164536021813566620594
a(63) = 138640756509660316406784011503406776251102650
a(64) = 758666019800455898894649181755436185393776398
a(65) = 4152963953842347348773744745263238467792828452
a(66) = 22740984719754352405174804203399674031858147358
a(67) = 124566103637732311039126428263011950345375244694
a(68) = 682536844567246389589877312054852782088049392936
a(69) = 3740969611339586736385345225070491921446223747866
a(70) = 20510229589258180807480555108733770121061845427836
a(71) = 112481647149131036766375073433856979932047545901152
a(72) = 617041385702582885604335191818253237575097638651940
a(73) = 3385830436509172065458191011400105448102329071918506
a(74) = 18583663202334515544672305234027981498020035619123768
a(75) = 102025727105138124468280880189869297389744227730387236
a(76) = 560270135196768784092577296755045142330775356735626124
a(77) = 3077456382221083298039198629794055819861730385484727472
a(78) = 16907926573972718519314186446267070972396808436878051428
a(79) = 92915948623576826987216935566397134925942295714007124604
a(80) = 510727431138142145301602643837468379561293718337837455788
a(81) = 2807920061546951991952464529311359104242038110226226751776
a(82) = 15440972265344428680180342416642355567108078700101641811098
a(83) = 84929131864567548285395181232402532005994312366029941652994
a(84) = 467227860918016936492791941216589308494964424418547512178464
a(85) = 2570920949805897940902105089217690837665251132032656135619602
a(86) = 14149290610888287040900652080498457617299440447712383474611292
a(87) = 77886939008259661862346071066211196539632607397853761150654560
a(88) = 428821715110557048013544061444523326130773577902442676339003008
a(89) = 2361398399391291700323498805052717197863278009945787205314239406
a(90) = 13005899011759990452273248338443413893878679738372497181742637040
a(91) = 71645417882123683522124971960378536900102920528647246724726223616
a(92) = 394740564222477252310548879857294601655255025513043592076831585120
a(93) = 2175248140357780664907542886270198312202255039288358577221255704708
a(94) = 11988863925493528852371774943538237204721129568305920621414187612480
a(95) = 66087290194149736941527483726939211973475257515478434339749376930932
a(96) = 364356989304500435046570857865441677323840632582573169052109004702012
a(97) = 2009111837333771928158576309555751927989040762151599957923889517931150
a(98) = 11080200273229253366944253129217662294367972522989335070250198437050340
a(99) = 61116191234042631986998809283994835597867319721561667523421028543310064
a(100) = 337154411357607412625021649796766575258021599518953868308507271144721292
a(101) = 1860218951087313366781077854415765211701321976213816879646885945608683264
a(102) = 10265041970821065769868218401389042232839383098858038817134197432241019740
a(103) = 56652316094623213313456643071132920456910950848357494884546237976178933416
a(104) = 312704223198846767941584365598947113000880422669880443980658510164132299952
a(105) = 1726266543089994010734078893145819920789384172293722265098864566027807532174
a(106) = 9531009760288515817023558330259465518700402650587187625159518387117759895438
a(107) = 52629092613852267872403663382643236299437755256519467357020796198959091685522
a(108) = 290648268196636744601422255663081110617493149263079806844620949454103506887484
a(109) = 1605326945427730818743527030711689592620627373124596928035046788459915737200658
a(110) = 8867724366727647689040590075641227098188210211493282784069892798862207654637064
a(111) = 48990612765586445454174804384466545623109784436014930067562111820312068798938868
a(112) = 270685280080698671470384487298030578327135450677049815877679879780155768207609708
a(113) = 1495776131990083686063644380144809286857035651928871414951768078122746697743485412
a{\left(n + 114 \right)} = - \frac{2 n \left(n - 1\right) \left(n + 1\right) \left(2 n - 3\right) \left(2 n - 1\right) \left(2 n + 1\right) \left(2 n + 3\right) a{\left(n \right)}}{18025 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{n \left(n + 1\right) \left(2 n - 1\right) \left(2 n + 1\right) \left(2 n + 3\right) \left(1342 n^{2} + 7579 n + 10546\right) a{\left(n + 1 \right)}}{36050 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(n + 1\right) \left(2 n + 1\right) \left(2 n + 3\right) \left(542944 n^{4} + 6923824 n^{3} + 31722071 n^{2} + 62042543 n + 43895040\right) a{\left(n + 2 \right)}}{72100 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(991682 n^{3} + 331699297 n^{2} + 36976209505 n + 1373744326466\right) a{\left(n + 113 \right)}}{2575 \left(n + 113\right) \left(n + 115\right) \left(2 n + 227\right)} - \frac{\left(697127332 n^{5} + 384886948984 n^{4} + 84993768143363 n^{3} + 9383910176288672 n^{2} + 517992512179247721 n + 11436575801983768728\right) a{\left(n + 112 \right)}}{10300 \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{3 \left(177455295588 n^{6} + 116464729763796 n^{5} + 31847171928163447 n^{4} + 4644386058140216245 n^{3} + 380969821120207946677 n^{2} + 16666096343132008203559 n + 303772401984444018485328\right) a{\left(n + 111 \right)}}{144200 \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(2 n + 3\right) \left(195269104 n^{6} + 4287981912 n^{5} + 37951520566 n^{4} + 173723726451 n^{3} + 434662943887 n^{2} + 564503845914 n + 297640212240\right) a{\left(n + 3 \right)}}{288400 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(8032410462 n^{7} + 247885617784 n^{6} + 3196554772278 n^{5} + 22375505606860 n^{4} + 91975250566878 n^{3} + 222298395336346 n^{2} + 292802159401557 n + 162257725797615\right) a{\left(n + 4 \right)}}{288400 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(435421321516 n^{7} + 16018918063932 n^{6} + 247793031584728 n^{5} + 2093806210031340 n^{4} + 10456174092389179 n^{3} + 30905323939489608 n^{2} + 50120852955635967 n + 34439426850070620\right) a{\left(n + 5 \right)}}{2307200 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(2925300507296 n^{7} + 2221937436414372 n^{6} + 723275872372315946 n^{5} + 130795026630860187225 n^{4} + 14191142115451959292004 n^{3} + 923809326360072649611303 n^{2} + 33408922019828983475668734 n + 517789737339014658723976080\right) a{\left(n + 110 \right)}}{20600 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(59282492152448 n^{7} + 2903270994200192 n^{6} + 59374366403858408 n^{5} + 659889134739356480 n^{4} + 4317011358002885297 n^{3} + 16660585026347575838 n^{2} + 35181432591196203237 n + 31401000463297288320\right) a{\left(n + 6 \right)}}{18457600 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(1190381941583124 n^{7} + 896189436448782896 n^{6} + 289151042499851668983 n^{5} + 51828119104221363776285 n^{4} + 5573726380144335038271051 n^{3} + 359637826598942553619196099 n^{2} + 12891423099846164009041198962 n + 198037697908073036628105991080\right) a{\left(n + 109 \right)}}{288400 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(6498995707009408 n^{7} + 359162042293136320 n^{6} + 8320383294379772728 n^{5} + 105146959463301029680 n^{4} + 785031415490404908427 n^{3} + 3469902648239431139365 n^{2} + 8420839606440888909162 n + 8666408546154801454320\right) a{\left(n + 7 \right)}}{73830400 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(27280394905717700 n^{7} + 20356788814589871490 n^{6} + 6509985968697820736351 n^{5} + 1156557666238573894692775 n^{4} + 123280605446538060772269515 n^{3} + 7884287771053232870671088455 n^{2} + 280121650244039181603096159594 n + 4265236512448618083090200073720\right) a{\left(n + 108 \right)}}{288400 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(253397876862929688 n^{7} + 187415001319632187822 n^{6} + 59404408309205398345410 n^{5} + 10460446951349442861128665 n^{4} + 1105154058475349650685300292 n^{3} + 70054564130526758802142855753 n^{2} + 2466989715182410292925183560370 n + 37231563051594000480105546894720\right) a{\left(n + 107 \right)}}{144200 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(636002244963595056 n^{7} + 40123168888278562688 n^{6} + 1058790065291032757928 n^{5} + 15229709478794029016000 n^{4} + 129427563487412703438639 n^{3} + 651528192789211619014952 n^{2} + 1802251444601875994705817 n + 2116409365819816443147240\right) a{\left(n + 8 \right)}}{590643200 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(15546719011007535014 n^{7} + 11396974593856921198626 n^{6} + 3580586921723275088127713 n^{5} + 624938053927920369819106785 n^{4} + 65442759333090679957772926151 n^{3} + 4111763574808026957297818294829 n^{2} + 143520133406027976188570800323042 n + 2146898057950705551485178512849760\right) a{\left(n + 106 \right)}}{576800 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(20955653353274850736 n^{7} + 1497415255794134100592 n^{6} + 44622669446668098622312 n^{5} + 723910869321102650813920 n^{4} + 6936474641789238894840079 n^{3} + 39380610444412048975728733 n^{2} + 122933626469991744906066798 n + 163050404171482716474181680\right) a{\left(n + 9 \right)}}{2362572800 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(65294688831444327280 n^{7} + 5122219280980344884432 n^{6} + 168208128747977808688597 n^{5} + 3016904785493450822857040 n^{4} + 32051609335876056670812880 n^{3} + 202277937383767469121275588 n^{2} + 703557180000267113209576233 n + 1041879422494263781483765290\right) a{\left(n + 10 \right)}}{1181286400 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(199170089872977793879 n^{7} + 144726008514730222584298 n^{6} + 45069611998282688417381809 n^{5} + 7797226016208727267152335905 n^{4} + 809355404721045698758495199506 n^{3} + 50405889421948416695491523422177 n^{2} + 1743983693638418918109991951695786 n + 25859398701621766085817418401886800\right) a{\left(n + 105 \right)}}{576800 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{3 \left(300728112819339428936 n^{7} + 21815953237878204301456 n^{6} + 674446565113028803632677 n^{5} + 11547960350526924287141010 n^{4} + 118530040529736178316808499 n^{3} + 730685897225890480172975894 n^{2} + 2508705755348250575898753568 n + 3704892972899839000896030240\right) a{\left(n + 11 \right)}}{4725145600 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(4286553190058272378384 n^{7} + 3087814466885815922336648 n^{6} + 953256980397374528626480618 n^{5} + 163489139159321734159821577745 n^{4} + 16823320232811369739293836261236 n^{3} + 1038672008967164584342539690834647 n^{2} + 35625856943592528973646518083633762 n + 523682577665335518432659280252029520\right) a{\left(n + 104 \right)}}{1153600 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(15392142479152734715429 n^{7} + 1977224230264209398940636 n^{6} + 94559115320256301376438140 n^{5} + 2333851939503961196959641030 n^{4} + 33025368611924255988690213301 n^{3} + 271874123934727450637511094854 n^{2} + 1215973890390755495585256378090 n + 2291798702007390643310569523400\right) a{\left(n + 12 \right)}}{9450291200 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(77434454999216988557582 n^{7} + 55309004238282785245738672 n^{6} + 16930674892245284707608863015 n^{5} + 2879213287909309290976687103005 n^{4} + 293777355814746744232851262454093 n^{3} + 17984887624562192247166900961080963 n^{2} + 611671625309597672402602954410152910 n + 8915503493250593147527621577420937840\right) a{\left(n + 103 \right)}}{2307200 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(581172923720863969886610 n^{7} + 411799418381361355077307540 n^{6} + 125049902411821576494403086366 n^{5} + 21096118527177237089708020144825 n^{4} + 2135340329894851235489998372517670 n^{3} + 129681197878839745438768779480524215 n^{2} + 4375307218559986126568023057335233094 n + 63264118353669816932603419293131413200\right) a{\left(n + 102 \right)}}{2307200 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(1447612012691716065576785 n^{7} + 173648243405428343224164093 n^{6} + 8330228711990739993599595071 n^{5} + 212661194946145650597172287735 n^{4} + 3163193977269251883457359489350 n^{3} + 27634968904582247210903108518422 n^{2} + 131973030082064959576928865156924 n + 266684624991595288363274912421360\right) a{\left(n + 13 \right)}}{37801164800 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(7045381350703186539102808 n^{7} + 4957463716274363602400791608 n^{6} + 1494957844626068845054956314587 n^{5} + 250447692180218410557381563866095 n^{4} + 25173732024141080807973816090151807 n^{3} + 1518171031928348295192713871709088337 n^{2} + 50864245590810070216412751636538089438 n + 730329910973407101019833708563790432360\right) a{\left(n + 101 \right)}}{4614400 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(7143531608156706055904355 n^{7} + 899791707846186223397681926 n^{6} + 45773637160252200819504411450 n^{5} + 1245292908985396496590917431110 n^{4} + 19794449616986806524880568697645 n^{3} + 185117703094420103552177623736284 n^{2} + 947358917470345909906155472465650 n + 2052923501089416818498455327136580\right) a{\left(n + 14 \right)}}{18900582400 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(10537212667138199595291190 n^{7} + 7504947002625977369153851760 n^{6} + 2288337190132716471977518183849 n^{5} + 387236815663577542271994977194205 n^{4} + 39279686753479950900152579840813635 n^{3} + 2388463160416117640802559360605913835 n^{2} + 80617028547404017572873193617072174126 n + 1165222603116549864612214765075675983960\right) a{\left(n + 99 \right)}}{659200 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - 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26454733266810280597780147809510138302216481405344769055 n^{2} - 758186675225259279867553018451963564342900486867295651606 n - 8701879959316056467185326432774563193800076283883574984360\right) a{\left(n + 64 \right)}}{18900582400 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(1166676767278324800481897803529192720388631558 n^{7} + 328276870158826730137723308582788628363203744945 n^{6} + 39580050476160263020818101307515916095722491911841 n^{5} + 2650703330325515637719433047368638274543577868305735 n^{4} + 106491858254312056081244905279480172214347859721858737 n^{3} + 2566493224934013814639322329830478127174610256683777020 n^{2} + 34356297603991407054394418081702958612819956371905792924 n + 197064577048873589456607241170825903309293767801957484640\right) a{\left(n + 41 \right)}}{604818636800 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(3453841767429870540244439723640057099276182671 n^{7} + 1471216248161513195655143027871614472233523707417 n^{6} + 268167940763764383937906015101997916594186962886980 n^{5} + 27111162018478508226303938304930578184572667738243905 n^{4} + 1641603082403879930207871065838459275220110036825800339 n^{3} + 59525572788380614629786248131448943759863643801030753518 n^{2} + 1196626245101900601803835652298799333879321180755102742390 n + 10285990634158107293939465523128818274240419940255313904980\right) a{\left(n + 63 \right)}}{4725145600 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(3714882888143949508227176091721861463565143726 n^{7} + 1754611419021324946047958216683343447552380041028 n^{6} + 355037657512508851845241468848710635787561978418755 n^{5} + 39896485882435844653312451879375214679625172138127635 n^{4} + 2688994751667937590414043745299264288404662914102113029 n^{3} + 108703788712562645912629638562089623975038390270179635337 n^{2} + 2440502027254070458977908619066763032448428392111705464050 n + 23474321170224832396829859105861865692949103634316118203800\right) a{\left(n + 67 \right)}}{9450291200 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(4428059261972844287405022345538792217539074324 n^{7} + 2081918136216274819808958043055655571349372086838 n^{6} + 419239309473598671232509435298156973819097484137162 n^{5} + 46873240617234160591248922158319227552102705176938985 n^{4} + 3142590061442629758970643133295699579579509218192325816 n^{3} + 126345815520695223922330485772551225757576800688068233597 n^{2} + 2820528666308093640201344419503029627626814247830400861198 n + 26971287389352343980738801531012137102788646432487780502920\right) a{\left(n + 66 \right)}}{9450291200 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(5954167781635451095687746163961136510171067957 n^{7} + 1716049100477261667886349376787642659288742952133 n^{6} + 211926444723814057759942172556100644688268511643339 n^{5} + 14537504089207253241054795674058854545532011133719815 n^{4} + 598226494687525462775964338152986501198696236748596968 n^{3} + 14767620657811629771124427218164950902151718162703056012 n^{2} + 202487700397126965342280619254346530640907311541846944976 n + 1189661828320865235963051695349648496039768117322456544480\right) a{\left(n + 42 \right)}}{1209637273600 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(6696096962226986654955767357545632550132014514 n^{7} + 3176781694284024797455855574990472456437097821860 n^{6} + 644621256029313466210231273696782571089967796167189 n^{5} + 72535208552508039383493337835728014143416072071860020 n^{4} + 4888846837319126803779536600878294082031643273334107561 n^{3} + 197393429136069703996575404319430327757434627770281845060 n^{2} + 4421331851839401305827759742462673625432254247505570784996 n + 42384529993221155076770855927767170895773954324383307029760\right) a{\left(n + 65 \right)}}{18900582400 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(7477453940593778248729212766249906257513380123 n^{7} + 2310745578073477126639840078474753083021790699023 n^{6} + 305990915314844854251251291575941676143751160762210 n^{5} + 22507426334860969055507016300498778746042022795719210 n^{4} + 993176290788788613236394164217913903193460153156148577 n^{3} + 26291086338829006146685190902274794609790590126442643207 n^{2} + 386586835654943958032917399096413408585143591344588106730 n + 2435768447597256875187620494977172950016049041824785765640\right) a{\left(n + 45 \right)}}{151204659200 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(13927950753948104797485259709369276083010107587 n^{7} + 4110357702253543302429372049364803672437673393693 n^{6} + 519781701285665509183012647016180332570546512093655 n^{5} + 36510172166825219586392456659464218968838371703115295 n^{4} + 1538438883706393883199796066249411166300256272321015598 n^{3} + 38888231528849214548328395486975595993297403599207537652 n^{2} + 546011739783453278809896527743021305946153805591086958280 n + 3284923464794196170877823401449347952177776627478671503840\right) a{\left(n + 43 \right)}}{1209637273600 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(15011652772226086634542142730757033663191004347 n^{7} + 4534468599282737104755143504123155432680245912156 n^{6} + 586917391351422921047180927361636969386710183956786 n^{5} + 42197133052030006927591468826699876995067058618495740 n^{4} + 1819979083523336859575028220125976971826234392805682223 n^{3} + 47089664984153450852544285750541858923815076653128828664 n^{2} + 676760482045553101076291377357192432364286124472214894324 n + 4167622719360294398157749671747758927546266029812166024800\right) a{\left(n + 44 \right)}}{604818636800 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(37058137659285016608985369473661090774226848452 n^{7} + 12222071545317157624425200890037927608045679247791 n^{6} + 1727389134903374785475490288880227529852772720647647 n^{5} + 135619893786729213836725607262127395076263198354445205 n^{4} + 6388040340528420657564931642053397796480075540759885433 n^{3} + 180518758472226924270903567895377277623015401128093115444 n^{2} + 2833760170324407164517654494863401849001599427880396497788 n + 19062725503885162295875155614247901706282069344959381723120\right) a{\left(n + 48 \right)}}{151204659200 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(55154673054395802786342209741080472056490828639 n^{7} + 17428381639844556128298664334864299913918878167329 n^{6} + 2359917762152893307613877368970885573104134510332715 n^{5} + 177502656811030472804132360542033348606287581062435295 n^{4} + 8009466249950370732027870571848721377502881979492213166 n^{3} + 216816218715298893422487007807500188238815133732942120296 n^{2} + 3260200924179095117285593846741947308314380731433448579920 n + 21006598592097832825683863030131633793846600455180940364960\right) a{\left(n + 46 \right)}}{604818636800 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(59824763294903452336105394608430721707393118520 n^{7} + 25564542393638882530189505001784665111641985118838 n^{6} + 4679344434566049124234114136751657146773008189617419 n^{5} + 475576025826807950838709862821416762985165130401784420 n^{4} + 28984099743481566682956629404452646065433081742601626665 n^{3} + 1059247101090635805421405327083820613310848871783580378682 n^{2} + 21493181692677799886229618431598035955480529353418660283136 n + 186791579274330004238981599688276055688955672015201275116960\right) a{\left(n + 62 \right)}}{37801164800 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{3 \left(76708914427716330269670560874037602618673753725 n^{7} + 31646489542150350488676527293103917415678033034423 n^{6} + 5593417439715525655821702719449869246059086369619634 n^{5} + 549044323666642523446856634600109763724200116364444685 n^{4} + 32325248425647867763657518101611395480862214749825225765 n^{3} + 1141517363200923995623166833175822612534232876446369079732 n^{2} + 22387589939344968591229881945307512908834254509882278865236 n + 188110765799515248080050476196646186980623084710806331344560\right) a{\left(n + 59 \right)}}{75602329600 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(86800085565472332716983829698688680985347381945 n^{7} + 34473608492798650861600972684740535016895905858932 n^{6} + 5854394603717750076996951836931249203721222816955855 n^{5} + 551179230235950628220407601525450662945610709968241130 n^{4} + 31075291872541953891735805003381149003025301014262163820 n^{3} + 1049330861418116938248723075585321186794932466001574003858 n^{2} + 19652447838990000651877510180021349737276475505299705655420 n + 157497286978581370914152153440228870808169529699625197452480\right) a{\left(n + 55 \right)}}{151204659200 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(90229129864920906931405913874061051359809798569 n^{7} + 38210484082529279482029857140003417152474754251564 n^{6} + 6932363347469263216951755738517742578443817060996423 n^{5} + 698467699056229535913955993609349554917240998859762015 n^{4} + 42208517416321562212212322169763396472195758336730059166 n^{3} + 1529823156640239593638206951548900681677970507630123800101 n^{2} + 30792460326177124809909344615591088287823383532457113961602 n + 265523848439713435687683490290828441445905729315243501422760\right) a{\left(n + 61 \right)}}{37801164800 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(94106042186013230503606831514649522929574181061 n^{7} + 30389539176680431557660601378275109479442805677969 n^{6} + 4205373249656559981664655178497836163024987766350975 n^{5} + 323267622170930471277657174160869156103451036003051875 n^{4} + 14908019050423607862843383277537343751318024153076469844 n^{3} + 412455206921895594986402051915463259642966266708045876436 n^{2} + 6338814231911639100498355378986503254139392770753176743440 n + 41745372451273107079508296993238866664813309407277589960480\right) a{\left(n + 47 \right)}}{604818636800 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(110458115342262201819604379590348543021629445960 n^{7} + 46200866225437716080263663574259211826488132258571 n^{6} + 8279061211020792926085024973825054856379518063300779 n^{5} + 823940151991081902064744264389093383504634300991060475 n^{4} + 49183371052569735508108130916556972907474029523605027525 n^{3} + 1760960168888983440973513180752047189939352057560200781114 n^{2} + 35015962403055118182313720752950694164551148898168528114576 n + 298307326572209753109421858343488479526200053452776899592600\right) a{\left(n + 60 \right)}}{37801164800 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(112488263392409967905322714840234975134534606347 n^{7} + 39842850489277961893499722220945290762913106799671 n^{6} + 6043411309183601899968951013083744408967040578430623 n^{5} + 508854114494914701190942737855622525746392460892720245 n^{4} + 25685809734313469698671039661245523477713383025023600998 n^{3} + 777260913989489448975725999511212623476090819237114238524 n^{2} + 13054913279697461302196990712246747206738279971335306305112 n + 93884331352485617804957374852652072420929363679698886969760\right) a{\left(n + 53 \right)}}{302409318400 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(158886602222875615647184525255487293559993985722 n^{7} + 63747705661235168108302448997585385029745525073792 n^{6} + 10955512672470028665939236216006291080032556686549119 n^{5} + 1045450293347617366152740186936604846840298273527569195 n^{4} + 59828381566725597662057756589879518686950160892185761593 n^{3} + 2053292080915673485451964326284299799528406025597392483573 n^{2} + 39130560258975322109223959711323481688511572362256214947126 n + 319451240642740084576560116119126473209902143508268012148240\right) a{\left(n + 57 \right)}}{75602329600 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(161048907491186078216592841817829348585987042277 n^{7} + 57015428266990292004210690580154341798418417225181 n^{6} + 8650032026783487613524541697260041718516200913708345 n^{5} + 729020629101262988680701700269517129109719144450720035 n^{4} + 36862464371360945287269690582312677068350342295519032178 n^{3} + 1118287347167007379691815023959927402895856871764336662384 n^{2} + 18846269423348553705628883380423371360822388151277045730080 n + 136112618472167087809527471646603712872196819960977244935680\right) a{\left(n + 52 \right)}}{302409318400 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(164129410123961967380727034627086371637630506459 n^{7} + 57308218847271733597133747481100134654487820645906 n^{6} + 8575514470005892838246268966086226023940551652034202 n^{5} + 712888349418748323201525274377863339184548214075448010 n^{4} + 35557049474813717385557292272134832955351301580299447271 n^{3} + 1064079005895655986770455006773378535404494938990684364324 n^{2} + 17690633155580312454564843315459551690140928270020708666548 n + 126046597571621618729309910456254347557721049944589226124080\right) a{\left(n + 51 \right)}}{302409318400 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(199660675038076155200048580521652545095814607535 n^{7} + 79219202563081279246118193373069300895216725757125 n^{6} + 13459136785215457866567996967967454898712369493219184 n^{5} + 1269329617365917535141669885496287880949720230735993705 n^{4} + 71769810054866408606851874652055299658280483314662819985 n^{3} + 2432954748685929093015027724459384960580374698133276028770 n^{2} + 45786862094599014773413876846601537379586881118225908576576 n + 369037533235734412829859802530412163735253710014793679439920\right) a{\left(n + 56 \right)}}{151204659200 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(206799660655640225013429468179137105576200729661 n^{7} + 84114428694575641283097673163571845682284366699050 n^{6} + 14656764488161789648046657947101073028279888122968997 n^{5} + 1418276533250466428506237482847167370938135810118990870 n^{4} + 82312616418781348817182363351274601478285720150222918234 n^{3} + 2865220596474863329189073819837007060221192518131787610380 n^{2} + 55387963066592448389578771221003513080356961270425178166528 n + 458708891477914765084612579765430012123041824349182977531520\right) a{\left(n + 58 \right)}}{75602329600 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} + \frac{\left(214397462582502645158753244355946100849599634205 n^{7} + 72160016801962828998998755206989065468054524478969 n^{6} + 10408042955773663712003801207406380345601832527388159 n^{5} + 833952081274200500384786890210988064194378983387211275 n^{4} + 40090019077937500612848049133511176142322768862905091740 n^{3} + 1156257033633854545126927509815673701304047174532784593556 n^{2} + 18525567618641650237032111049626657942616098776090739002016 n + 127198852411390743973306957328676599110331801266746488785920\right) a{\left(n + 49 \right)}}{604818636800 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)} - \frac{\left(281595187866345549094538697249055792836373518841 n^{7} + 96617173147628910276458714563829887050082554579671 n^{6} + 14206593285967821803156464277953903313762593162452061 n^{5} + 1160477387274332617370503436204565036338821619151816365 n^{4} + 56874633209437210039116946950716926631933598571057674874 n^{3} + 1672384218347481330833596103630876896132564412138941762484 n^{2} + 27319052191489276372713262727538790473074593002116551974024 n + 191250856375632357460969885879216756387603348072558896855840\right) a{\left(n + 50 \right)}}{604818636800 \left(n + 110\right) \left(n + 111\right) \left(n + 112\right) \left(n + 113\right) \left(n + 115\right) \left(2 n + 225\right) \left(2 n + 227\right)}, \quad n \geq 114

Specification 1
Strategy pack name: insertion_row_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/25053/
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[15,x]*F[4,x]
F[4,x] = F[5,x]+F[6,x]
F[5,x] = 1+x*F[5,x]^4+F[5,x]^2*(x^2-2*x+3)+F[5,x]^3*(-1-x)+(-2+2*x)*F[5,x]
F[6,x] = F[2,x]+F[7,x]
F[7,x] = F[43,x]+F[8,x]+F[9,x]
F[8,x] = 0
F[9,x] = F[10,x]*F[15,x]
F[10,x] = F[11,x]+F[24,x]
F[11,x] = F[12,x]+F[16,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]^2*F[15,x]
F[14,x] = F[1,x]+F[12,x]
F[15,x] = x
F[16,x] = F[17,x]
F[17,x] = F[15,x]*F[18,x]
F[18,x] = F[19,x]+F[21,x]
F[19,x] = F[16,x]+F[20,x]
F[20,x] = (1+F[20,x])*(x*F[20,x]^3+(2*x-1)*F[20,x]^2+(x^2-x+1)*F[20,x]+x^2)
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[14,x]*F[19,x]
F[23,x] = F[19,x]*F[20,x]
F[24,x] = F[25,x]+F[32,x]
F[25,x] = F[26,x]
F[26,x] = F[15,x]*F[27,x]
F[27,x] = F[28,x]+F[29,x]
F[28,x] = F[2,x]+F[25,x]
F[29,x] = F[30,x]+F[31,x]
F[30,x] = F[14,x]*F[28,x]
F[31,x] = F[2,x]*F[28,x]
F[32,x] = F[33,x]
F[33,x] = F[15,x]*F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[32,x]+F[7,x]
F[36,x] = F[37,x]+F[42,x]
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[19,x]*F[2,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[14,x]*F[35,x]
F[41,x] = F[19,x]*F[7,x]
F[42,x] = F[2,x]*F[35,x]
F[43,x] = F[15,x]*F[44,x]
F[44,x] = F[28,x]+F[35,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_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{6}\! \left(x \right)
F_{5}\! \left(x \right) = x F_{5} \left(x \right)^{4}+x^{2} F_{5} \left(x \right)^{2}-F_{5} \left(x \right)^{3} x -2 x F_{5} \left(x \right)^{2}-F_{5} \left(x \right)^{3}+2 F_{5}\! \left(x \right) x +3 F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+1
F_{6}\! \left(x \right) = F_{2}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{43}\! \left(x \right)+F_{8}\! \left(x \right)+F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = 0
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{15}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{24}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{16}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14} \left(x \right)^{2} F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{21}\! \left(x \right)
F_{19}\! \left(x \right) = F_{16}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = x F_{20} \left(x \right)^{4}+x^{2} F_{20} \left(x \right)^{2}+3 x F_{20} \left(x \right)^{3}+2 x^{2} F_{20}\! \left(x \right)+x F_{20} \left(x \right)^{2}-F_{20} \left(x \right)^{3}+x^{2}-F_{20}\! \left(x \right) x +F_{20}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{14}\! \left(x \right) F_{19}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right) F_{20}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{32}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{15}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)
F_{28}\! \left(x \right) = F_{2}\! \left(x \right)+F_{25}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{31}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right) F_{28}\! \left(x \right)
F_{31}\! \left(x \right) = F_{2}\! \left(x \right) F_{28}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{15}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{32}\! \left(x \right)+F_{7}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{42}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{19}\! \left(x \right) F_{2}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{14}\! \left(x \right) F_{35}\! \left(x \right)
F_{41}\! \left(x \right) = F_{19}\! \left(x \right) F_{7}\! \left(x \right)
F_{42}\! \left(x \right) = F_{2}\! \left(x \right) F_{35}\! \left(x \right)
F_{43}\! \left(x \right) = F_{15}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{28}\! \left(x \right)+F_{35}\! \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_15(x)*F_4(x))
Eq(F_4(x), F_5(x) + F_6(x))
Eq(F_5(x), x*F_5(x)**4 + (-x - 1)*F_5(x)**3 + (2*x - 2)*F_5(x) + (x**2 - 2*x + 3)*F_5(x)**2 + 1)
Eq(F_6(x), F_2(x) + F_7(x))
Eq(F_7(x), F_43(x) + F_8(x) + F_9(x))
Eq(F_8(x), 0)
Eq(F_9(x), F_10(x)*F_15(x))
Eq(F_10(x), F_11(x) + F_24(x))
Eq(F_11(x), F_12(x) + F_16(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)**2*F_15(x))
Eq(F_14(x), F_1(x) + F_12(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_15(x)*F_18(x))
Eq(F_18(x), F_19(x) + F_21(x))
Eq(F_19(x), F_16(x) + F_20(x))
Eq(F_20(x), x*(F_20(x) + 1)**4 + (-x - 1)*(F_20(x) + 1)**3 + (2*x - 3)*(F_20(x) + 1) + (F_20(x) + 1)**2*(x**2 - 2*x + 3) + F_20(x) + 1)
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_14(x)*F_19(x))
Eq(F_23(x), F_19(x)*F_20(x))
Eq(F_24(x), F_25(x) + F_32(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_15(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_29(x))
Eq(F_28(x), F_2(x) + F_25(x))
Eq(F_29(x), F_30(x) + F_31(x))
Eq(F_30(x), F_14(x)*F_28(x))
Eq(F_31(x), F_2(x)*F_28(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_15(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_32(x) + F_7(x))
Eq(F_36(x), F_37(x) + F_42(x))
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_19(x)*F_2(x))
Eq(F_39(x), F_40(x) + F_41(x))
Eq(F_40(x), F_14(x)*F_35(x))
Eq(F_41(x), F_19(x)*F_7(x))
Eq(F_42(x), F_2(x)*F_35(x))
Eq(F_43(x), F_15(x)*F_44(x))
Eq(F_44(x), F_28(x) + F_35(x))
Pack JSON:
{"name": "insertion_row_and_col_placements_tracked_fusion", "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": "CellInsertionFactory", "ignore_parent": true, "maxreqlen": 1, "extra_basis": [], "one_cell_only": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": 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}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "place_row": true, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "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, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "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, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "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, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], 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{"patt": [0, 1, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [3, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 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], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}], [{"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}], [{"patt": [0], "pos": [[6, 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": "EquivalenceRule", "original_rule": {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "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, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "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": "EquivalenceRule", "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": [[1, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "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, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 4, 0, 1, 3], [2, 4, 1, 0, 3]], "symmetry": false}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "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, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 4, 0, 1, 3], [2, 4, 1, 0, 3]], "symmetry": false}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "comb_spec_searcher.strategies.strategy", "strategy_class": "EmptyStrategy"}}]}

Specification 2
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25121/
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[17,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[17,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[17,x]
F[12,x] = F[13,x]+F[43,x]
F[13,x] = F[14,x]+F[28,x]
F[14,x] = F[15,x]*F[18,x]
F[15,x] = 1/F[17,x]*F[16,x]
F[16,x] = F[5,x]
F[17,x] = x
F[18,x] = F[19,x]+F[20,x]
F[19,x] = 1+x*F[19,x]^4+F[19,x]^2*(x^2-2*x+3)+F[19,x]^3*(-1-x)+(-2+2*x)*F[19,x]
F[20,x] = F[21,x]
F[21,x] = F[17,x]*F[22,x]
F[22,x] = F[19,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[17,x]*F[19,x]*F[22,x]*F[25,x]
F[25,x] = F[1,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[25,x]^2*F[17,x]
F[28,x] = F[29,x]
F[29,x] = F[25,x]*F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[17,x]*F[32,x]
F[32,x] = F[33,x]+F[42,x]
F[33,x] = F[34,x]+F[41,x]
F[34,x] = F[0,x]*F[35,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[0,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[15,x]*F[17,x]
F[39,x] = F[40,x]
F[40,x] = F[17,x]*F[32,x]
F[41,x] = F[22,x]*F[37,x]
F[42,x] = F[25,x]*F[39,x]
F[43,x] = F[29,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_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{17}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{43}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{28}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{17}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{5}\! \left(x \right)
F_{17}\! \left(x \right) = x
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)
F_{19}\! \left(x \right) = x F_{19} \left(x \right)^{4}+x^{2} F_{19} \left(x \right)^{2}-F_{19} \left(x \right)^{3} x -2 x F_{19} \left(x \right)^{2}-F_{19} \left(x \right)^{3}+2 F_{19}\! \left(x \right) x +3 F_{19} \left(x \right)^{2}-2 F_{19}\! \left(x \right)+1
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{17}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{19}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{17}\! \left(x \right) F_{19}\! \left(x \right) F_{22}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{25} \left(x \right)^{2} F_{17}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{25}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{17}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{42}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{41}\! \left(x \right)
F_{34}\! \left(x \right) = F_{0}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{0}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{15}\! \left(x \right) F_{17}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{17}\! \left(x \right) F_{32}\! \left(x \right)
F_{41}\! \left(x \right) = F_{22}\! \left(x \right) F_{37}\! \left(x \right)
F_{42}\! \left(x \right) = F_{25}\! \left(x \right) F_{39}\! \left(x \right)
F_{43}\! \left(x \right) = F_{29}\! \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_17(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_17(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_17(x))
Eq(F_12(x), F_13(x) + F_43(x))
Eq(F_13(x), F_14(x) + F_28(x))
Eq(F_14(x), F_15(x)*F_18(x))
Eq(F_15(x), F_16(x)/F_17(x))
Eq(F_16(x), F_5(x))
Eq(F_17(x), x)
Eq(F_18(x), F_19(x) + F_20(x))
Eq(F_19(x), x*F_19(x)**4 + (-x - 1)*F_19(x)**3 + (2*x - 2)*F_19(x) + (x**2 - 2*x + 3)*F_19(x)**2 + 1)
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_17(x)*F_22(x))
Eq(F_22(x), F_19(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_17(x)*F_19(x)*F_22(x)*F_25(x))
Eq(F_25(x), F_1(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_17(x)*F_25(x)**2)
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_25(x)*F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_17(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_42(x))
Eq(F_33(x), F_34(x) + F_41(x))
Eq(F_34(x), F_0(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_0(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_15(x)*F_17(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_17(x)*F_32(x))
Eq(F_41(x), F_22(x)*F_37(x))
Eq(F_42(x), F_25(x)*F_39(x))
Eq(F_43(x), F_29(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, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 4, 0, 1, 3], [2, 4, 1, 0, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 4, 0, 1, 3], [2, 4, 1, 0, 3]], "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, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "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, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 0, 3], "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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [2, 1], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [2, 1], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], 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[3, 2], [3, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [4, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [4, 1], [4, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [4, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [4, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 1], [4, 1], [4, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"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, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]], "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, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "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, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 4, 0, 1, 3], [2, 4, 1, 0, 3]], "symmetry": false}}]}

Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25811/
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[17,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[17,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[17,x]
F[12,x] = F[13,x]+F[43,x]
F[13,x] = F[14,x]+F[28,x]
F[14,x] = F[15,x]*F[18,x]
F[15,x] = 1/F[17,x]*F[16,x]
F[16,x] = F[5,x]
F[17,x] = x
F[18,x] = F[19,x]+F[20,x]
F[19,x] = 1+x*F[19,x]^4+F[19,x]^2*(x^2-2*x+3)+F[19,x]^3*(-1-x)+(-2+2*x)*F[19,x]
F[20,x] = F[21,x]
F[21,x] = F[17,x]*F[22,x]
F[22,x] = F[19,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[17,x]*F[19,x]*F[22,x]*F[25,x]
F[25,x] = F[1,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[25,x]^2*F[17,x]
F[28,x] = F[29,x]
F[29,x] = F[25,x]*F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[17,x]*F[32,x]
F[32,x] = F[33,x]+F[42,x]
F[33,x] = F[34,x]+F[41,x]
F[34,x] = F[0,x]*F[35,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[0,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[15,x]*F[17,x]
F[39,x] = F[40,x]
F[40,x] = F[17,x]*F[32,x]
F[41,x] = F[22,x]*F[37,x]
F[42,x] = F[25,x]*F[39,x]
F[43,x] = F[29,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_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{17}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{43}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{28}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{17}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{5}\! \left(x \right)
F_{17}\! \left(x \right) = x
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)
F_{19}\! \left(x \right) = x F_{19} \left(x \right)^{4}+x^{2} F_{19} \left(x \right)^{2}-F_{19} \left(x \right)^{3} x -2 x F_{19} \left(x \right)^{2}-F_{19} \left(x \right)^{3}+2 F_{19}\! \left(x \right) x +3 F_{19} \left(x \right)^{2}-2 F_{19}\! \left(x \right)+1
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{17}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{19}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{17}\! \left(x \right) F_{19}\! \left(x \right) F_{22}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{25} \left(x \right)^{2} F_{17}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{25}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{17}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{42}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{41}\! \left(x \right)
F_{34}\! \left(x \right) = F_{0}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{0}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{15}\! \left(x \right) F_{17}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{17}\! \left(x \right) F_{32}\! \left(x \right)
F_{41}\! \left(x \right) = F_{22}\! \left(x \right) F_{37}\! \left(x \right)
F_{42}\! \left(x \right) = F_{25}\! \left(x \right) F_{39}\! \left(x \right)
F_{43}\! \left(x \right) = F_{29}\! \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_17(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_17(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_17(x))
Eq(F_12(x), F_13(x) + F_43(x))
Eq(F_13(x), F_14(x) + F_28(x))
Eq(F_14(x), F_15(x)*F_18(x))
Eq(F_15(x), F_16(x)/F_17(x))
Eq(F_16(x), F_5(x))
Eq(F_17(x), x)
Eq(F_18(x), F_19(x) + F_20(x))
Eq(F_19(x), x*F_19(x)**4 + (-x - 1)*F_19(x)**3 + (2*x - 2)*F_19(x) + (x**2 - 2*x + 3)*F_19(x)**2 + 1)
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_17(x)*F_22(x))
Eq(F_22(x), F_19(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_17(x)*F_19(x)*F_22(x)*F_25(x))
Eq(F_25(x), F_1(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_17(x)*F_25(x)**2)
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_25(x)*F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_17(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_42(x))
Eq(F_33(x), F_34(x) + F_41(x))
Eq(F_34(x), F_0(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_0(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_15(x)*F_17(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_17(x)*F_32(x))
Eq(F_41(x), F_22(x)*F_37(x))
Eq(F_42(x), F_25(x)*F_39(x))
Eq(F_43(x), F_29(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, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 4, 0, 1, 3], [2, 4, 1, 0, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 4, 0, 1, 3], [2, 4, 1, 0, 3]], "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, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "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, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 1, 0, 3], "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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [2, 1], [2, 2]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [2, 1], [2, 2]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 2], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 2], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 2], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 1], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], 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{"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [2, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [2, 1], [2, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [2, 2], [2, 1], [2, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 2], [2, 2], [2, 1], [2, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[2, 2], [2, 2], [2, 2], [2, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 1], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 1, 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2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 1], [0, 2]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 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[[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[5, 0]]}, {"patt": [0], "pos": [[5, 1]]}, {"patt": [0], "pos": [[6, 0]]}, {"patt": [0], "pos": [[6, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [3, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [5, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[4, 1], [5, 2]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [5, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [3, 2], [5, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [5, 2], [5, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [6, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [4, 1], [6, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [6, 1], [6, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 2], [3, 2], [5, 2]]}, {"patt": [0, 2, 1], "pos": [[3, 2], [5, 2], [5, 2]]}, {"patt": [0, 2, 1], "pos": [[4, 1], [4, 1], [6, 1]]}, {"patt": [0, 2, 1], "pos": [[4, 1], [6, 1], [6, 1]]}, {"patt": [0, 2, 1], "pos": [[5, 2], [5, 2], [5, 2]]}, {"patt": [0, 2, 1], "pos": [[6, 1], [6, 1], [6, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [3, 2], [3, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [4, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [4, 1], [4, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [4, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 1], [1, 1], [4, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [1, 1], [4, 1], [4, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"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, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 4, 0, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 1, 4, 0, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 1, 0, 3], "pos": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]], "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, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "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, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 4, 0, 1, 3], [2, 4, 1, 0, 3]], "symmetry": false}}]}

Specification 4
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/25910/
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[17,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[17,x]*F[7,x]
F[7,x] = F[23,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[17,x]*F[18,x]
F[11,x] = F[12,x]+F[21,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = 1+x*F[14,x]^4+F[14,x]^2*(x^2-2*x+3)+F[14,x]^3*(-1-x)+(-2+2*x)*F[14,x]
F[15,x] = F[16,x]
F[16,x] = F[13,x]*F[14,x]*F[17,x]*F[18,x]
F[17,x] = x
F[18,x] = F[1,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[18,x]^2*F[17,x]
F[21,x] = F[0,x]*F[22,x]
F[22,x] = -F[13,x]+F[8,x]
F[23,x] = F[24,x]
F[24,x] = F[17,x]*F[25,x]
F[25,x] = 1/F[17,x]*F[26,x]
F[26,x] = F[9,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_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{17}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{23}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{17}\! \left(x \right) F_{18}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{21}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = x F_{14} \left(x \right)^{4}+x^{2} F_{14} \left(x \right)^{2}-F_{14} \left(x \right)^{3} x -2 x F_{14} \left(x \right)^{2}-F_{14} \left(x \right)^{3}+2 F_{14}\! \left(x \right) x +3 F_{14} \left(x \right)^{2}-2 F_{14}\! \left(x \right)+1
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{14}\! \left(x \right) F_{17}\! \left(x \right) F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = x
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{18} \left(x \right)^{2} F_{17}\! \left(x \right)
F_{21}\! \left(x \right) = F_{0}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = -F_{13}\! \left(x \right)+F_{8}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{17}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = \frac{F_{26}\! \left(x \right)}{F_{17}\! \left(x \right)}
F_{26}\! \left(x \right) = F_{9}\! \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_17(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_17(x)*F_7(x))
Eq(F_7(x), F_23(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_17(x)*F_18(x))
Eq(F_11(x), F_12(x) + F_21(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), x*F_14(x)**4 + (-x - 1)*F_14(x)**3 + (2*x - 2)*F_14(x) + (x**2 - 2*x + 3)*F_14(x)**2 + 1)
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_13(x)*F_14(x)*F_17(x)*F_18(x))
Eq(F_17(x), x)
Eq(F_18(x), F_1(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_17(x)*F_18(x)**2)
Eq(F_21(x), F_0(x)*F_22(x))
Eq(F_22(x), -F_13(x) + F_8(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_17(x)*F_25(x))
Eq(F_25(x), F_26(x)/F_17(x))
Eq(F_26(x), F_9(x))
Pack JSON:
{"name": "point_placements_tracked_fusion", "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.fusion.fusion", "strategy_class": "FusionFactory", "tracked": 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}], "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:
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"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, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 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, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 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": 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[{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "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, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 4, 0, 1, 3], [2, 4, 1, 0, 3]], "symmetry": false}}]}

Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25958/
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[17,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[17,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[2,x]*F[4,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[17,x]
F[12,x] = F[13,x]+F[51,x]
F[13,x] = F[14,x]+F[28,x]
F[14,x] = F[15,x]*F[18,x]
F[15,x] = 1/F[17,x]*F[16,x]
F[16,x] = F[5,x]
F[17,x] = x
F[18,x] = F[19,x]+F[20,x]
F[19,x] = 1+x*F[19,x]^4+F[19,x]^2*(x^2-2*x+3)+F[19,x]^3*(-1-x)+(-2+2*x)*F[19,x]
F[20,x] = F[21,x]
F[21,x] = F[17,x]*F[22,x]
F[22,x] = F[19,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[17,x]*F[19,x]*F[22,x]*F[25,x]
F[25,x] = F[1,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[25,x]^2*F[17,x]
F[28,x] = F[29,x]
F[29,x] = F[25,x]*F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[17,x]*F[32,x]
F[32,x] = F[33,x]+F[50,x]
F[33,x] = F[34,x]+F[38,x]
F[34,x] = F[22,x]*F[35,x]
F[35,x] = F[0,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[15,x]*F[17,x]
F[38,x] = F[0,x]*F[39,x]
F[39,x] = -F[44,x]+F[40,x]
F[40,x] = 1/F[17,x]*F[41,x]
F[41,x] = F[42,x]
F[42,x] = -F[2,x]+F[43,x]
F[43,x] = -F[19,x]+F[35,x]
F[44,x] = -F[47,x]+F[45,x]
F[45,x] = 1/F[17,x]*F[46,x]
F[46,x] = F[36,x]
F[47,x] = F[35,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[17,x]*F[32,x]
F[50,x] = F[25,x]*F[48,x]
F[51,x] = F[29,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_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{17}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{51}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{28}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{18}\! \left(x \right)
F_{15}\! \left(x \right) = \frac{F_{16}\! \left(x \right)}{F_{17}\! \left(x \right)}
F_{16}\! \left(x \right) = F_{5}\! \left(x \right)
F_{17}\! \left(x \right) = x
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)
F_{19}\! \left(x \right) = x F_{19} \left(x \right)^{4}+x^{2} F_{19} \left(x \right)^{2}-F_{19} \left(x \right)^{3} x -2 x F_{19} \left(x \right)^{2}-F_{19} \left(x \right)^{3}+2 F_{19}\! \left(x \right) x +3 F_{19} \left(x \right)^{2}-2 F_{19}\! \left(x \right)+1
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{17}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{19}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{17}\! \left(x \right) F_{19}\! \left(x \right) F_{22}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{25} \left(x \right)^{2} F_{17}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{25}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{17}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{50}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
F_{34}\! \left(x \right) = F_{22}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{0}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{15}\! \left(x \right) F_{17}\! \left(x \right)
F_{38}\! \left(x \right) = F_{0}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = -F_{44}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = \frac{F_{41}\! \left(x \right)}{F_{17}\! \left(x \right)}
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = -F_{2}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = -F_{19}\! \left(x \right)+F_{35}\! \left(x \right)
F_{44}\! \left(x \right) = -F_{47}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = \frac{F_{46}\! \left(x \right)}{F_{17}\! \left(x \right)}
F_{46}\! \left(x \right) = F_{36}\! \left(x \right)
F_{47}\! \left(x \right) = F_{35}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{17}\! \left(x \right) F_{32}\! \left(x \right)
F_{50}\! \left(x \right) = F_{25}\! \left(x \right) F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = F_{29}\! \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_17(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_17(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_2(x)*F_4(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_17(x))
Eq(F_12(x), F_13(x) + F_51(x))
Eq(F_13(x), F_14(x) + F_28(x))
Eq(F_14(x), F_15(x)*F_18(x))
Eq(F_15(x), F_16(x)/F_17(x))
Eq(F_16(x), F_5(x))
Eq(F_17(x), x)
Eq(F_18(x), F_19(x) + F_20(x))
Eq(F_19(x), x*F_19(x)**4 + (-x - 1)*F_19(x)**3 + (2*x - 2)*F_19(x) + (x**2 - 2*x + 3)*F_19(x)**2 + 1)
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_17(x)*F_22(x))
Eq(F_22(x), F_19(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_17(x)*F_19(x)*F_22(x)*F_25(x))
Eq(F_25(x), F_1(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_17(x)*F_25(x)**2)
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_25(x)*F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_17(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_50(x))
Eq(F_33(x), F_34(x) + F_38(x))
Eq(F_34(x), F_22(x)*F_35(x))
Eq(F_35(x), F_0(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_15(x)*F_17(x))
Eq(F_38(x), F_0(x)*F_39(x))
Eq(F_39(x), F_40(x) - F_44(x))
Eq(F_40(x), F_41(x)/F_17(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), -F_2(x) + F_43(x))
Eq(F_43(x), -F_19(x) + F_35(x))
Eq(F_44(x), F_45(x) - F_47(x))
Eq(F_45(x), F_46(x)/F_17(x))
Eq(F_46(x), F_36(x))
Eq(F_47(x), F_35(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_17(x)*F_32(x))
Eq(F_50(x), F_25(x)*F_48(x))
Eq(F_51(x), F_29(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, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 4, 0, 1, 3], [2, 4, 1, 0, 3]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 2, 4, 3], [0, 2, 1, 4, 3], [0, 2, 4, 1, 3], [1, 0, 2, 4, 3], [1, 2, 0, 4, 3], [1, 2, 4, 0, 3], [2, 0, 1, 4, 3], [2, 0, 4, 1, 3], [2, 1, 0, 4, 3], [2, 1, 4, 0, 3], [2, 4, 0, 1, 3], [2, 4, 1, 0, 3]], "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:
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