01342_01423_01432_10342_10423_10432_13042_13402_14023_14032_14302
Counting sequence:
1, 1, 2, 6, 24, 109, 525, 2616, 13339, 69182, 363566, 1930899, 10344571, 55826876, 303176871, 1655444598, 9082702762, 50045694695, 276808270700, 1536358812213, 8554060056905, 47764150053855, 267412401566999, 1500800807773384, 8442077535604664, 47587387833151770, 268775369485186850, 1520852891553186337, 8620560471592743138, 48942864698697118332, 278296603124863751530, 1584723962004864143002, 9036332468695097378429, 51593148622209507347748, 294933399238300643495579, 1687955490513581886400865, 9671149886796643616633263, 55469221826864315466335858, 318464636802141854114898811, 1830144312811579308641743603, 10527022839472147465961755961, 60604410959151686289772481039, 349192404158794380880299302657, 2013592978102148684908365036834, 11620112529191234117691778220990, 67106871001868028287962199078191, 387818674792608004603849660214107, 2242762688329165328846755945331694, 12978344291349191950117629653238295, 75149440117963414219292838212431914, 435404000411603057336226202116253441, 2524117435892343823216154504124049913, 14640906192845016386198377282860884452, 84968681945707500830983688571620080350, 493371476889187038114801490195988978373, 2866193842910565622066304827662397681895, 16658886380909889662022671643459707565609, 96869743876288471060740896506201452813162, 563540782459245486556796752705918417976364, 3279828412317690029209582291781053872902082, 19096744388961691508786006453464362683461213, 111235685429935088294740440354420508740537952, 648186444133791762054033491825596071833982785, 3778517476717692959348188988842012183789298633, 22034516291588435486158642049317883681437964067, 128540901007514381084880664494458716511185622843, 750119130798636334303254266095338577453166659352, 4378907573486713166830203100824741238128983559206, 25570763271583797683520181911287488519062547808629, 149368803406476264292232045658267499765390314650214, 872791483683550885324149673714558852870479596865317, 5101427715945381901271601142497132259273637252227648, 29826343687492461294750674175909819969730200499756371, 174434301225272336428186629847759316915602198578586521, 1020431926977724535123276427877440786389777282009617944, 5971085339873993657281490624243300582921775764084685129, 34949144418845019483737348981981626591409387238100316085, 204611907590040373258287998137333539030301543207245374497, 1198211582149833848117741579255037071247342274936209639474, 7018457079156110165336560573084510045066071494717383398207, 41119960012483630870626121360830625120102890666266689149198, 240970616731861042820768384601766213177890314870469557938919, 1412451117116054528582804689312293099868978408080511584310574, 8280915330980360945200478473179759107926578541766724983634397, 48559764759712217186696526543299594644177043997537916807250798, 284817013109567325553414218328904687439558802061424106961696651, 1670876270923935513165446356011588865156087326597892472406757576, 9804142716811740690239913379445699957450723675606150081805041582, 57538688062547547415453179266371455278200429692425049026255203766, 337748460355602133709358325460594028632108657876212641817168771226, 1982933042736538562093832364117765047934743437530045633218666800017, 11643999776224315077324552985354254410963848208567101339831805298638, 68387081417013322092528056210901114765061568283808120646279213263783, 401718677301424965448538682677733090625027249435670527426316522625700, 2360176250022776810590432857679294360371934962156132449717909783608585, 13868827281436614826064079664109782513977903271217305259370204744601066, 81509160253836638198881834270046075388917593530398432374757808705687881, 479118569888289302741736614712842621529954307173215318565818969294311576, 2816748484797549250191614010294673146409502259386259056448789436178020095, 16562284243197694838091683286429565339511254279215444734922029819713458360, 97399820467791938488666599444922457425701005082187398203135745893571180372
Implicit equation for the generating function in Maple syntax:
(2*x^2-5*x+4)*x^2*F(x)^9-3*x^2*(3*x^2-7*x+6)*F(x)^8+x*(18*x^3-45*x^2+46*x-5)*F(x)^7-x*(19*x^3-63*x^2+84*x-23)*F(x)^6+(12*x^4-57*x^3+102*x^2-45*x+1)*F(x)^5+(-3*x^4+29*x^3-76*x^2+50*x-5)*F(x)^4+(-6*x^3+32*x^2-35*x+10)*F(x)^3+(-6*x^2+15*x-10)*F(x)^2+(-3*x+5)*F(x)-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x^{2}-5 x +4\right) x^{2} F \! \left(x \right)^{9}-3 x^{2} \left(3 x^{2}-7 x +6\right) F \! \left(x \right)^{8}+x \left(18 x^{3}-45 x^{2}+46 x -5\right) F \! \left(x \right)^{7}-x \left(19 x^{3}-63 x^{2}+84 x -23\right) F \! \left(x \right)^{6}+\left(12 x^{4}-57 x^{3}+102 x^{2}-45 x +1\right) F \! \left(x \right)^{5}+\left(-3 x^{4}+29 x^{3}-76 x^{2}+50 x -5\right) F \! \left(x \right)^{4}+\left(-6 x^{3}+32 x^{2}-35 x +10\right) F \! \left(x \right)^{3}+\left(-6 x^{2}+15 x -10\right) F \! \left(x \right)^{2}+\left(-3 x +5\right) F \! \left(x \right)-1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 109
a(6) = 525
a(7) = 2616
a(8) = 13339
a(9) = 69182
a(10) = 363566
a(11) = 1930899
a(12) = 10344571
a(13) = 55826876
a(14) = 303176871
a(15) = 1655444598
a(16) = 9082702762
a(17) = 50045694695
a(18) = 276808270700
a(19) = 1536358812213
a(20) = 8554060056905
a(21) = 47764150053855
a(22) = 267412401566999
a(23) = 1500800807773384
a(24) = 8442077535604664
a(25) = 47587387833151770
a(26) = 268775369485186850
a(27) = 1520852891553186337
a(28) = 8620560471592743138
a(29) = 48942864698697118332
a(30) = 278296603124863751530
a(31) = 1584723962004864143002
a(32) = 9036332468695097378429
a(33) = 51593148622209507347748
a(34) = 294933399238300643495579
a(35) = 1687955490513581886400865
a(36) = 9671149886796643616633263
a(37) = 55469221826864315466335858
a(38) = 318464636802141854114898811
a(39) = 1830144312811579308641743603
a(40) = 10527022839472147465961755961
a(41) = 60604410959151686289772481039
a(42) = 349192404158794380880299302657
a(43) = 2013592978102148684908365036834
a(44) = 11620112529191234117691778220990
a(45) = 67106871001868028287962199078191
a(46) = 387818674792608004603849660214107
a(47) = 2242762688329165328846755945331694
a(48) = 12978344291349191950117629653238295
a(49) = 75149440117963414219292838212431914
a(50) = 435404000411603057336226202116253441
a(51) = 2524117435892343823216154504124049913
a(52) = 14640906192845016386198377282860884452
a(53) = 84968681945707500830983688571620080350
a(54) = 493371476889187038114801490195988978373
a(55) = 2866193842910565622066304827662397681895
a(56) = 16658886380909889662022671643459707565609
a(57) = 96869743876288471060740896506201452813162
a(58) = 563540782459245486556796752705918417976364
a(59) = 3279828412317690029209582291781053872902082
a(60) = 19096744388961691508786006453464362683461213
a(61) = 111235685429935088294740440354420508740537952
a(62) = 648186444133791762054033491825596071833982785
a(63) = 3778517476717692959348188988842012183789298633
a(64) = 22034516291588435486158642049317883681437964067
a(65) = 128540901007514381084880664494458716511185622843
a(66) = 750119130798636334303254266095338577453166659352
a(67) = 4378907573486713166830203100824741238128983559206
a(68) = 25570763271583797683520181911287488519062547808629
a(69) = 149368803406476264292232045658267499765390314650214
a(70) = 872791483683550885324149673714558852870479596865317
a(71) = 5101427715945381901271601142497132259273637252227648
a(72) = 29826343687492461294750674175909819969730200499756371
a(73) = 174434301225272336428186629847759316915602198578586521
a(74) = 1020431926977724535123276427877440786389777282009617944
a(75) = 5971085339873993657281490624243300582921775764084685129
a(76) = 34949144418845019483737348981981626591409387238100316085
a(77) = 204611907590040373258287998137333539030301543207245374497
a(78) = 1198211582149833848117741579255037071247342274936209639474
a(79) = 7018457079156110165336560573084510045066071494717383398207
a(80) = 41119960012483630870626121360830625120102890666266689149198
a(81) = 240970616731861042820768384601766213177890314870469557938919
a(82) = 1412451117116054528582804689312293099868978408080511584310574
a(83) = 8280915330980360945200478473179759107926578541766724983634397
a(84) = 48559764759712217186696526543299594644177043997537916807250798
a(85) = 284817013109567325553414218328904687439558802061424106961696651
a(86) = 1670876270923935513165446356011588865156087326597892472406757576
a(87) = 9804142716811740690239913379445699957450723675606150081805041582
a(88) = 57538688062547547415453179266371455278200429692425049026255203766
a(89) = 337748460355602133709358325460594028632108657876212641817168771226
a(90) = 1982933042736538562093832364117765047934743437530045633218666800017
a(91) = 11643999776224315077324552985354254410963848208567101339831805298638
a(92) = 68387081417013322092528056210901114765061568283808120646279213263783
a(n+93) = 243/75591424409600*(24873169452821208470436732534282046551344339370577073*n^8+6716386878742548144447027794697707426527313995389506972*n^7+793899239879867625999811637426574119770000816373895768116*n^6+53654707207861109038886922654548141237655203315735800405022*n^5+2267696052821994845995284851461750083818884098450433622912147*n^4+61376212966372009111272932574683158446759196899912329443426358*n^3+1038860504844275074898037036907014318577864315038727520928263784*n^2+10054066544095715714196597284944041985463834818421590331891739888*n+42596426176477111621787449167818797265706016227868171563481254720)/(2*n+187)/(2*n+185)/(2*n+183)/(4*n+369)/(n+93)/(n+92)/(n+91)/(4*n+367)*a(n+33)-243/18897856102400*(9123879169112863132714633085947326245541445392540528*n^8+2526249527559526389168367618841691223226859327275595075*n^7+306218920719677070706177101452655027299813828490695087008*n^6+21224307000828485247596998446380189948273011770093005077656*n^5+920029078456029380446629308420994847171482928922974271060122*n^4+25541052826167576554724125573286692298344274735223028490025785*n^3+443453352913371247018459625394322823269753631196655908271128202*n^2+4402643413578124226535820614962327250468535584175901528475022944*n+19136129162059474860042707607798451365879976688029071214426156320)/(2*n+187)/(2*n+185)/(2*n+183)/(4*n+369)/(n+93)/(n+92)/(n+91)/(4*n+367)*a(n+34)+243/18897856102400*(12612175698122921115279927083839387321998656292976037*n^8+3581874833066749581491649867525576390474613776062993696*n^7+445368866678708360620318500578486633541171843866226262868*n^6+31666792095273570687870809154724352921593325291696214268174*n^5+1408260114443786134171021167737889052913872037195971447882223*n^4+40110486429832289926633622228709573456744179938182130024100194*n^3+714547131179489288696212797065832039257561133981528272639724252*n^2+7279225890862860027599153171553380480734210797502361912088267836*n+32466720122353561430243520882371080195040561332464257205836903760)/(2*n+187)/(2*n+185)/(2*n+183)/(4*n+369)/(n+93)/(n+92)/(n+91)/(4*n+367)*a(n+35)+243/37795712204800*(4710343121069257199226521019543640972307857491594911*n^8+1211078829310391920323767782080781873600122293253226028*n^7+136279949064999905436821430782374962202481080284043929122*n^6+8766405727048257981313846897603619320120015059926955638336*n^5+352586442138974560725124653850455982975293915191237550092699*n^4+9079672033889620279123910588843849749817765623594851122005772*n^3+146197904813932063585616101944606355479679762220725900840072788*n^2+1345755328029015551096987091786504293504995845035328711022193784*n+5422086476507821036471602135205899391324024151118408199825548960)/(2*n+187)/(2*n+185)/(2*n+183)/(4*n+369)/(n+93)/(n+92)/(n+91)/(4*n+367)*a(n+31)-729/37795712204800*(2644603139175327006905603392107163472288729258399549*n^8+696671200356114122456643592110546268612723100742569338*n^7+80330747306896679913439630151112654476708364190348400992*n^6+5295551165151232956814707633736790990906003552435232494416*n^5+218292525489004341878825478882010491089143002554044982257271*n^4+5761951778129263085999739247891463316646675681895243228320382*n^3+95106042955424680478323253782432825662282094610962092833350588*n^2+897513021323706487342097761578795611856001735476905281763855384*n+3707557961953224104928853956189432484710957502816004173958658240)/(2*n+187)/(2*n+185)/(2*n+183)/(4*n+369)/(n+93)/(n+92)/(n+91)/(4*n+367)*a(n+32)+2187/75591424409600*(291014287980171698697748153121254979249678542879329*n^8+71418093694835969589564052771236090102542797080973440*n^7+7667964762782262399642002076498133481908164174774223952*n^6+470465104318817720511049156411285217114725025346036675666*n^5+18041852685616523314519560519028293240640361912053579482731*n^4+442846608001676385703417172686242044613997467961501304584710*n^3+6794466114027673834579706117307642583452704930296417020612068*n^2+59577132845537986596552854769493985609498660652237329401310664*n+228587181092619709281693143138654765377977566368077407017258080)/(2*n+187)/(2*n+185)/(2*n+183)/(4*n+369)/(n+93)/(n+92)/(n+91)/(4*n+367)*a(n+29)-729/37795712204800*(862907636960965903816127127940601913948636606216137*n^8+216664682760207297118122075137436674054290080442072265*n^7+23806058284364223573218152428918922158650381298282747981*n^6+1495048527527653149685905949995546880242075639742800762731*n^5+58697310798246752875390922904456601120833334573042920330438*n^4+1475313843420036564143060732768823514758512587477884129618860*n^3+23182579584949786400404712723884228697143685156612603251660324*n^2+208228169754954010500937723517728102613370093317454435151213344*n+818541132928344368040039394248174778544036581064836261346136240)/(2*n+187)/(2*n+185)/(2*n+183)/(4*n+369)/(n+93)/(n+92)/(n+91)/(4*n+367)*a(n+30)-6561/37795712204800*(22423463580119845590092064996506509261155615076841*n^8+5385788858115921212958874443401836634309662935865664*n^7+565734094135782373724756552355840536504032133658676913*n^6+33946827541980636654655145591229603810201180975658411553*n^5+12727694635041231636927087142215965535668766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3/37795712204800*(6092888469116345168345618943466*n^8+631179271610998261165011438039950*n^7+28428398186338879134825553040096659*n^6+728130278990111219005801103533703151*n^5+11610494092089853915704456713594506709*n^4+118100707438618706714722503732387557915*n^3+748676556895327168814906592729116773646*n^2+2705008513052502748098786011179662083864*n+4265329541710389105890965213059340509120)/(2*n+187)/(2*n+185)/(2*n+183)/(4*n+369)/(n+93)/(n+92)/(n+91)/(4*n+367)*a(n+10)+124551425588121/37795712204800*(71738642474897902023620056416030*n^8+7710714522513646600439979837709900*n^7+361395469863431394712471898008852003*n^6+9653502812516595599062741623807830947*n^5+160810163024572829672683403741058031005*n^4+1711187843939483901934586444155509101185*n^3+11361085415406731092646890040042011244402*n^2+43033833007768380126355178599840401135168*n+71204610024484872643089259946839688142960)/(2*n+187)/(2*n+185)/(2*n+183)/(4*n+369)/(n+93)/(n+92)/(n+91)/(4*n+367)*a(n+11)-1/220*(1176608*n^4+423152592*n^3+57061050118*n^2+3419360752197*n+76828946090490)/(2*n+187)/(4*n+369)/(n+93)/(4*n+367)*a(n+92)+10088665472637801/75591424409600*(n+7)*(2044419753933881307611914317*n^7+197749389527978536166472876809*n^6+7517243710919848732386973315329*n^5+150911476089300133104326141057863*n^4+1758054265197258190515632998919522*n^3+11997904236410643920679925801511248*n^2+44665245718699332496865314528284672*n+70220155797384703489657301274679200)/(2*n+187)/(2*n+185)/(2*n+183)/(4*n+369)/(n+93)/(n+92)/(n+91)/(4*n+367)*a(n+7)+635585924776181463/75591424409600*(n+4)*(n+5)*(n+6)*(n+7)*(709965823977384758215327*n^4+26480562654623077856239476*n^3+368693769869404431994170173*n^2+2307583704011652601468657644*n+5502220779528981454903841940)/(2*n+187)/(2*n+185)/(2*n+183)/(4*n+369)/(n+93)/(n+92)/(n+91)/(4*n+367)*a(n+4)-336655646005580274795046783926630575769/151182848819200*n*(n+7)*(n+6)*(n+5)*(n+4)*(n+3)*(n+2)*(n+1)/(2*n+187)/(2*n+185)/(2*n+183)/(4*n+369)/(n+93)/(n+92)/(n+91)/(4*n+367)*a(n), n >= 93
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 109
a(6) = 525
a(7) = 2616
a(8) = 13339
a(9) = 69182
a(10) = 363566
a(11) = 1930899
a(12) = 10344571
a(13) = 55826876
a(14) = 303176871
a(15) = 1655444598
a(16) = 9082702762
a(17) = 50045694695
a(18) = 276808270700
a(19) = 1536358812213
a(20) = 8554060056905
a(21) = 47764150053855
a(22) = 267412401566999
a(23) = 1500800807773384
a(24) = 8442077535604664
a(25) = 47587387833151770
a(26) = 268775369485186850
a(27) = 1520852891553186337
a(28) = 8620560471592743138
a(29) = 48942864698697118332
a(30) = 278296603124863751530
a(31) = 1584723962004864143002
a(32) = 9036332468695097378429
a(33) = 51593148622209507347748
a(34) = 294933399238300643495579
a(35) = 1687955490513581886400865
a(36) = 9671149886796643616633263
a(37) = 55469221826864315466335858
a(38) = 318464636802141854114898811
a(39) = 1830144312811579308641743603
a(40) = 10527022839472147465961755961
a(41) = 60604410959151686289772481039
a(42) = 349192404158794380880299302657
a(43) = 2013592978102148684908365036834
a(44) = 11620112529191234117691778220990
a(45) = 67106871001868028287962199078191
a(46) = 387818674792608004603849660214107
a(47) = 2242762688329165328846755945331694
a(48) = 12978344291349191950117629653238295
a(49) = 75149440117963414219292838212431914
a(50) = 435404000411603057336226202116253441
a(51) = 2524117435892343823216154504124049913
a(52) = 14640906192845016386198377282860884452
a(53) = 84968681945707500830983688571620080350
a(54) = 493371476889187038114801490195988978373
a(55) = 2866193842910565622066304827662397681895
a(56) = 16658886380909889662022671643459707565609
a(57) = 96869743876288471060740896506201452813162
a(58) = 563540782459245486556796752705918417976364
a(59) = 3279828412317690029209582291781053872902082
a(60) = 19096744388961691508786006453464362683461213
a(61) = 111235685429935088294740440354420508740537952
a(62) = 648186444133791762054033491825596071833982785
a(63) = 3778517476717692959348188988842012183789298633
a(64) = 22034516291588435486158642049317883681437964067
a(65) = 128540901007514381084880664494458716511185622843
a(66) = 750119130798636334303254266095338577453166659352
a(67) = 4378907573486713166830203100824741238128983559206
a(68) = 25570763271583797683520181911287488519062547808629
a(69) = 149368803406476264292232045658267499765390314650214
a(70) = 872791483683550885324149673714558852870479596865317
a(71) = 5101427715945381901271601142497132259273637252227648
a(72) = 29826343687492461294750674175909819969730200499756371
a(73) = 174434301225272336428186629847759316915602198578586521
a(74) = 1020431926977724535123276427877440786389777282009617944
a(75) = 5971085339873993657281490624243300582921775764084685129
a(76) = 34949144418845019483737348981981626591409387238100316085
a(77) = 204611907590040373258287998137333539030301543207245374497
a(78) = 1198211582149833848117741579255037071247342274936209639474
a(79) = 7018457079156110165336560573084510045066071494717383398207
a(80) = 41119960012483630870626121360830625120102890666266689149198
a(81) = 240970616731861042820768384601766213177890314870469557938919
a(82) = 1412451117116054528582804689312293099868978408080511584310574
a(83) = 8280915330980360945200478473179759107926578541766724983634397
a(84) = 48559764759712217186696526543299594644177043997537916807250798
a(85) = 284817013109567325553414218328904687439558802061424106961696651
a(86) = 1670876270923935513165446356011588865156087326597892472406757576
a(87) = 9804142716811740690239913379445699957450723675606150081805041582
a(88) = 57538688062547547415453179266371455278200429692425049026255203766
a(89) = 337748460355602133709358325460594028632108657876212641817168771226
a(90) = 1982933042736538562093832364117765047934743437530045633218666800017
a(91) = 11643999776224315077324552985354254410963848208567101339831805298638
a(92) = 68387081417013322092528056210901114765061568283808120646279213263783
a{\left(n + 93 \right)} = - \frac{336655646005580274795046783926630575769 n \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(n + 4\right) \left(n + 5\right) \left(n + 6\right) \left(n + 7\right) a{\left(n \right)}}{151182848819200 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{840880178478888075549 \left(n + 1\right) \left(n + 2\right) \left(n + 3\right) \left(n + 4\right) \left(n + 5\right) \left(n + 6\right) \left(n + 7\right) \left(4051044582195698225 n + 12037379015989728384\right) a{\left(n + 1 \right)}}{302365697638400 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{40041913260899432169 \left(n + 2\right) \left(n + 3\right) \left(n + 4\right) \left(n + 5\right) \left(n + 6\right) \left(n + 7\right) \left(93321071266006295529 n^{2} + 2102356901951570014941 n + 10408738330858728560534\right) a{\left(n + 2 \right)}}{18897856102400 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{13347304420299810723 \left(n + 3\right) \left(n + 4\right) \left(n + 5\right) \left(n + 6\right) \left(n + 7\right) \left(262204754480641558145 n^{3} - 28346744378922181842069 n^{2} - 796755505732230987315790 n - 4280757417122382047520352\right) a{\left(n + 3 \right)}}{151182848819200 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{635585924776181463 \left(n + 4\right) \left(n + 5\right) \left(n + 6\right) \left(n + 7\right) \left(709965823977384758215327 n^{4} + 26480562654623077856239476 n^{3} + 368693769869404431994170173 n^{2} + 2307583704011652601468657644 n + 5502220779528981454903841940\right) a{\left(n + 4 \right)}}{75591424409600 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{635585924776181463 \left(n + 5\right) \left(n + 6\right) \left(n + 7\right) \left(1300907476949690200596705 n^{5} + 1574105105849315492133554 n^{4} - 1071073950299296876877724937 n^{3} - 20020921773049475262011445698 n^{2} - 138865819965214084861008104712 n - 341712597951784752606836986752\right) a{\left(n + 5 \right)}}{151182848819200 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{30265996417913403 \left(n + 6\right) \left(n + 7\right) \left(29747500923684780372823742 n^{6} + 711659207958042924126763274 n^{5} - 3374257547790083451199734785 n^{4} - 260899340155800900940723725582 n^{3} - 3150969193609405689823728089291 n^{2} - 15945654997869832074016141773338 n - 30141801097688626270926218770480\right) a{\left(n + 6 \right)}}{37795712204800 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{10088665472637801 \left(n + 7\right) \left(2044419753933881307611914317 n^{7} + 197749389527978536166472876809 n^{6} + 7517243710919848732386973315329 n^{5} + 150911476089300133104326141057863 n^{4} + 1758054265197258190515632998919522 n^{3} + 11997904236410643920679925801511248 n^{2} + 44665245718699332496865314528284672 n + 70220155797384703489657301274679200\right) a{\left(n + 7 \right)}}{75591424409600 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{\left(1176608 n^{4} + 423152592 n^{3} + 57061050118 n^{2} + 3419360752197 n + 76828946090490\right) a{\left(n + 92 \right)}}{220 \left(n + 93\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{\left(880344256 n^{6} + 474323172672 n^{5} + 106483561738180 n^{4} + 12749325004299000 n^{3} + 858641778705380839 n^{2} + 30841340578679761518 n + 461573557617418834995\right) a{\left(n + 91 \right)}}{440 \left(n + 92\right) \left(n + 93\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{\left(231195461888 n^{8} + 166288110498560 n^{7} + 52324558554851408 n^{6} + 9407981756915081480 n^{5} + 1057187664387387612212 n^{4} + 76027818698611812051530 n^{3} + 3417102273980708168862042 n^{2} + 87758763852964602106854585 n + 986021373209648603802899400\right) a{\left(n + 90 \right)}}{1760 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{3 \left(18154969535616 n^{8} + 12611145177755072 n^{7} + 3831205924792956248 n^{6} + 664838487305411678308 n^{5} + 72078877180111362171562 n^{4} + 4999241071585963643920479 n^{3} + 216619229736313814983522134 n^{2} + 5361185889404435695526911251 n + 58023427953858054888126545010\right) a{\left(n + 89 \right)}}{14080 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{\left(79034989376703616 n^{8} + 54316883789755026880 n^{7} + 16329297113539356144184 n^{6} + 2804791894848557375951980 n^{5} + 301059119984780310789957454 n^{4} + 20678560427976406400563619305 n^{3} + 887576210625619327267850890071 n^{2} + 21766530495536299924855651305360 n + 233499800636582836753151442330300\right) a{\left(n + 88 \right)}}{281600 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{\left(36685638692547223552 n^{8} + 25135132219904414591872 n^{7} + 7534044185879247807556576 n^{6} + 1290389708780948728548567160 n^{5} + 138126615185279852103410546668 n^{4} + 9462317177446336075367206258078 n^{3} + 405117753877698804869932332006339 n^{2} + 9910842467782331256187225563198405 n + 106072167775764217684090117721990400\right) a{\left(n + 87 \right)}}{563200 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{\left(9320858638002314528896 n^{8} + 6329204219237385760300480 n^{7} + 1880241057988602705781711480 n^{6} + 319178102280065677541704531804 n^{5} + 33863032494388978868679376851334 n^{4} + 2299279510270415833767574283634325 n^{3} + 97573279029174712188703566359619225 n^{2} + 2366056857179985035594648761067079276 n + 25100981724823888659506988203738418480\right) a{\left(n + 86 \right)}}{2252800 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{\left(701862758866126077916160 n^{8} + 471837442800493383783127040 n^{7} + 138774199352047591846636295264 n^{6} + 23323036996595257644702354094328 n^{5} + 2449850602623884622754730868296420 n^{4} + 164691887447224545525945511627432790 n^{3} + 6919631744162184402422641811960998461 n^{2} + 166132224905498258131984923225941230917 n + 1745022492507935934012962346595733110680\right) a{\left(n + 85 \right)}}{4505600 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{\left(75420937888144104084119936 n^{8} + 50163703023594523253743809728 n^{7} + 14597107958568029442912635025608 n^{6} + 2427211083479052726726363105654692 n^{5} + 252249237058896445819684065041322554 n^{4} + 16777751127878590820669878811655517907 n^{3} + 697459953277269882095137489417619510007 n^{2} + 16567935923762868430798985933819997847938 n + 172185774768198895943691115380151755581520\right) a{\left(n + 84 \right)}}{18022400 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{21 \left(304764225473020405857557376 n^{8} + 200409595638677101059015447488 n^{7} + 57657476592384229840280171397768 n^{6} + 9478929113436371050033281189548252 n^{5} + 973974408672432262201074118932289254 n^{4} + 64050191730983049061077229122329200217 n^{3} + 2632558421408096482453052024093882987952 n^{2} + 61830429632771682346722540584499883168293 n + 635344554870064068409665131524999771328460\right) a{\left(n + 83 \right)}}{72089600 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{3362888490879267 \left(22821639083727900029551115883 n^{8} + 2214219619752171664118726457133 n^{7} + 91208752281651362882994312079013 n^{6} + 2101100313551837997166187938753711 n^{5} + 29758461424908533114956340323590512 n^{4} + 266236796981155390675582632096033412 n^{3} + 1472579478691467755057475447288891032 n^{2} + 4610824004691614043501882616657086744 n + 6263786911096803900449150646638445360\right) a{\left(n + 8 \right)}}{37795712204800 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{\left(230151433160386018602860336128 n^{8} + 149530153322362600726343756897536 n^{7} + 42503896226677785242477631960362368 n^{6} + 6903948180522922381152847979763139816 n^{5} + 700895446762377344002088500960225289332 n^{4} + 45540301141364458135760285433942674379754 n^{3} + 1849377611208928950131212763473773157105947 n^{2} + 42916501891627901707022712946629029202905619 n + 435720720394867265192709079404614494992697680\right) a{\left(n + 82 \right)}}{144179200 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{1120962830293089 \left(423970155152378302576100524286 n^{8} + 42210024498283130082137653207938 n^{7} + 1815264141518968049324814091061789 n^{6} + 44177701660540289727895844588269425 n^{5} + 666779184735955799011205232799917789 n^{4} + 6399499253310610503682422788374453777 n^{3} + 38174484113182169596449475641999117416 n^{2} + 129477290738221832334491917620868973420 n + 191241156399988362124021854830658447120\right) a{\left(n + 9 \right)}}{37795712204800 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{373654276764363 \left(6092888469116345168345618943466 n^{8} + 631179271610998261165011438039950 n^{7} + 28428398186338879134825553040096659 n^{6} + 728130278990111219005801103533703151 n^{5} + 11610494092089853915704456713594506709 n^{4} + 118100707438618706714722503732387557915 n^{3} + 748676556895327168814906592729116773646 n^{2} + 2705008513052502748098786011179662083864 n + 4265329541710389105890965213059340509120\right) a{\left(n + 10 \right)}}{37795712204800 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{\left(7302501373100256924832493344640 n^{8} + 4685558284176315149826349041958592 n^{7} + 1315335424492373900225701539198629480 n^{6} + 210999356259612262935216356956321106372 n^{5} + 21155014307068129049550686831287305200210 n^{4} + 1357479012252382122445938011025360266118743 n^{3} + 54442824129069947626174239311650071885662385 n^{2} + 1247722171010253701451599177567965179723344658 n + 12510683563939630257854971098971711953350971760\right) a{\left(n + 81 \right)}}{288358400 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{124551425588121 \left(71738642474897902023620056416030 n^{8} + 7710714522513646600439979837709900 n^{7} + 361395469863431394712471898008852003 n^{6} + 9653502812516595599062741623807830947 n^{5} + 160810163024572829672683403741058031005 n^{4} + 1711187843939483901934586444155509101185 n^{3} + 11361085415406731092646890040042011244402 n^{2} + 43033833007768380126355178599840401135168 n + 71204610024484872643089259946839688142960\right) a{\left(n + 11 \right)}}{37795712204800 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{\left(102928717936144808599073843206784 n^{8} + 65219621121380724508782689137249472 n^{7} + 18080252209911921863156994458580192848 n^{6} + 2864172513549601032307380569766921050108 n^{5} + 283583187127618828287158202608571538473836 n^{4} + 17970014886946897440688692994299542554895453 n^{3} + 711710159700954984637572814658947328671296972 n^{2} + 16107445653289412919240596989309503631669117107 n + 159490620028447955030804201598663036985824186480\right) a{\left(n + 80 \right)}}{288358400 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{41517141862707 \left(789730931764724547757478202784279 n^{8} + 89130092906973073372199248373869316 n^{7} + 4398476357093728185314687470163964006 n^{6} + 124007443441501254073222690065921457304 n^{5} + 2185165122848948518056301890369954187551 n^{4} + 24647977261530456867188240618207115328244 n^{3} + 173812103989843790271904858416939584776244 n^{2} + 700617228421419353448674177632597571891376 n + 1235947157927684781177631100983924504435920\right) a{\left(n + 12 \right)}}{37795712204800 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{3 \left(847615996140069944044070203693440 n^{8} + 530482246892115098001846951389595712 n^{7} + 145253178043857756054462691571643335944 n^{6} + 22727280378098721272852114057913485561580 n^{5} + 2222564969244829524759844002868641653700150 n^{4} + 139106252466892132517126523000532848657870443 n^{3} + 5441568943108941974297228086803808876844230751 n^{2} + 121637901614175757669763531982808456344535113240 n + 1189589638955513611773770123131724493367779860880\right) a{\left(n + 79 \right)}}{576716800 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{\left(27071848851029128795922019810481216 n^{8} + 16738223886866917406447160897200142976 n^{7} + 4527755326167865745081291627232921937036 n^{6} + 699878400796820064213767100053313218879788 n^{5} + 67615522512320548960112316203550749883675349 n^{4} + 4180752015590902929701242348906613261110422439 n^{3} + 161564775089848713908850629016962229287683199049 n^{2} + 3567838672282732879151362845716581489733108710107 n + 34470386032235813352409250383293714413495094086400\right) a{\left(n + 78 \right)}}{576716800 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{1977006755367 \left(102400338500019030055137988720035567 n^{8} + 11948085040426174582284803301936168908 n^{7} + 609237989900094837321941505212698888246 n^{6} + 17731897539811683049080648044998510791952 n^{5} + 322181045902261782247509170363669591064823 n^{4} + 3741789967488436192869481625773651574396692 n^{3} + 27122787236754855803118529433350004313774724 n^{2} + 112168991677828820086275797061995276089537328 n + 202593091141400287896803989255518324963832800\right) a{\left(n + 13 \right)}}{75591424409600 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{3 \left(163918780923919670777706020245662976 n^{8} + 100136713119681861130578830359745591936 n^{7} + 26763321464090432133932873728278741685432 n^{6} + 4087452107199121401161754547965532726049672 n^{5} + 390166007557194351167269885572418188100928884 n^{4} + 23835828801352097000162999947176169482118803989 n^{3} + 910112829795106091217489619832383261572862006728 n^{2} + 19857580605283301358589785184397647855253916547833 n + 189556939998500811316455600729062449485383081671830\right) a{\left(n + 77 \right)}}{1153433600 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - 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\frac{3 \left(12833715985585582444089382447331875084943306711584440 n^{8} + 5254132100793527747711704661756017627345865759778572348 n^{7} + 941294688416214780974590885317814341710219691477602149802 n^{6} + 96385721546557896088740178096216721253811854143822248178630 n^{5} + 6169967026144368335105452393146829249104405710363058594160745 n^{4} + 252835741566290088672369321004976387842955375542564392025946117 n^{3} + 6477121933126924951901719063948860750896041175594511418516329023 n^{2} + 94841413496736128127878725177413782083664909210881616407762108515 n + 607721774266096386754928266407196267757084620164137269254738371280\right) a{\left(n + 52 \right)}}{1181116006400 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{9 \left(18955706575178540948653249804652217271998393229465595 n^{8} + 7359994259754428754955841411736236265705238238796014902 n^{7} + 1250689079594842061288963192090231101512192907002362921070 n^{6} + 121490236675478168042962190166628609077496342772837907462107 n^{5} + 7378589322413053813583797270347913213729830857862933337242100 n^{4} + 286910740050900565772768102040787360170831192191847979463243658 n^{3} + 6975306531971778304827107284289483571253707936120391637130774780 n^{2} + 96940686075456456235460241475686503784047847035977398024506923008 n + 589647534884500354679068817529081014202334074049380393716122150740\right) a{\left(n + 49 \right)}}{1181116006400 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{\left(20162278461135509067181971324366608476965219694303330 n^{8} + 8396713020371622853457354376737042081263736039879030644 n^{7} + 1530176214927475059075728614709332833433121056598001415801 n^{6} + 159375954333181867942049170359324593124925862779352174592031 n^{5} + 10377060156737507874058656930524353763754237723064934743846375 n^{4} + 432512766556827020357256391298217699798527294848640798519403166 n^{3} + 11269368051231240860714796482853416109672341783911443165925660059 n^{2} + 167826718473117151487657205932296303048513117829809958426040810504 n + 1093711051371597954237355408729626800165784559537146172436212440120\right) a{\left(n + 53 \right)}}{1181116006400 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{243 \left(24873169452821208470436732534282046551344339370577073 n^{8} + 6716386878742548144447027794697707426527313995389506972 n^{7} + 793899239879867625999811637426574119770000816373895768116 n^{6} + 53654707207861109038886922654548141237655203315735800405022 n^{5} + 2267696052821994845995284851461750083818884098450433622912147 n^{4} + 61376212966372009111272932574683158446759196899912329443426358 n^{3} + 1038860504844275074898037036907014318577864315038727520928263784 n^{2} + 10054066544095715714196597284944041985463834818421590331891739888 n + 42596426176477111621787449167818797265706016227868171563481254720\right) a{\left(n + 33 \right)}}{75591424409600 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{81 \left(99252248197416127607479450803454909155345744156571481 n^{8} + 28919343236188313661551470621870631099361933622427591015 n^{7} + 3689350528797028704545477028504253841704077194730796897327 n^{6} + 269159397326470248816657605274635850932307890898559192119269 n^{5} + 12282480297114526287678926681320059074423209880371713443778604 n^{4} + 358988098682094661551649634029650173201797331112754356908022380 n^{3} + 6562842577417498880856093851520973108199673778024626779725526948 n^{2} + 68612646822801017137678313310659398670562047745740908350992395776 n + 314074697262037624324767346213197024872738031876973408632028253760\right) a{\left(n + 36 \right)}}{37795712204800 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{27 \left(112409876704189471083495129955914691555026184330804622 n^{8} + 34481743607398851048617235288079218694109794546750795097 n^{7} + 4631349206864709643742301389491942332003568983016080551771 n^{6} + 355747615170814797759685430540596090804847032367258408737490 n^{5} + 17092641238377565650202501104456209974041456177211986131012228 n^{4} + 526026119543844575795273371452724718510587560387355927011194483 n^{3} + 10125921024400340433632985482192546638425904487789209502493461439 n^{2} + 111473263815356939507753013184299111489615534852453209642633146290 n + 537315941239011713669885000552265296200022677402460675344245622200\right) a{\left(n + 38 \right)}}{9448928051200 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{27 \left(130767484440277062840761364017091789520048770251588966 n^{8} + 41144006068066840461071508768454633892867714952663327014 n^{7} + 5668118388838534143101401849303823632603890801795270480107 n^{6} + 446558594454016589722724845189046831918847527189230404690473 n^{5} + 22005984624243197374582645215250124582926285309151873593449224 n^{4} + 694581579913171837578007503034937971845022333341681792598288841 n^{3} + 13712701003229332522083784044291286380706258159604884249925740173 n^{2} + 154817104748525483903644306641866037782327776967262755175701031042 n + 765286380734789107704655660446612314055647189869916979780191741880\right) a{\left(n + 39 \right)}}{9448928051200 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{\left(136008339017734915875427405695046960504956037256534338 n^{8} + 54727637615123293875896173178070230086567915198772755108 n^{7} + 9637023865679199110508060920821745983923078618772039768669 n^{6} + 969974712569750298669824480752501336355340890691472225401007 n^{5} + 61035067133221575006308706842508445893914925988991460335230987 n^{4} + 2458680504675945475111974892721454981458644182234254312513437027 n^{3} + 61919945561295521662836454915801482340780869080471956542947134716 n^{2} + 891351072737381496749665574813955461378142899731481356750514858688 n + 5615324156237599112132577454394876466890023014800986985583252375000\right) a{\left(n + 51 \right)}}{2362232012800 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{27 \left(147153566091182959412437791075306631005389110983935933 n^{8} + 47462227664208701265831870113921826736369698815362547639 n^{7} + 6702420212538633606593349388481588302107526930247478549163 n^{6} + 541255634608369423841398964822610619315021539108865295168988 n^{5} + 27338547720255937430762135490541278820415850781524882682447532 n^{4} + 884397210372262944761458752638897620630481900973633376831832311 n^{3} + 17894303336472864676861353070155679651907792265315447208808731222 n^{2} + 207040859687418596581339905699599679479332165452445477967466767412 n + 1048777912217908977472972084522017040496357702337948117667811978880\right) a{\left(n + 40 \right)}}{9448928051200 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{3 \left(162575600420062305239118627656824991533048431732779233 n^{8} + 61971820346496364011758455871280287782704231703606207699 n^{7} + 10339106094348810362314375605508897358896957230345526892236 n^{6} + 986068370797233736456447528017303449611470906864747570543439 n^{5} + 58801152530911958423956048588185456314012255890697307748911532 n^{4} + 2245022206773865226660747494801840823908902847487970382333156276 n^{3} + 53593558396160328474851132458434798866616028546400645687798706069 n^{2} + 731382544009302908808951804495751837836200421922820637215512189596 n + 4368512143535252022495146938769376666241345695701556080845490066880\right) a{\left(n + 48 \right)}}{2362232012800 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{27 \left(186589953917245603675181681704372261689000669229090433 n^{8} + 55785084885366881749182772987533480244974955234544129918 n^{7} + 7302593052115215718809161169659819589185488702092836620037 n^{6} + 546699797499441565292417551596815477073561512484784432650353 n^{5} + 25600661560406317708227068679295006782966457643500966734982652 n^{4} + 767862220750956258688167630576174179675008381383274098306482897 n^{3} + 14406037941926032292717729249589667569391853416884226010024213178 n^{2} + 154566720848313365519125728462560181601620593252830261263920216892 n + 726127172343835552424301688150689170939134596818563300802635164240\right) a{\left(n + 37 \right)}}{18897856102400 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{\left(223118441937070734906556106964945302827129899590736982 n^{8} + 88208875422645422734391917453471964376281079514876262278 n^{7} + 15261760359947987468985227946786457130242171301152495554178 n^{6} + 1509379612532613003276594012782243183657664367948716838353442 n^{5} + 93328414823100224040721428187866102600275909334276908091773683 n^{4} + 3694474785492396302078372797481992873208365026965724442852558552 n^{3} + 91435904011169547618662708270478387059047637057977597684575125457 n^{2} + 1293569217489487370569414778976657262875336364063408323510328797948 n + 8009199466752550867215526756760187590320733439713935504764840029880\right) a{\left(n + 50 \right)}}{2362232012800 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{3 \left(435287335348118460598502590778816271312169284145506946 n^{8} + 162846087358408361059434005152642047312186162609481179820 n^{7} + 26664932641297415234151689106821163147412021629584412935932 n^{6} + 2496034097460072129711259213076358370181213091467804794427779 n^{5} + 146091993017113374081965193685926322065103857514502758769758159 n^{4} + 5474808681779830480689901460621680197046525917820949377756421845 n^{3} + 128285864307151985743865613929142497429388199742208746313875121453 n^{2} + 1718455987991525930349517406847937176110890056081070143880891344306 n + 10075444662682148566814620416232931248607536671732846513440422732560\right) a{\left(n + 47 \right)}}{4724464025600 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{9 \left(502296050932605788973902142451078565020224620452804042 n^{8} + 169788813038581675806333960205191379023247375180296416572 n^{7} + 25125090410491196621565872930950815135654949750543613873365 n^{6} + 2125869290025164357158326068715359473822166708126493978616648 n^{5} + 112489238182568307480015020231734678441124038558164429989035573 n^{4} + 3811779465745254467270310150343079134450664471170375761947363068 n^{3} + 80776266635095396657769421992757831272999412241379042231853529200 n^{2} + 978718147806552620686265905620937676411720877007962488754019308612 n + 5191132066785577380040757678403248137030525822542917592709109125680\right) a{\left(n + 42 \right)}}{9448928051200 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{3 \left(546635453610093568578221935944213248522936923945844894 n^{8} + 200640624809190582546529419393137132393953266395075946182 n^{7} + 32233844841609420381598851437302199752382053092930520394705 n^{6} + 2960478285507929751689402908977630430824953573750474271046202 n^{5} + 170014737751415966313598670888064562987012739062604200190981936 n^{4} + 6251529978388692561582369464748349775833790278573071023620872908 n^{3} + 143734560445024028922428243836305485850370229117077126528616898435 n^{2} + 1889265790705594398504806400227504472928983674462780808783434484798 n + 10869204191802590867202929511534801855960226713145141042325036182800\right) a{\left(n + 46 \right)}}{4724464025600 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{3 \left(645115524609527878295107333942082124703549406706744145 n^{8} + 232216611864333322189806061063517155558100833808345744590 n^{7} + 36587506075296390049986509900630189819571321206874148254256 n^{6} + 3295638979430950031061769608400016747271961637249243694767983 n^{5} + 185622815871980431893992203697941350693700380805505615184022270 n^{4} + 6694333507437841251787055372004589525837375221967665890088221605 n^{3} + 150961747515894851211767627950451128841973069971818026708250630419 n^{2} + 1946216509156342077868748307841358764389995362961757984387334986132 n + 10982347945503094877952001628997521251283079571603233964370868429480\right) a{\left(n + 45 \right)}}{4724464025600 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{9 \left(960064343889212867148302564813614991273959552743342128 n^{8} + 317164346836396420943396713792827215036116417691026095608 n^{7} + 45871978238480754635771899160274567377214701659939697384333 n^{6} + 3793765636293109537186399311479801596337718958695001278745037 n^{5} + 196231292769205378641494627358091555018619110338398702568137777 n^{4} + 6500358513906409927193488336276742037976770583645913158927690667 n^{3} + 134671008969013059040372221452308189411217167895632585449448874082 n^{2} + 1595353471576367093521289892569667475022550049032029143447332913488 n + 8273667107428822286510444592413095555433154136026977276048126922720\right) a{\left(n + 41 \right)}}{18897856102400 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} - \frac{3 \left(1434514517293776545455497370571788515828152095665799594 n^{8} + 506097560326170564630840495378849603173090675940899598214 n^{7} + 78156156210916639614348164256414003461980468988903750130499 n^{6} + 6900403018726885717254161833860712352715904009043508846838465 n^{5} + 380964704354571739779837174063417010942700898136799936202163891 n^{4} + 13467671616354609804922858944451386554760403135585345693284432721 n^{3} + 297711927315433011434207852231497684701423463408687246732275010836 n^{2} + 3762496630274824098072045608564679647337915615808241099397656798700 n + 20813565370753045189536585455380752586257493831012465805740702296960\right) a{\left(n + 44 \right)}}{9448928051200 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)} + \frac{3 \left(1508099744188070965652481436449979929504918555560008657 n^{8} + 521053588324222764545452505035627786018385733068973108418 n^{7} + 78805479016460572045886578600672155949104311281163685664246 n^{6} + 6814498735667794457603965974384735716220652734758522088152854 n^{5} + 368494250982405169412281078224795010495720300310006390858552053 n^{4} + 12759815800858981829754933836674452260853878690549735818919702872 n^{3} + 276294694442626218977585570449052561984686576705265226355881941184 n^{2} + 3420538611228281743300024539242438047360755943826094209457219735996 n + 18536328068935053757219165149199210824674555775385416520243562052240\right) a{\left(n + 43 \right)}}{9448928051200 \left(n + 91\right) \left(n + 92\right) \left(n + 93\right) \left(2 n + 183\right) \left(2 n + 185\right) \left(2 n + 187\right) \left(4 n + 367\right) \left(4 n + 369\right)}, \quad n \geq 93
Specification 1
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24402/
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[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[15,x]*F[8,x]
F[8,x] = F[22,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[15,x]*F[19,x]
F[11,x] = F[12,x]+F[17,x]
F[12,x] = F[13,x]*F[16,x]
F[13,x] = 1/F[15,x]*F[14,x]
F[14,x] = F[2,x]
F[15,x] = x
F[16,x] = 1+(F[16,x]^3-F[16,x]^2+F[16,x])*x
F[17,x] = F[0,x]*F[18,x]
F[18,x] = -F[16,x]+F[13,x]
F[19,x] = F[16,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[16,x]^2*F[15,x]*F[19,x]
F[22,x] = F[23,x]+F[24,x]
F[23,x] = F[13,x]*F[2,x]
F[24,x] = F[25,x]
F[25,x] = F[15,x]*F[26,x]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[2,x]*F[28,x]
F[28,x] = 1/F[15,x]*F[29,x]
F[29,x] = F[9,x]
F[30,x] = F[0,x]*F[13,x]*F[16,x]*F[5,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_{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_{15}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{22}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right) F_{19}\! \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_{16}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = x F_{16} \left(x \right)^{3}-x F_{16} \left(x \right)^{2}+x F_{16}\! \left(x \right)+1
F_{17}\! \left(x \right) = F_{0}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{16}\! \left(x \right)+F_{13}\! \left(x \right)
F_{19}\! \left(x \right) = F_{16}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16} \left(x \right)^{2} F_{15}\! \left(x \right) F_{19}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{23}\! \left(x \right) = F_{13}\! \left(x \right) F_{2}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{15}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{2}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{9}\! \left(x \right)
F_{30}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{5}\! \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_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_15(x)*F_8(x))
Eq(F_8(x), F_22(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_15(x)*F_19(x))
Eq(F_11(x), F_12(x) + F_17(x))
Eq(F_12(x), F_13(x)*F_16(x))
Eq(F_13(x), F_14(x)/F_15(x))
Eq(F_14(x), F_2(x))
Eq(F_15(x), x)
Eq(F_16(x), x*F_16(x)**3 - x*F_16(x)**2 + x*F_16(x) + 1)
Eq(F_17(x), F_0(x)*F_18(x))
Eq(F_18(x), F_13(x) - F_16(x))
Eq(F_19(x), F_16(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_15(x)*F_16(x)**2*F_19(x))
Eq(F_22(x), F_23(x) + F_24(x))
Eq(F_23(x), F_13(x)*F_2(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_15(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_2(x)*F_28(x))
Eq(F_28(x), F_29(x)/F_15(x))
Eq(F_29(x), F_9(x))
Eq(F_30(x), F_0(x)*F_13(x)*F_16(x)*F_5(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "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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"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": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.factor", "strategy_class": "FactorStrategy", "ignore_parent": true, "workable": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]]}}, "idx": 0}, {"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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 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[3, 2], [3, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[4, 1], [4, 1], [4, 1], [4, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[4, 4], [4, 4], [4, 4], [4, 4]]}, {"patt": [1, 0, 2, 3], "pos": [[5, 0], [5, 0], [7, 0], [7, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[5, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [7, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[5, 0], [5, 0], [7, 0], [7, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[5, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[5, 0], [5, 0], [5, 0], [7, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[5, 0], [5, 0], [7, 0], [7, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[5, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[5, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [2, 4]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [3, 2]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[5, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[5, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [2, 4]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [3, 2]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [2, 4]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [3, 2]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}], "requirements": [[{"patt": [0], "pos": [[5, 0]]}, {"patt": [0], "pos": [[7, 0]]}], [{"patt": [0], "pos": [[6, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}}]}
Specification 2
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/24565/
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[11,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[11,x]*F[7,x]
F[7,x] = F[12,x]+F[8,x]
F[8,x] = F[0,x]*F[9,x]
F[9,x] = 1/F[11,x]*F[10,x]
F[10,x] = F[2,x]
F[11,x] = x
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[14,x]
F[14,x] = F[15,x]+F[24,x]
F[15,x] = F[0,x]*F[16,x]*F[21,x]
F[16,x] = F[17,x]+F[19,x]
F[17,x] = F[18,x]*F[9,x]
F[18,x] = 1+(F[18,x]^3-F[18,x]^2+F[18,x])*x
F[19,x] = F[0,x]*F[20,x]
F[20,x] = -F[18,x]+F[9,x]
F[21,x] = F[18,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[18,x]^2*F[11,x]*F[21,x]
F[24,x] = F[0,x]*F[18,x]*F[5,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_{11}\! \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_{11}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{0}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = \frac{F_{10}\! \left(x \right)}{F_{11}\! \left(x \right)}
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{24}\! \left(x \right)
F_{15}\! \left(x \right) = F_{0}\! \left(x \right) F_{16}\! \left(x \right) F_{21}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{19}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{9}\! \left(x \right)
F_{18}\! \left(x \right) = x F_{18} \left(x \right)^{3}-x F_{18} \left(x \right)^{2}+x F_{18}\! \left(x \right)+1
F_{19}\! \left(x \right) = F_{0}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = -F_{18}\! \left(x \right)+F_{9}\! \left(x \right)
F_{21}\! \left(x \right) = F_{18}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{18} \left(x \right)^{2} F_{11}\! \left(x \right) F_{21}\! \left(x \right)
F_{24}\! \left(x \right) = F_{0}\! \left(x \right) F_{18}\! \left(x \right) F_{5}\! \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_11(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_11(x)*F_7(x))
Eq(F_7(x), F_12(x) + F_8(x))
Eq(F_8(x), F_0(x)*F_9(x))
Eq(F_9(x), F_10(x)/F_11(x))
Eq(F_10(x), F_2(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_14(x))
Eq(F_14(x), F_15(x) + F_24(x))
Eq(F_15(x), F_0(x)*F_16(x)*F_21(x))
Eq(F_16(x), F_17(x) + F_19(x))
Eq(F_17(x), F_18(x)*F_9(x))
Eq(F_18(x), x*F_18(x)**3 - x*F_18(x)**2 + x*F_18(x) + 1)
Eq(F_19(x), F_0(x)*F_20(x))
Eq(F_20(x), -F_18(x) + F_9(x))
Eq(F_21(x), F_18(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_11(x)*F_18(x)**2*F_21(x))
Eq(F_24(x), F_0(x)*F_18(x)*F_5(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:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": 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"Tiling", "obstructions": [{"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], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RequirementPlacementStrategy", "ignore_parent": false, "gps": [{"patt": [0], "pos": [[1, 0]]}], "indices": [0], "direction": 1, "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, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0], "pos": [[4, 2]]}, {"patt": [0], "pos": [[4, 3]]}, {"patt": [0, 1], "pos": [[3, 2], [3, 2]]}, {"patt": [1, 0], "pos": [[3, 2], [3, 2]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [4, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [4, 0], [4, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[4, 0], [4, 0], [4, 0], [4, 0]]}], "requirements": [[{"patt": [0], "pos": [[3, 2]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}}]}
Specification 3
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/24920/
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[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[15,x]*F[8,x]
F[8,x] = F[22,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[15,x]*F[19,x]
F[11,x] = F[12,x]+F[16,x]
F[12,x] = F[0,x]*F[13,x]
F[13,x] = 1/F[15,x]*F[14,x]
F[14,x] = F[2,x]
F[15,x] = x
F[16,x] = F[17,x]*F[18,x]
F[17,x] = -F[0,x]+F[13,x]
F[18,x] = 1+(F[18,x]^3-F[18,x]^2+F[18,x])*x
F[19,x] = F[18,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[18,x]^2*F[15,x]*F[19,x]
F[22,x] = F[23,x]+F[24,x]
F[23,x] = F[13,x]*F[2,x]
F[24,x] = F[25,x]
F[25,x] = F[15,x]*F[26,x]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[2,x]*F[28,x]
F[28,x] = 1/F[15,x]*F[29,x]
F[29,x] = F[9,x]
F[30,x] = F[0,x]*F[13,x]*F[18,x]*F[5,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_{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_{15}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{22}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right) F_{19}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{16}\! \left(x \right)
F_{12}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{13}\! \left(x \right)
F_{18}\! \left(x \right) = x F_{18} \left(x \right)^{3}-x F_{18} \left(x \right)^{2}+x F_{18}\! \left(x \right)+1
F_{19}\! \left(x \right) = F_{18}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{18} \left(x \right)^{2} F_{15}\! \left(x \right) F_{19}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{23}\! \left(x \right) = F_{13}\! \left(x \right) F_{2}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{15}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{2}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{9}\! \left(x \right)
F_{30}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{18}\! \left(x \right) F_{5}\! \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_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_15(x)*F_8(x))
Eq(F_8(x), F_22(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_15(x)*F_19(x))
Eq(F_11(x), F_12(x) + F_16(x))
Eq(F_12(x), F_0(x)*F_13(x))
Eq(F_13(x), F_14(x)/F_15(x))
Eq(F_14(x), F_2(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x)*F_18(x))
Eq(F_17(x), -F_0(x) + F_13(x))
Eq(F_18(x), x*F_18(x)**3 - x*F_18(x)**2 + x*F_18(x) + 1)
Eq(F_19(x), F_18(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_15(x)*F_18(x)**2*F_19(x))
Eq(F_22(x), F_23(x) + F_24(x))
Eq(F_23(x), F_13(x)*F_2(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_15(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_2(x)*F_28(x))
Eq(F_28(x), F_29(x)/F_15(x))
Eq(F_29(x), F_9(x))
Eq(F_30(x), F_0(x)*F_13(x)*F_18(x)*F_5(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": 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{"patt": [1, 0, 4, 2, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [2, 4]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [3, 2]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [2, 4]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [3, 2]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}], "requirements": [[{"patt": [0], "pos": [[5, 0]]}, {"patt": [0], "pos": [[7, 0]]}], [{"patt": [0], "pos": [[6, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}}]}
Specification 4
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25312/
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[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[15,x]*F[8,x]
F[8,x] = F[22,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[15,x]*F[19,x]
F[11,x] = F[12,x]+F[17,x]
F[12,x] = F[13,x]*F[16,x]
F[13,x] = 1/F[15,x]*F[14,x]
F[14,x] = F[2,x]
F[15,x] = x
F[16,x] = 1+(F[16,x]^3-F[16,x]^2+F[16,x])*x
F[17,x] = F[0,x]*F[18,x]
F[18,x] = -F[16,x]+F[13,x]
F[19,x] = F[16,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[16,x]^2*F[15,x]*F[19,x]
F[22,x] = F[23,x]+F[24,x]
F[23,x] = F[13,x]*F[2,x]
F[24,x] = F[25,x]
F[25,x] = F[15,x]*F[26,x]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[2,x]*F[28,x]
F[28,x] = 1/F[15,x]*F[29,x]
F[29,x] = F[9,x]
F[30,x] = F[0,x]*F[13,x]*F[16,x]*F[5,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_{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_{15}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{22}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right) F_{19}\! \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_{16}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = x F_{16} \left(x \right)^{3}-x F_{16} \left(x \right)^{2}+x F_{16}\! \left(x \right)+1
F_{17}\! \left(x \right) = F_{0}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = -F_{16}\! \left(x \right)+F_{13}\! \left(x \right)
F_{19}\! \left(x \right) = F_{16}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16} \left(x \right)^{2} F_{15}\! \left(x \right) F_{19}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{23}\! \left(x \right) = F_{13}\! \left(x \right) F_{2}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{15}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{2}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{9}\! \left(x \right)
F_{30}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{5}\! \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_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_15(x)*F_8(x))
Eq(F_8(x), F_22(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_15(x)*F_19(x))
Eq(F_11(x), F_12(x) + F_17(x))
Eq(F_12(x), F_13(x)*F_16(x))
Eq(F_13(x), F_14(x)/F_15(x))
Eq(F_14(x), F_2(x))
Eq(F_15(x), x)
Eq(F_16(x), x*F_16(x)**3 - x*F_16(x)**2 + x*F_16(x) + 1)
Eq(F_17(x), F_0(x)*F_18(x))
Eq(F_18(x), F_13(x) - F_16(x))
Eq(F_19(x), F_16(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_15(x)*F_16(x)**2*F_19(x))
Eq(F_22(x), F_23(x) + F_24(x))
Eq(F_23(x), F_13(x)*F_2(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_15(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_2(x)*F_28(x))
Eq(F_28(x), F_29(x)/F_15(x))
Eq(F_29(x), F_9(x))
Eq(F_30(x), F_0(x)*F_13(x)*F_16(x)*F_5(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "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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0], [5, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[0, 4], [0, 4], [0, 4], [0, 4], [0, 4]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[5, 0], [5, 0], [5, 0], [5, 0], [5, 0]]}, {"patt": [1, 4, 3, 0, 2], "pos": [[7, 0], [7, 0], [7, 0], [7, 0], [7, 0]]}], "requirements": [[{"patt": [0], "pos": [[5, 0]]}, {"patt": [0], "pos": [[7, 0]]}], [{"patt": [0], "pos": [[6, 3]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}}]}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "VerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"class_module": "tilings.strategies.verification", "rule_class": "OneByOneVerificationRule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}}]}
Specification 5
Strategy pack name: point_placements_req_corrob
Tree: http://permpal.com/tree/25476/
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[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[15,x]*F[8,x]
F[8,x] = F[22,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[15,x]*F[19,x]
F[11,x] = F[12,x]+F[16,x]
F[12,x] = F[0,x]*F[13,x]
F[13,x] = 1/F[15,x]*F[14,x]
F[14,x] = F[2,x]
F[15,x] = x
F[16,x] = F[17,x]*F[18,x]
F[17,x] = -F[0,x]+F[13,x]
F[18,x] = 1+(F[18,x]^3-F[18,x]^2+F[18,x])*x
F[19,x] = F[18,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[18,x]^2*F[15,x]*F[19,x]
F[22,x] = F[23,x]+F[24,x]
F[23,x] = F[13,x]*F[2,x]
F[24,x] = F[25,x]
F[25,x] = F[15,x]*F[26,x]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[2,x]*F[28,x]
F[28,x] = 1/F[15,x]*F[29,x]
F[29,x] = F[9,x]
F[30,x] = F[0,x]*F[13,x]*F[18,x]*F[5,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_{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_{15}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{22}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{15}\! \left(x \right) F_{19}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{16}\! \left(x \right)
F_{12}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = \frac{F_{14}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{14}\! \left(x \right) = F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = x
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{13}\! \left(x \right)
F_{18}\! \left(x \right) = x F_{18} \left(x \right)^{3}-x F_{18} \left(x \right)^{2}+x F_{18}\! \left(x \right)+1
F_{19}\! \left(x \right) = F_{18}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{18} \left(x \right)^{2} F_{15}\! \left(x \right) F_{19}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{23}\! \left(x \right) = F_{13}\! \left(x \right) F_{2}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{15}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{2}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = \frac{F_{29}\! \left(x \right)}{F_{15}\! \left(x \right)}
F_{29}\! \left(x \right) = F_{9}\! \left(x \right)
F_{30}\! \left(x \right) = F_{0}\! \left(x \right) F_{13}\! \left(x \right) F_{18}\! \left(x \right) F_{5}\! \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_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_15(x)*F_8(x))
Eq(F_8(x), F_22(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_15(x)*F_19(x))
Eq(F_11(x), F_12(x) + F_16(x))
Eq(F_12(x), F_0(x)*F_13(x))
Eq(F_13(x), F_14(x)/F_15(x))
Eq(F_14(x), F_2(x))
Eq(F_15(x), x)
Eq(F_16(x), F_17(x)*F_18(x))
Eq(F_17(x), -F_0(x) + F_13(x))
Eq(F_18(x), x*F_18(x)**3 - x*F_18(x)**2 + x*F_18(x) + 1)
Eq(F_19(x), F_18(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_15(x)*F_18(x)**2*F_19(x))
Eq(F_22(x), F_23(x) + F_24(x))
Eq(F_23(x), F_13(x)*F_2(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_15(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_2(x)*F_28(x))
Eq(F_28(x), F_29(x)/F_15(x))
Eq(F_29(x), F_9(x))
Eq(F_30(x), F_0(x)*F_13(x)*F_18(x)*F_5(x))
Pack JSON:
{"name": "point_placements_req_corrob", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [[0, 1, 3, 4, 2], [0, 1, 4, 2, 3], [0, 1, 4, 3, 2], [1, 0, 3, 4, 2], [1, 0, 4, 2, 3], [1, 0, 4, 3, 2], [1, 3, 0, 4, 2], [1, 3, 4, 0, 2], [1, 4, 0, 2, 3], [1, 4, 0, 3, 2], [1, 4, 3, 0, 2]], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 0, 2], "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": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], 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