01243_01342_01432_02143_02341_02431_03142_03241_10243_10342_10432_12043_13042_20143_21043
Counting sequence:
1, 1, 2, 6, 24, 105, 481, 2274, 11014, 54382, 272737, 1385583, 7115727, 36880923, 192673918, 1013523658, 5363743486, 28537896798, 152560501032, 819057033504, 4414234927027, 23873114990059, 129520731244336, 704738066889216, 3844773223733041, 21026979720775822, 115256460554675834, 633087629946236557, 3484240617676903834, 19210576995062611222, 106098333599556813038, 586901908120797747366, 3251386390232021798200, 18037606079347518722444, 100198452975509351193800, 557291609048613825395568, 3103227471647198769530258, 17299238350081135158742298, 96537802170430657654356278, 539264214325312342109919232, 3015213130794540822635988267, 16874335043493007881363093877, 94516796588191417462159479558, 529843629744757871152836569442, 2972533326386845072450353880546, 16689026389041564479026033494981, 93766231402796659809461023693941, 527181234265312800787992294754608, 2965917683270620845812724080285719, 16696764232621811763695447697690567, 94052143964368781593508647279194487, 530100215282490101293942763958328253, 2989444381171612894201091364544136556, 16867746195799641141251315878878366529, 95224585673473679242797100654748712562, 537846590069429896578303662612498508625, 3039326216139541319834253074196547611762, 17182979073152565276451521127276930208542, 97188507144226400186996811938973925124082, 549946034065119779903821265906236909317810, 3113204770383213301191528984170952136712320, 17630790813434295600046715770499166289446548, 99886482735753513576936737755732076330544716, 566118139407287031043269420259392036930369060, 3209724029070901101934977352444210677498128046, 18204706320166167449253644153911835630450587490, 103288110358260514660191289174277765263750796226, 586223437391755998991865129995467267136582155528, 3328265247453846266150264589833537946788609216012, 18902118953056251500291537047012254318806588607030, 107383347809637216479320811994819187565082364257218, 610229944774681475746787665555349151701581427646866, 3468778887152258061970966457425029440799408591545928, 19723445801860014485898722460804190498056781126214850, 112178265838518901601102356726591369101647950095785066, 638191811211058605146902474286157157712834996380876616, 3631677285608992833938279082190762485831407836655562084, 20671588465560789757948867906246465007238943309336601532, 117692341487516800355879277445575219091680440511559783080, 670235750049917414260687253573508746700234622236487614058, 3817766746003520914223330891025875493595367515457348095431, 21751593941376219594591984973595954408606148270554696487855, 123956769593187897400832827256103626621820096407733483368202, 706552661563679483951747757743197547212198701874013251056724, 4028206170236318028044798863659931146272895358875015250397928, 22970451524049689938415010042505056520719718164703055863353159, 131013472924060217138091823767023703285562127511504119896188407, 747392853793153272369315744179796982865136132835297391060729422, 4264484264992926397893061220515793131405239542161509538426394744, 24336985841242399441506254721431393212421490180577393117987741400, 138914611261903483220745257028651235273281404388266715977729780279, 793063860009884852446363832945597143296715156534246694844120757937, 4528410299328331313472787289679899991162173610754988189750803192307, 25861820817772898703635379740285081692297208060049108584715118901165, 147722462826727765697170986720053256896130144376968275358493097614970, 843930216747451502281884426136631902141419214347938248284065825124776, 4822115217639211533722857891904617124605755675964305237004307456300215, 27557398508458465523402413060755329109667403279228879861923934533138927, 157509597363164378778502151243310643829316564087637279236676147788088920, 900414797268850283781687672082283128113144816789504717562055288751386244, 5148061075257129535196947611327268332210630107639039498675255416128732333
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: https://permpal.com/tree/24292/
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[4,x]
F[3,x] = x
F[4,x] = F[1,x]+F[5,x]+F[64,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[1,x]+F[61,x]+F[63,x]+F[7,x]
F[7,x] = F[3,x]*F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[12,x,k[0]]+F[18,x,k[0]]+F[60,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[3,x]
F[11,x,k[0]] = 1/(-1+k[0])*(F[9,x,k[0]]*k[0]-F[9,x,1])
F[12,x,k[0]] = F[13,x,k[0]]*F[3,x]
F[13,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[14,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[35,x,k[0]]+F[37,x,k[0]]+F[59,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[3,x]
F[16,x,k[0]] = 1/(-1+k[0])*(F[17,x,k[0]]*k[0]-F[17,x,1])
F[17,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[12,x,k[0]]+F[18,x,k[0]]+F[29,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[3,x]
F[19,x,k[0]] = 1/(-1+k[0])*(F[20,x,k[0]]*k[0]-F[20,x,1])
F[20,x,k[0]] = F[1,x]+F[21,x,k[0]]+F[47,x,k[0]]+F[48,x,k[0]]+F[56,x,k[0]]
F[21,x,k[0]] = F[22,x,k[0]]*F[3,x]
F[22,x,k[0]] = F[1,x]+F[18,x,k[0]]+F[23,x,k[0]]+F[25,x,k[0]]+F[27,x,k[0]]+F[29,x,k[0]]
F[23,x,k[0]] = F[24,x,k[0]]*F[3,x]
F[24,x,k[0]] = 1/(-1+k[0])*(F[11,x,k[0]]*k[0]-F[11,x,1])
F[25,x,k[0]] = F[26,x,k[0]]*F[3,x]
F[26,x,k[0]] = 1/(-1+k[0])*(F[13,x,k[0]]*k[0]-F[13,x,1])
F[27,x,k[0]] = F[28,x,k[0]]*F[3,x]
F[28,x,k[0]] = 1/(-1+k[0])*(F[19,x,k[0]]*k[0]-F[19,x,1])
F[29,x,k[0]] = F[30,x,k[0]]*F[31,x,k[0]]
F[30,x,k[0]] = k[0]*x
F[31,x,k[0]] = F[1,x]+F[32,x,k[0]]+F[33,x,k[0]]+F[47,x,k[0]]
F[32,x,k[0]] = F[17,x,k[0]]*F[3,x]
F[33,x,k[0]] = F[3,x]*F[34,x,k[0]]
F[34,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[35,x,k[0]]+F[37,x,k[0]]+F[41,x,k[0]]
F[35,x,k[0]] = F[3,x]*F[36,x,k[0]]
F[36,x,k[0]] = 1/(-1+k[0])*(F[34,x,k[0]]*k[0]-F[34,x,1])
F[37,x,k[0]] = F[3,x]*F[38,x,k[0]]
F[38,x,k[0]] = 1/(-1+k[0])*(F[39,x,k[0]]*k[0]-F[39,x,1])
F[39,x,k[0]] = 1/(-1+k[0])*(F[40,x,k[0]]*k[0]-F[40,x,1])
F[40,x,k[0]] = F[1,x]+F[32,x,k[0]]+F[33,x,k[0]]+F[41,x,k[0]]
F[41,x,k[0]] = F[30,x,k[0]]*F[42,x,k[0]]
F[42,x,k[0]] = F[1,x]+F[41,x,k[0]]+F[43,x,k[0]]
F[43,x,k[0]] = F[3,x]*F[44,x,k[0]]
F[44,x,k[0]] = F[1,x]+F[29,x,k[0]]+F[45,x,k[0]]+F[46,x,k[0]]
F[45,x,k[0]] = F[3,x]*F[9,x,k[0]]
F[46,x,k[0]] = F[14,x,k[0]]*F[3,x]
F[47,x,k[0]] = F[30,x,k[0]]*F[40,x,k[0]]
F[48,x,k[0]] = F[3,x]*F[49,x,k[0]]
F[49,x,k[0]] = F[1,x]+F[37,x,k[0]]+F[41,x,k[0]]+F[50,x,k[0]]+F[52,x,k[0]]+F[54,x,k[0]]
F[50,x,k[0]] = F[3,x]*F[51,x,k[0]]
F[51,x,k[0]] = 1/(-1+k[0])*(F[16,x,k[0]]*k[0]-F[16,x,1])
F[52,x,k[0]] = F[3,x]*F[53,x,k[0]]
F[53,x,k[0]] = 1/(-1+k[0])*(F[36,x,k[0]]*k[0]-F[36,x,1])
F[54,x,k[0]] = F[3,x]*F[55,x,k[0]]
F[55,x,k[0]] = 1/(-1+k[0])*(F[38,x,k[0]]*k[0]-F[38,x,1])
F[56,x,k[0]] = F[3,x]*F[57,x,k[0]]
F[57,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[35,x,k[0]]+F[41,x,k[0]]+F[58,x,k[0]]
F[58,x,k[0]] = F[3,x]*F[39,x,k[0]]
F[59,x,k[0]] = F[30,x,k[0]]*F[39,x,k[0]]
F[60,x,k[0]] = F[20,x,k[0]]*F[30,x,k[0]]
F[61,x] = F[3,x]*F[62,x]
F[62,x] = F[14,x,1]
F[63,x] = F[60,x,1]
F[64,x] = F[3,x]*F[65,x]
F[65,x] = F[1,x]+F[66,x]+F[67,x]+F[68,x]
F[66,x] = F[32,x,1]
F[67,x] = F[33,x,1]
F[68,x] = F[3,x]*F[69,x]
F[69,x] = F[70,x,1]
F[70,x,k[0]] = 1/(-1+k[0])*(F[40,x,k[0]]*k[0]-F[40,x,1])
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{64}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{61}\! \left(x \right)+F_{63}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{3}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x , 1\right)
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{60}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{11}\! \left(x , y\right) = -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}
F_{12}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{13}\! \left(x , y\right) = -\frac{-y F_{14}\! \left(x , y\right)+F_{14}\! \left(x , 1\right)}{-1+y}
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{37}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{16}\! \left(x , y\right) = -\frac{-y F_{17}\! \left(x , y\right)+F_{17}\! \left(x , 1\right)}{-1+y}
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{19}\! \left(x , y\right) = -\frac{-y F_{20}\! \left(x , y\right)+F_{20}\! \left(x , 1\right)}{-1+y}
F_{20}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)+F_{47}\! \left(x , y\right)+F_{48}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{22}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{23}\! \left(x , y\right)+F_{25}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{24}\! \left(x , y\right) = -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{26}\! \left(x , y\right) = -\frac{-y F_{13}\! \left(x , y\right)+F_{13}\! \left(x , 1\right)}{-1+y}
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{28}\! \left(x , y\right) = -\frac{-y F_{19}\! \left(x , y\right)+F_{19}\! \left(x , 1\right)}{-1+y}
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = y x
F_{31}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{32}\! \left(x , y\right)+F_{33}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{33}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{37}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = -\frac{-y F_{34}\! \left(x , y\right)+F_{34}\! \left(x , 1\right)}{-1+y}
F_{37}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{38}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = -\frac{-y F_{39}\! \left(x , y\right)+F_{39}\! \left(x , 1\right)}{-1+y}
F_{39}\! \left(x , y\right) = -\frac{-y F_{40}\! \left(x , y\right)+F_{40}\! \left(x , 1\right)}{-1+y}
F_{40}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{32}\! \left(x , y\right)+F_{33}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{41}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y\right)+F_{45}\! \left(x , y\right)+F_{46}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{47}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{40}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{37}\! \left(x , y\right)+F_{41}\! \left(x , y\right)+F_{50}\! \left(x , y\right)+F_{52}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = -\frac{-y F_{16}\! \left(x , y\right)+F_{16}\! \left(x , 1\right)}{-1+y}
F_{52}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = -\frac{-y F_{36}\! \left(x , y\right)+F_{36}\! \left(x , 1\right)}{-1+y}
F_{54}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = -\frac{-y F_{38}\! \left(x , y\right)+F_{38}\! \left(x , 1\right)}{-1+y}
F_{56}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{41}\! \left(x , y\right)+F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{39}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{39}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{61}\! \left(x \right) = F_{3}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{14}\! \left(x , 1\right)
F_{63}\! \left(x \right) = F_{60}\! \left(x , 1\right)
F_{64}\! \left(x \right) = F_{3}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{1}\! \left(x \right)+F_{66}\! \left(x \right)+F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{66}\! \left(x \right) = F_{32}\! \left(x , 1\right)
F_{67}\! \left(x \right) = F_{33}\! \left(x , 1\right)
F_{68}\! \left(x \right) = F_{3}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x , 1\right)
F_{70}\! \left(x , y\right) = -\frac{-y F_{40}\! \left(x , y\right)+F_{40}\! \left(x , 1\right)}{-1+y}
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)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_5(x) + F_64(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_1(x) + F_61(x) + F_63(x) + F_7(x))
Eq(F_7(x), F_3(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_12(x, k_0) + F_18(x, k_0) + F_60(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_3(x))
Eq(F_11(x, k_0), (k_0*F_9(x, k_0) - F_9(x, 1))/(k_0 - 1))
Eq(F_12(x, k_0), F_13(x, k_0)*F_3(x))
Eq(F_13(x, k_0), (k_0*F_14(x, k_0) - F_14(x, 1))/(k_0 - 1))
Eq(F_14(x, k_0), F_1(x) + F_15(x, k_0) + F_35(x, k_0) + F_37(x, k_0) + F_59(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_3(x))
Eq(F_16(x, k_0), (k_0*F_17(x, k_0) - F_17(x, 1))/(k_0 - 1))
Eq(F_17(x, k_0), F_1(x) + F_10(x, k_0) + F_12(x, k_0) + F_18(x, k_0) + F_29(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_3(x))
Eq(F_19(x, k_0), (k_0*F_20(x, k_0) - F_20(x, 1))/(k_0 - 1))
Eq(F_20(x, k_0), F_1(x) + F_21(x, k_0) + F_47(x, k_0) + F_48(x, k_0) + F_56(x, k_0))
Eq(F_21(x, k_0), F_22(x, k_0)*F_3(x))
Eq(F_22(x, k_0), F_1(x) + F_18(x, k_0) + F_23(x, k_0) + F_25(x, k_0) + F_27(x, k_0) + F_29(x, k_0))
Eq(F_23(x, k_0), F_24(x, k_0)*F_3(x))
Eq(F_24(x, k_0), (k_0*F_11(x, k_0) - F_11(x, 1))/(k_0 - 1))
Eq(F_25(x, k_0), F_26(x, k_0)*F_3(x))
Eq(F_26(x, k_0), (k_0*F_13(x, k_0) - F_13(x, 1))/(k_0 - 1))
Eq(F_27(x, k_0), F_28(x, k_0)*F_3(x))
Eq(F_28(x, k_0), (k_0*F_19(x, k_0) - F_19(x, 1))/(k_0 - 1))
Eq(F_29(x, k_0), F_30(x, k_0)*F_31(x, k_0))
Eq(F_30(x, k_0), k_0*x)
Eq(F_31(x, k_0), F_1(x) + F_32(x, k_0) + F_33(x, k_0) + F_47(x, k_0))
Eq(F_32(x, k_0), F_17(x, k_0)*F_3(x))
Eq(F_33(x, k_0), F_3(x)*F_34(x, k_0))
Eq(F_34(x, k_0), F_1(x) + F_15(x, k_0) + F_35(x, k_0) + F_37(x, k_0) + F_41(x, k_0))
Eq(F_35(x, k_0), F_3(x)*F_36(x, k_0))
Eq(F_36(x, k_0), (k_0*F_34(x, k_0) - F_34(x, 1))/(k_0 - 1))
Eq(F_37(x, k_0), F_3(x)*F_38(x, k_0))
Eq(F_38(x, k_0), (k_0*F_39(x, k_0) - F_39(x, 1))/(k_0 - 1))
Eq(F_39(x, k_0), (k_0*F_40(x, k_0) - F_40(x, 1))/(k_0 - 1))
Eq(F_40(x, k_0), F_1(x) + F_32(x, k_0) + F_33(x, k_0) + F_41(x, k_0))
Eq(F_41(x, k_0), F_30(x, k_0)*F_42(x, k_0))
Eq(F_42(x, k_0), F_1(x) + F_41(x, k_0) + F_43(x, k_0))
Eq(F_43(x, k_0), F_3(x)*F_44(x, k_0))
Eq(F_44(x, k_0), F_1(x) + F_29(x, k_0) + F_45(x, k_0) + F_46(x, k_0))
Eq(F_45(x, k_0), F_3(x)*F_9(x, k_0))
Eq(F_46(x, k_0), F_14(x, k_0)*F_3(x))
Eq(F_47(x, k_0), F_30(x, k_0)*F_40(x, k_0))
Eq(F_48(x, k_0), F_3(x)*F_49(x, k_0))
Eq(F_49(x, k_0), F_1(x) + F_37(x, k_0) + F_41(x, k_0) + F_50(x, k_0) + F_52(x, k_0) + F_54(x, k_0))
Eq(F_50(x, k_0), F_3(x)*F_51(x, k_0))
Eq(F_51(x, k_0), (k_0*F_16(x, k_0) - F_16(x, 1))/(k_0 - 1))
Eq(F_52(x, k_0), F_3(x)*F_53(x, k_0))
Eq(F_53(x, k_0), (k_0*F_36(x, k_0) - F_36(x, 1))/(k_0 - 1))
Eq(F_54(x, k_0), F_3(x)*F_55(x, k_0))
Eq(F_55(x, k_0), (k_0*F_38(x, k_0) - F_38(x, 1))/(k_0 - 1))
Eq(F_56(x, k_0), F_3(x)*F_57(x, k_0))
Eq(F_57(x, k_0), F_1(x) + F_15(x, k_0) + F_35(x, k_0) + F_41(x, k_0) + F_58(x, k_0))
Eq(F_58(x, k_0), F_3(x)*F_39(x, k_0))
Eq(F_59(x, k_0), F_30(x, k_0)*F_39(x, k_0))
Eq(F_60(x, k_0), F_20(x, k_0)*F_30(x, k_0))
Eq(F_61(x), F_3(x)*F_62(x))
Eq(F_62(x), F_14(x, 1))
Eq(F_63(x), F_60(x, 1))
Eq(F_64(x), F_3(x)*F_65(x))
Eq(F_65(x), F_1(x) + F_66(x) + F_67(x) + F_68(x))
Eq(F_66(x), F_32(x, 1))
Eq(F_67(x), F_33(x, 1))
Eq(F_68(x), F_3(x)*F_69(x))
Eq(F_69(x), F_70(x, 1))
Eq(F_70(x, k_0), (-k_0*F_40(x, k_0) + F_40(x, 1))/(1 - k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "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, 2, 0, 4, 3], "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": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "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, 2, 0, 4, 3], "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": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 2, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, 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