02341_02431_03142_03241_12340_12430_13042_13240_21340_21430_23041_23140_31240_32041_32140

Counting sequence:
1, 1, 2, 6, 24, 105, 479, 2243, 10681, 51439, 249696, 1219062, 5977226, 29402945, 145004863, 716543825, 3546482080, 17575812695, 87195384223, 432964124645, 2151429534632, 10697152486412, 53214971955402, 264844147093226, 1318590875288149, 6567043376982895, 32715278729248394, 163018220934253768, 812480280126990218, 4050131204607393829, 20192731422727876347, 100689063239753590417, 502138487765855389217, 2504450279099183915043, 12492333346722521997044, 62317815990822998526006, 310895375245262524621614, 1551122367019553307985999, 7739349303307272075195317, 38617720508907979018060995, 192703747344902133385387388, 961640728093223445581570284, 4799022368649270046481804166, 23950149412006340284218528022, 119530211100289964626691400992, 596567785001480363769815316884, 2977510835943163835252056178020, 14861315857322351529658383437208, 74177223091278269168485664151336, 370247727174867347960334256089459, 1848085140758771851164294026817881, 9224834665718181967129223259036007, 46047029304133020440081023242313596, 229853162436544981930430542514709536, 1147373130184251459805144650569486498, 5727481924947764917844129736131724454, 28590860003307934302673409283298658469, 142723263883763162448829478226199380179, 712469095934956240130624807108299575726, 3556646415600401969622503867820478163508, 17754909622763720471410482105396250169242, 88633743824784268731575535995079080985413, 442468481438506701030933675383431767044403, 2208858971658617291949682395905411401899177, 11026961134195455283635537463181323942238720, 55048530105854370645668218248060257244914167, 274813127504381496986045235643782814592240151, 1371926791920999962805309956038368367904842733, 6848981273759803945469678068314187746439675200, 34191840106510998552739388961355838935620479748, 170694806798504356101783119025649913157132542442, 852156532184722404760354570778319503873247981866, 4254216473160234383911647602505856697315484678931, 21238353387018571865686912272251033137086357235405, 106028610516125947902363376491313748823028632790178, 529329614918904843157818643828834780779774747598660, 2642592158331592830833792370385365738697406535489830, 13192735500560480792523173033967144060882365251474255, 65862812972678406929032350619178754773931928643255945, 328811007976282680079029318895721700885630322380373835, 1641545882156504478132786574491925580430958481600786780, 8195213323882571927503714837116996764482122418153702420, 40913630394558401141240944884566728636408811838926462350, 204256672050953880718573143902945413886409539736045132310, 1019729374983757689432064118910110630414939605749239984700, 5090893596514877938470979981507168012662844166353317543760, 25415782870432364623945369346630112899404125803213891202420, 126885886120201799181025662404167269344446005632992769489600, 633466234077350153675948930565457696071716256403444457369048, 3162524716277526127755844458552887847448772822272816592288620, 15788638050640685735781290697325459142941001523580254507142716, 78823492109360616854621158455529606209004172370477720816671908, 393520097924614763902737560502102475004402970019608126920632256, 1964619226605377951893429769788478016587146115188813498280986256, 9808217148071620627067323852012013330729250264840186256933329064, 48966825510230872243693750289562932791032826379624542011726885944, 244463490764700497971405408588466352562767353292093016727158579601, 1220467549259542038035693968028324847166002311814113068157877758495, 6093104422316164621110911542154543140671542520431466617864991429798, 30419435561620826322409295953601695316136970301106144794926875763680, 151867141090314332462886990274069589888079586217414219416724705024602

Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: https://permpal.com/tree/24319/
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[6,x]
F[3,x] = F[1,x]+F[4,x]+F[42,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[6,x]*F[7,x,k[0]]
F[6,x] = x
F[7,x,k[0]] = F[1,x]+F[38,x,k[0]]+F[40,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[6,x]*F[9,x,k[0]]
F[9,x,k[0]] = 1/(-1+k[0])*(F[10,x,k[0]]*k[0]-F[10,x,1])
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[33,x,k[0]]+F[36,x,k[0]]
F[11,x,k[0]] = F[12,x,1,k[0]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[6,x]
F[13,x,k[0],k[1]] = F[1,x]+F[14,x,k[0],k[1]]+F[18,x,k[0],k[1]]+F[20,x,k[0],k[1]]+F[22,x,k[0],k[1]]
F[14,x,k[0],k[1]] = F[15,x,k[1],k[0]]
F[15,x,k[0],k[1]] = F[16,x,k[0]]*F[6,x]*F[9,x,k[1]]
F[16,x,k[0]] = F[1,x]+F[17,x,k[0]]
F[17,x,k[0]] = k[0]*x
F[18,x,k[0],k[1]] = F[19,x,k[0],k[1]]*F[6,x]
F[19,x,k[0],k[1]] = 1/(-1+k[0])*(F[13,x,k[0],k[1]]*k[0]-F[13,x,1,k[1]])
F[20,x,k[0],k[1]] = F[21,x,k[0],k[1]]
F[21,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[16,x,k[0]]*F[17,x,k[0]]
F[22,x,k[0],k[1]] = F[23,x,k[1],k[0]]
F[23,x,k[0],k[1]] = F[17,x,k[0]]*F[24,x,k[0]]*F[32,x,k[0],k[1]]
F[25,x,k[0]] = F[24,x,k[0]]*F[6,x]
F[26,x,k[0]] = F[1,x]+F[25,x,k[0]]+F[30,x,k[0]]
F[26,x,k[0]] = F[1,x]+F[27,x,k[0]]+F[28,x,k[0]]
F[27,x,k[0]] = F[10,x,k[0]]*F[6,x]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[16,x,k[0]]*F[17,x,k[0]]*F[26,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[16,x,k[0]]*F[17,x,k[0]]*F[26,x,k[0]]
F[32,x,k[0],k[1]] = F[16,x,k[1]]+F[17,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[16,x,k[0]]*F[35,x]*F[6,x]
F[35,x] = F[10,x,1]
F[36,x,k[0]] = F[37,x,k[0]]
F[37,x,k[0]] = F[10,x,k[0]]*F[16,x,k[0]]*F[17,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]*F[6,x]
F[39,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[40,x,k[0]] = F[41,x,k[0]]
F[41,x,k[0]] = F[16,x,k[0]]*F[17,x,k[0]]*F[7,x,k[0]]
F[42,x] = F[35,x]*F[6,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_{6}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{42}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{6}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{6}\! \left(x \right) = x
F_{7}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{38}\! \left(x , y\right)+F_{40}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{6}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = \frac{y F_{10}\! \left(x , y\right)-F_{10}\! \left(x , 1\right)}{-1+y}
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{33}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , 1, y\right)
F_{12}\! \left(x , y , z\right) = F_{13}\! \left(x , y , z\right) F_{6}\! \left(x \right)
F_{13}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y , z\right)+F_{18}\! \left(x , y , z\right)+F_{20}\! \left(x , y , z\right)+F_{22}\! \left(x , y , z\right)
F_{14}\! \left(x , y , z\right) = F_{15}\! \left(x , z , y\right)
F_{15}\! \left(x , y , z\right) = F_{16}\! \left(x , y\right) F_{6}\! \left(x \right) F_{9}\! \left(x , z\right)
F_{16}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = y x
F_{18}\! \left(x , y , z\right) = F_{19}\! \left(x , y , z\right) F_{6}\! \left(x \right)
F_{19}\! \left(x , y , z\right) = \frac{y F_{13}\! \left(x , y , z\right)-F_{13}\! \left(x , 1, z\right)}{-1+y}
F_{20}\! \left(x , y , z\right) = F_{21}\! \left(x , y , z\right)
F_{21}\! \left(x , y , z\right) = F_{13}\! \left(x , y , z\right) F_{16}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{22}\! \left(x , y , z\right) = F_{23}\! \left(x , z , y\right)
F_{23}\! \left(x , y , z\right) = F_{17}\! \left(x , y\right) F_{24}\! \left(x , y\right) F_{32}\! \left(x , y , z\right)
F_{25}\! \left(x , y\right) = F_{24}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{26}\! \left(x , y\right)
F_{32}\! \left(x , y , z\right) = F_{16}\! \left(x , z\right)+F_{17}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{35}\! \left(x \right) F_{6}\! \left(x \right)
F_{35}\! \left(x \right) = F_{10}\! \left(x , 1\right)
F_{36}\! \left(x , y\right) = F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{16}\! \left(x , y\right) F_{17}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right) F_{6}\! \left(x \right)
F_{39}\! \left(x , y\right) = \frac{y F_{7}\! \left(x , y\right)-F_{7}\! \left(x , 1\right)}{-1+y}
F_{40}\! \left(x , y\right) = F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{7}\! \left(x , y\right)
F_{42}\! \left(x \right) = F_{35}\! \left(x \right) F_{6}\! \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)*F_6(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_42(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_6(x)*F_7(x, k_0))
Eq(F_6(x), x)
Eq(F_7(x, k_0), F_1(x) + F_38(x, k_0) + F_40(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_6(x)*F_9(x, k_0))
Eq(F_9(x, k_0), (k_0*F_10(x, k_0) - F_10(x, 1))/(k_0 - 1))
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0) + F_33(x, k_0) + F_36(x, k_0))
Eq(F_11(x, k_0), F_12(x, 1, k_0))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1)*F_6(x))
Eq(F_13(x, k_0, k_1), F_1(x) + F_14(x, k_0, k_1) + F_18(x, k_0, k_1) + F_20(x, k_0, k_1) + F_22(x, k_0, k_1))
Eq(F_14(x, k_0, k_1), F_15(x, k_1, k_0))
Eq(F_15(x, k_0, k_1), F_16(x, k_0)*F_6(x)*F_9(x, k_1))
Eq(F_16(x, k_0), F_1(x) + F_17(x, k_0))
Eq(F_17(x, k_0), k_0*x)
Eq(F_18(x, k_0, k_1), F_19(x, k_0, k_1)*F_6(x))
Eq(F_19(x, k_0, k_1), (k_0*F_13(x, k_0, k_1) - F_13(x, 1, k_1))/(k_0 - 1))
Eq(F_20(x, k_0, k_1), F_21(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), F_13(x, k_0, k_1)*F_16(x, k_0)*F_17(x, k_0))
Eq(F_22(x, k_0, k_1), F_23(x, k_1, k_0))
Eq(F_23(x, k_0, k_1), F_17(x, k_0)*F_24(x, k_0)*F_32(x, k_0, k_1))
Eq(F_25(x, k_0), F_24(x, k_0)*F_6(x))
Eq(F_26(x, k_0), F_1(x) + F_25(x, k_0) + F_30(x, k_0))
Eq(F_26(x, k_0), F_1(x) + F_27(x, k_0) + F_28(x, k_0))
Eq(F_27(x, k_0), F_10(x, k_0)*F_6(x))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_16(x, k_0)*F_17(x, k_0)*F_26(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_16(x, k_0)*F_17(x, k_0)*F_26(x, k_0))
Eq(F_32(x, k_0, k_1), F_16(x, k_1) + F_17(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_16(x, k_0)*F_35(x)*F_6(x))
Eq(F_35(x), F_10(x, 1))
Eq(F_36(x, k_0), F_37(x, k_0))
Eq(F_37(x, k_0), F_10(x, k_0)*F_16(x, k_0)*F_17(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0)*F_6(x))
Eq(F_39(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_40(x, k_0), F_41(x, k_0))
Eq(F_41(x, k_0), F_16(x, k_0)*F_17(x, k_0)*F_7(x, k_0))
Eq(F_42(x), F_35(x)*F_6(x))
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:
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