01234_01243_01324_02314_10234_10243_10324_12304_20134_20143_20314_21304_30124_30214_31204
Counting sequence:
1, 1, 2, 6, 24, 105, 478, 2233, 10608, 50965, 246805, 1202100, 5880279, 28859168, 141997666, 700095688, 3457307802, 17095830445, 84627388440, 419294791155, 2078986186245, 10314681088384, 51202394844777, 254285045830729, 1263337101557845, 6278590347873276, 31212599151463807, 155205155381177133, 771928083997560950, 3839990822504370590, 19105396649159224425, 95070499303762101629, 473142383505750706405, 2354983251406873888338, 11722711191874285363845, 58358979510860105833171, 290551029426101190965846, 1446666777645176087953762, 7203485170422506609205227, 35870876912623273534103711, 178633920155641578572707364, 889623415414759000085220333, 4430643543393572370760716535, 22067033749030076272474508248, 109909708555933579410045302771, 547446497007630272981173003777, 2726839417157148966551302543178, 13582776809947855074184603133607, 67659325555691834179127257735291, 337035731413412064907105723727403, 1678929978969606550506796664683473, 8363668976101804682018187822711706, 41664678062266662171747376491571569, 207560908413239004013044616514510161, 1034019871439759861207584523547658572, 5151307807311829528483503830008086617, 25663209061372556020381711562394599386, 127852392466442110824899808914253090279, 636958038518913063981364396394896215311, 3173339340360039239309009199011958348282, 15809772896526957278134003970727742241925, 78765836678672484739671619076744489456894, 392421721469416542989695269292035371157394, 1955108406544745513420614853244480995876928, 9740720723905575172880919969663103848726228, 48530368721329811453663929538755541272826259, 241789904113895129847176287644003737160059778, 1204660431372606087335060982919222092607329381, 6001957142591568974739543722609192031870918445, 29903550768064889816794383802515250014955498116, 148988974200245108128491825535652868628138701231, 742312691442108511076291917895933802810461964335, 3698459964035519735546723792247204021008006911945, 18427063868320927300093891449843756588782085879376, 91810521583268502211040124060815078485839287332791, 457435410293217660110657105069257123980685114156411, 2279124466116969415184713487665812846121237010135914, 11355523839963994070678985717891809505815432487012494, 56577936896297130851472569172405183684680863761102013, 281895267477337801149946049399010425512582837142243903, 1404523961700711257790238037191048707455531570436556250, 6997955242724260113858863736106807565805189233337992633, 34866934154204408357480545710389317719347968833293550955, 173722837077911997431491122062197116285659321468323703240, 865566771642656079891825125318506577252513708733239234541, 4312654957905192070589464010425272517411806209820593852141, 21487668271211321843843861103843739320647774238041587178604, 107061735153355424906280341800968917171547608185335031924699, 533432712590269335346443933741040637183614011183548003331659, 2657818781957512027388246625295462083858285960932748799737072, 13242543732566891412910897490166306765913777182966966384266905, 65980829526593669581024609993146038783422528095762730520449601, 328748977845438236286883285879965795546890418863412811162899252, 1637990262809154101098530326065679071760938275832651507323830807, 8161283543643301506732422454953866381396777893453269938203439591, 40663602076364377989258890521593355669086565476382555380815962876, 202606530954223011697715613686150328745296783265571806954499661830, 1009488168535835665377935120097940361995858872803898951422220362288, 5029782566444471215291737333207837542270173330975056656654731315528, 25060940299464497718875292684537374287262014057787840041251580752858, 124866423775734119460894265611540184024866220897248576432862483830016
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: https://permpal.com/tree/24289/
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[22,x]+F[5,x]
F[5,x] = F[3,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[20,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[3,x]*F[9,x,k[0]]
F[9,x,k[0]] = 1/(-1+k[0])*(F[7,x,k[0]]*k[0]-F[7,x,1])
F[10,x,k[0]] = F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[14,x]*F[3,x]
F[12,x,k[0]] = F[1,x]+F[13,x,k[0]]
F[13,x,k[0]] = k[0]*x
F[14,x] = F[15,x,1]
F[15,x,k[0]] = F[1,x]+F[16,x,k[0]]+F[18,x,k[0]]+F[8,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]*F[3,x]
F[17,x,k[0]] = 1/(-1+k[0])*(F[15,x,k[0]]*k[0]-F[15,x,1])
F[18,x,k[0]] = F[19,x,k[0]]
F[19,x,k[0]] = F[12,x,k[0]]*F[13,x,k[0]]*F[15,x,k[0]]
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[12,x,k[0]]*F[13,x,k[0]]*F[7,x,k[0]]
F[22,x] = F[14,x]*F[3,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_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{20}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = -\frac{-y F_{7}\! \left(x , y\right)+F_{7}\! \left(x , 1\right)}{-1+y}
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{14}\! \left(x \right) F_{3}\! \left(x \right)
F_{12}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = y x
F_{14}\! \left(x \right) = F_{15}\! \left(x , 1\right)
F_{15}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{3}\! \left(x \right)
F_{17}\! \left(x , y\right) = -\frac{-y F_{15}\! \left(x , y\right)+F_{15}\! \left(x , 1\right)}{-1+y}
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{13}\! \left(x , y\right) F_{15}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{13}\! \left(x , y\right) F_{7}\! \left(x , y\right)
F_{22}\! \left(x \right) = F_{14}\! \left(x \right) F_{3}\! \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_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_1(x) + F_22(x) + F_5(x))
Eq(F_5(x), F_3(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_1(x) + F_10(x, k_0) + F_20(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_3(x)*F_9(x, k_0))
Eq(F_9(x, k_0), (k_0*F_7(x, k_0) - F_7(x, 1))/(k_0 - 1))
Eq(F_10(x, k_0), F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_14(x)*F_3(x))
Eq(F_12(x, k_0), F_1(x) + F_13(x, k_0))
Eq(F_13(x, k_0), k_0*x)
Eq(F_14(x), F_15(x, 1))
Eq(F_15(x, k_0), F_1(x) + F_16(x, k_0) + F_18(x, k_0) + F_8(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0)*F_3(x))
Eq(F_17(x, k_0), (k_0*F_15(x, k_0) - F_15(x, 1))/(k_0 - 1))
Eq(F_18(x, k_0), F_19(x, k_0))
Eq(F_19(x, k_0), F_12(x, k_0)*F_13(x, k_0)*F_15(x, k_0))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_12(x, k_0)*F_13(x, k_0)*F_7(x, k_0))
Eq(F_22(x), F_14(x)*F_3(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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3, 4], "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, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0, 4], "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, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"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, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3, 4], "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, 0], [1, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3, 4], "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, 0], [1, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3, 4], "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, 0], [1, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 2, 1, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0, 4], "pos": [[1, 0], [1, 0], [1, 0], [1, 0], [1, 0]]}], 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