02413_02431_20413_20431_24013_24031_24301
Counting sequence:
1, 1, 2, 6, 24, 113, 580, 3129, 17442, 99574, 579108, 3419056, 20440024, 123494294, 752913720, 4626460910, 28623829932, 178166605469, 1114930402440, 7010385859241, 44268641757686, 280626420185957, 1785180266234336, 11392541408667527, 72916422219043686, 467941980829808259, 3010430527688012228, 19411255413676902257, 125427990832979822646, 812056475420723211783, 5267089205038358557792, 34221205347220552639329, 222696131439707551192690, 1451375382406498882058182, 9472342505150837980903252, 61902740691871232108044808, 405046171027094337860731016, 2653452918572449121584479218, 17402149338897585751600805720, 114249329148950156856234234746, 750827625471004622211463752436, 4939021884727022458842867544952, 32518886411316671674479523832840, 214291873751757716767485377868124, 1413297776087416103371614244161400, 9328318771999552335668313231280520, 61616876783670657420750133354448784, 407294397185839959305030086486523312, 2694116644458775819191900360249028160, 17832454952556194793063448702441218878, 118108456133224054896712281881294073504, 782735441038084181873376174571921204798, 5190423904758211714925623093159987529940, 34437748604324370602921443095806124348670, 228613348802761193819299056898251103103520, 1518429584878699452758715737965618159089146, 10090339156041997714448904165769656482808836, 67085265469182269096371940696225176709087018, 446222470771400760685028301475826338589370968, 2969420268403659855286401721764792630621190430, 19768841311537724731476668187817715104569054612, 131666042922449537951834621280520110053303471010, 877290424015865818346880465873212379701063241152, 5847689920102773395759414557652760546802232350510, 38993408419116618105542020519109120925093028526268, 260111052357004245660027670908389957512466820743597, 1735730220114040026340897099386922165391833947865432, 11586619493088057882327621252793168906633250938259721, 77370938845319382687142128852935924146408932629941190, 516822353108239057057029437902042842148514674662419773, 3453368290932589431853552021684476899062661662140650512, 23082282473781244452295005277856353187419679309190452031, 154328124984472507651335696388666980554258774573424627974, 1032139183592163087017533898200918421374692470046418839071, 6904859429601032747058582816164952948679433476446939199924, 46205266536320181426487310344988988269089878831043923591709, 309275121223940447159630036857060836913341464544421031517550, 2070676670974641920906501287320278905499315655042971674572323, 13867253178811249227450625186077796703068596490980137353842544, 92891635992394003458122289441506064871757100155365375339409781, 622397819827856475992653514365555537205877166359004019148819498, 4171211114683363427571940726311192393941688810523954035950009817, 27961238701882598679447834359486732630441844324338482564095564756, 187477145923724981612292903698648795608425282097227497205342107555, 1257290403354177037223612728961396659821227768162891862633256099738, 8433657178969410678131440011101868721692491889501994028286162049357, 56583157089508627243158990205965857000513916886620191564623491222248, 379705761920781999657270131090422845850991964973181396964885522557739, 2548554599043140363443231873509704126193769692611360247388224330790142, 17109033305191955618097654053809021898880593578369070022649093578663029, 114878795834488059089903096169421685021220278083636011885606402267845476, 771498902416377410624559072179342466876146574738360664788940250559675835, 5182150333600908292783706121488990170282871900048595239396338176644084322, 34814666560135972710263317246810153243233673189827274867799009911758078385, 233932383133868249797258682403495809787396329184028403812999095922175026288, 1572145407395045149670521466060147900287845853819939769693645445770608553567, 10567391028374042932499173915192456572349859271146334217119048908545002501422, 71041812502192814388078254150442949034695626021661148811669323709035335648075, 477672249204505045222596299584128022762033334726637681936105232438962474568012, 3212286643394146533079755798626935388948238393497282286492182058292664002271913, 21605558511504029545830813337448516283122899753151114737788606128423697402175422
Specification 1
Strategy pack name: row_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/24143/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[24,x]*F[3,x]
F[3,x] = F[0,x]+F[4,x]
F[4,x] = F[24,x]*F[5,x]
F[5,x] = F[3,x]+F[46,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[24,x]*F[45,x]*F[8,x]
F[8,x] = F[9,x,1]
F[9,x,k[0]] = F[10,x,k[0]]+F[13,x,k[0]]+F[43,x,k[0]]
F[10,x,k[0]] = F[0,x]+F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[9,x,k[0]]
F[12,x,k[0]] = k[0]*x
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[15,x,k[0]]*F[24,x]
F[16,x,k[0]] = F[12,x,k[0]]*F[15,x,k[0]]
F[16,x,k[0]] = F[17,x,k[0]]
F[18,x,k[0]] = F[17,x,k[0]]+F[3,x]
F[18,x,k[0]] = F[1,x]+F[19,x,k[0]]+F[32,x,k[0]]+F[34,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]*F[24,x]
F[20,x,k[0]] = 1/(-1+k[0])*(F[21,x,k[0]]*k[0]-F[21,x,1])
F[21,x,k[0]] = F[22,x]+F[25,x,k[0]]
F[22,x] = F[0,x]+F[23,x]
F[23,x] = F[24,x]*F[8,x]
F[24,x] = x
F[25,x,k[0]] = F[26,x,k[0]]
F[26,x,k[0]] = F[12,x,k[0]]*F[27,x,k[0]]*F[8,x]
F[27,x,k[0]] = F[28,x,k[0]]+F[30,x,k[0]]
F[28,x,k[0]] = F[1,x]+F[29,x,k[0]]
F[29,x,k[0]] = F[12,x,k[0]]*F[27,x,k[0]]
F[30,x,k[0]] = F[31,x,k[0]]
F[31,x,k[0]] = F[27,x,k[0]]^2*F[12,x,k[0]]
F[32,x,k[0]] = F[24,x]*F[33,x,k[0]]
F[33,x,k[0]] = 1/(-1+k[0])*(F[18,x,k[0]]*k[0]-F[18,x,1])
F[34,x,k[0]] = F[35,x,k[0]]
F[35,x,k[0]] = F[12,x,k[0]]*F[36,x]*F[39,x,k[0]]
F[36,x] = F[1,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[36,x]^2*F[24,x]
F[40,x,k[0]] = F[12,x,k[0]]*F[39,x,k[0]]
F[10,x,k[0]] = F[1,x]+F[40,x,k[0]]+F[41,x,k[0]]
F[41,x,k[0]] = F[24,x]*F[42,x,k[0]]
F[42,x,k[0]] = 1/(-1+k[0])*(F[10,x,k[0]]*k[0]-F[10,x,1])
F[43,x,k[0]] = F[44,x,k[0]]
F[44,x,k[0]] = F[12,x,k[0]]*F[27,x,k[0]]*F[9,x,k[0]]
F[45,x] = F[27,x,1]
F[46,x] = F[47,x]
F[47,x] = F[24,x]*F[48,x]
F[48,x] = F[15,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_{24}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{0}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{24}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \left(x \right)+F_{46}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{24}\! \left(x \right) F_{45}\! \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_{10}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{43}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{0}\! \left(x \right)+F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = y x
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{24}\! \left(x \right)
F_{16}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{15}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{3}\! \left(x \right)
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)+F_{32}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{24}\! \left(x \right)
F_{20}\! \left(x , y\right) = -\frac{-y F_{21}\! \left(x , y\right)+F_{21}\! \left(x , 1\right)}{-1+y}
F_{21}\! \left(x , y\right) = F_{22}\! \left(x \right)+F_{25}\! \left(x , y\right)
F_{22}\! \left(x \right) = F_{0}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{8}\! \left(x \right)
F_{24}\! \left(x \right) = x
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{27}\! \left(x , y\right) F_{8}\! \left(x \right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{27}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{27}\! \left(x , y\right)^{2} F_{12}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{24}\! \left(x \right) F_{33}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = -\frac{-y F_{18}\! \left(x , y\right)+F_{18}\! \left(x , 1\right)}{-1+y}
F_{34}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{36}\! \left(x \right) F_{39}\! \left(x , y\right)
F_{36}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{36} \left(x \right)^{2} F_{24}\! \left(x \right)
F_{40}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{39}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{40}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{24}\! \left(x \right) F_{42}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = -\frac{-y F_{10}\! \left(x , y\right)+F_{10}\! \left(x , 1\right)}{-1+y}
F_{43}\! \left(x , y\right) = F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{27}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{45}\! \left(x \right) = F_{27}\! \left(x , 1\right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{24}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{15}\! \left(x , 1\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_24(x)*F_3(x))
Eq(F_3(x), F_0(x) + F_4(x))
Eq(F_4(x), F_24(x)*F_5(x))
Eq(F_5(x), F_3(x) + F_46(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_24(x)*F_45(x)*F_8(x))
Eq(F_8(x), F_9(x, 1))
Eq(F_9(x, k_0), F_10(x, k_0) + F_13(x, k_0) + F_43(x, k_0))
Eq(F_10(x, k_0), F_0(x) + F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_9(x, k_0))
Eq(F_12(x, k_0), k_0*x)
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_15(x, k_0)*F_24(x))
Eq(F_16(x, k_0), F_12(x, k_0)*F_15(x, k_0))
Eq(F_16(x, k_0), F_17(x, k_0))
Eq(F_18(x, k_0), F_17(x, k_0) + F_3(x))
Eq(F_18(x, k_0), F_1(x) + F_19(x, k_0) + F_32(x, k_0) + F_34(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0)*F_24(x))
Eq(F_20(x, k_0), (k_0*F_21(x, k_0) - F_21(x, 1))/(k_0 - 1))
Eq(F_21(x, k_0), F_22(x) + F_25(x, k_0))
Eq(F_22(x), F_0(x) + F_23(x))
Eq(F_23(x), F_24(x)*F_8(x))
Eq(F_24(x), x)
Eq(F_25(x, k_0), F_26(x, k_0))
Eq(F_26(x, k_0), F_12(x, k_0)*F_27(x, k_0)*F_8(x))
Eq(F_27(x, k_0), F_28(x, k_0) + F_30(x, k_0))
Eq(F_28(x, k_0), F_1(x) + F_29(x, k_0))
Eq(F_29(x, k_0), F_12(x, k_0)*F_27(x, k_0))
Eq(F_30(x, k_0), F_31(x, k_0))
Eq(F_31(x, k_0), F_12(x, k_0)*F_27(x, k_0)**2)
Eq(F_32(x, k_0), F_24(x)*F_33(x, k_0))
Eq(F_33(x, k_0), (k_0*F_18(x, k_0) - F_18(x, 1))/(k_0 - 1))
Eq(F_34(x, k_0), F_35(x, k_0))
Eq(F_35(x, k_0), F_12(x, k_0)*F_36(x)*F_39(x, k_0))
Eq(F_36(x), F_1(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_24(x)*F_36(x)**2)
Eq(F_40(x, k_0), F_12(x, k_0)*F_39(x, k_0))
Eq(F_10(x, k_0), F_1(x) + F_40(x, k_0) + F_41(x, k_0))
Eq(F_41(x, k_0), F_24(x)*F_42(x, k_0))
Eq(F_42(x, k_0), (k_0*F_10(x, k_0) - F_10(x, 1))/(k_0 - 1))
Eq(F_43(x, k_0), F_44(x, k_0))
Eq(F_44(x, k_0), F_12(x, k_0)*F_27(x, k_0)*F_9(x, k_0))
Eq(F_45(x), F_27(x, 1))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_24(x)*F_48(x))
Eq(F_48(x), F_15(x, 1))
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": true, "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": "row_and_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, 2, 4, 1, 3], "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": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 2, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [{"assumption": "TrackingAssumption", "class_module": 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