02314_02341_20314_20341_23014_23041_23401
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_placements_tracked_fusion
Tree: http://permpal.com/tree/24140/
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[7,x]
F[3,x] = F[4,x,1]
F[4,x,k[0]] = F[1,x]+F[5,x,k[0]]+F[8,x,k[0]]
F[5,x,k[0]] = F[6,x,k[0]]*F[7,x]
F[6,x,k[0]] = 1/(-1+k[0])*(F[4,x,k[0]]*k[0]-F[4,x,1])
F[7,x] = x
F[8,x,k[0]] = F[14,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[35,x,k[0]]+F[36,x,k[0]]
F[10,x,k[0]] = F[11,x,k[0]]*F[7,x]
F[11,x,k[0]] = F[12,x,1,k[0]]
F[12,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[15,x,k[0],k[1]]+F[17,x,k[0],k[1]]+F[33,x,k[0],k[1]]
F[13,x,k[0],k[1]] = F[12,x,k[0],k[1]]*F[14,x,k[0]]
F[14,x,k[0]] = k[0]*x
F[15,x,k[0],k[1]] = F[16,x,k[0],k[1]]*F[7,x]
F[16,x,k[0],k[1]] = (F[12,x,k[0],k[1]]*k[0]-F[12,x,1,k[1]])/(-1+k[0])
F[17,x,k[0],k[1]] = F[14,x,k[1]]*F[18,x,k[0],k[1]]
F[18,x,k[0],k[1]] = (F[19,x,k[0],k[1]]*k[0]-F[19,x,1,k[1]])/(-1+k[0])
F[19,x,k[0],k[1]] = (-F[20,x,1,k[1]]*k[1]+F[20,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[20,x,k[0],k[1]] = F[1,x]+F[21,x,k[0],k[1]]+F[22,x,k[0],k[1]]+F[24,x,k[0],k[1]]
F[21,x,k[0],k[1]] = F[14,x,k[1]]*F[20,x,k[0],k[1]]
F[22,x,k[0],k[1]] = F[23,x,k[0]*k[1],k[1]]
F[23,x,k[0],k[1]] = F[14,x,k[1]]*F[19,x,k[0],k[1]]
F[24,x,k[0],k[1]] = F[25,x,k[0]*k[1],k[1]]
F[25,x,k[0],k[1]] = F[14,x,k[1]]*F[26,x,k[0],k[1]]
F[26,x,k[0],k[1]] = (-F[27,x,1,k[1]]*k[1]+F[27,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[27,x,k[0],k[1]] = F[1,x]+F[28,x,k[0],k[1]]+F[29,x,k[0],k[1]]+F[31,x,k[0],k[1]]
F[28,x,k[0],k[1]] = F[14,x,k[1]]*F[27,x,k[0],k[1]]
F[29,x,k[0],k[1]] = F[30,x,k[0]*k[1],k[1]]
F[30,x,k[0],k[1]] = F[14,x,k[1]]*F[26,x,k[0],k[1]]
F[31,x,k[0],k[1]] = F[32,x,k[0]*k[1],k[1]]
F[32,x,k[0],k[1]] = F[14,x,k[1]]*F[19,x,k[0],k[1]]
F[33,x,k[0],k[1]] = F[14,x,k[1]]*F[34,x,k[0],k[1]]
F[34,x,k[0],k[1]] = (F[26,x,k[0],k[1]]*k[0]-F[26,x,1,k[1]])/(-1+k[0])
F[35,x,k[0]] = F[23,x,1,k[0]]
F[36,x,k[0]] = F[25,x,1,k[0]]
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_{7}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x , 1\right)
F_{4}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{5}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{5}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{6}\! \left(x , y\right) = \frac{F_{4}\! \left(x , y\right) y -F_{4}\! \left(x , 1\right)}{-1+y}
F_{7}\! \left(x \right) = x
F_{8}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , 1, y\right)
F_{12}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y , z\right)+F_{15}\! \left(x , y , z\right)+F_{17}\! \left(x , y , z\right)+F_{33}\! \left(x , y , z\right)
F_{13}\! \left(x , y , z\right) = F_{12}\! \left(x , y , z\right) F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = y x
F_{15}\! \left(x , y , z\right) = F_{16}\! \left(x , y , z\right) F_{7}\! \left(x \right)
F_{16}\! \left(x , y , z\right) = \frac{F_{12}\! \left(x , y , z\right) y -F_{12}\! \left(x , 1, z\right)}{-1+y}
F_{17}\! \left(x , y , z\right) = F_{14}\! \left(x , z\right) F_{18}\! \left(x , y , z\right)
F_{18}\! \left(x , y , z\right) = \frac{F_{19}\! \left(x , y , z\right) y -F_{19}\! \left(x , 1, z\right)}{-1+y}
F_{19}\! \left(x , y , z\right) = \frac{-F_{20}\! \left(x , 1, z\right) z +F_{20}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{20}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y , z\right)+F_{22}\! \left(x , y , z\right)+F_{24}\! \left(x , y , z\right)
F_{21}\! \left(x , y , z\right) = F_{14}\! \left(x , z\right) F_{20}\! \left(x , y , z\right)
F_{22}\! \left(x , y , z\right) = F_{23}\! \left(x , y z , z\right)
F_{23}\! \left(x , y , z\right) = F_{14}\! \left(x , z\right) F_{19}\! \left(x , y , z\right)
F_{24}\! \left(x , y , z\right) = F_{25}\! \left(x , y z , z\right)
F_{25}\! \left(x , y , z\right) = F_{14}\! \left(x , z\right) F_{26}\! \left(x , y , z\right)
F_{26}\! \left(x , y , z\right) = \frac{-F_{27}\! \left(x , 1, z\right) z +F_{27}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{27}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y , z\right)+F_{29}\! \left(x , y , z\right)+F_{31}\! \left(x , y , z\right)
F_{28}\! \left(x , y , z\right) = F_{14}\! \left(x , z\right) F_{27}\! \left(x , y , z\right)
F_{29}\! \left(x , y , z\right) = F_{30}\! \left(x , y z , z\right)
F_{30}\! \left(x , y , z\right) = F_{14}\! \left(x , z\right) F_{26}\! \left(x , y , z\right)
F_{31}\! \left(x , y , z\right) = F_{32}\! \left(x , y z , z\right)
F_{32}\! \left(x , y , z\right) = F_{14}\! \left(x , z\right) F_{19}\! \left(x , y , z\right)
F_{33}\! \left(x , y , z\right) = F_{14}\! \left(x , z\right) F_{34}\! \left(x , y , z\right)
F_{34}\! \left(x , y , z\right) = \frac{F_{26}\! \left(x , y , z\right) y -F_{26}\! \left(x , 1, z\right)}{-1+y}
F_{35}\! \left(x , y\right) = F_{23}\! \left(x , 1, y\right)
F_{36}\! \left(x , y\right) = F_{25}\! \left(x , 1, y\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_7(x))
Eq(F_3(x), F_4(x, 1))
Eq(F_4(x, k_0), F_1(x) + F_5(x, k_0) + F_8(x, k_0))
Eq(F_5(x, k_0), F_6(x, k_0)*F_7(x))
Eq(F_6(x, k_0), (k_0*F_4(x, k_0) - F_4(x, 1))/(k_0 - 1))
Eq(F_7(x), x)
Eq(F_8(x, k_0), F_14(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), F_1(x) + F_10(x, k_0) + F_35(x, k_0) + F_36(x, k_0))
Eq(F_10(x, k_0), F_11(x, k_0)*F_7(x))
Eq(F_11(x, k_0), F_12(x, 1, k_0))
Eq(F_12(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_15(x, k_0, k_1) + F_17(x, k_0, k_1) + F_33(x, k_0, k_1))
Eq(F_13(x, k_0, k_1), F_12(x, k_0, k_1)*F_14(x, k_0))
Eq(F_14(x, k_0), k_0*x)
Eq(F_15(x, k_0, k_1), F_16(x, k_0, k_1)*F_7(x))
Eq(F_16(x, k_0, k_1), (-k_0*F_12(x, k_0, k_1) + F_12(x, 1, k_1))/(1 - k_0))
Eq(F_17(x, k_0, k_1), F_14(x, k_1)*F_18(x, k_0, k_1))
Eq(F_18(x, k_0, k_1), (-k_0*F_19(x, k_0, k_1) + F_19(x, 1, k_1))/(1 - k_0))
Eq(F_19(x, k_0, k_1), (-k_0*F_20(x, k_0/k_1, k_1) + k_1*F_20(x, 1, k_1))/(-k_0 + k_1))
Eq(F_20(x, k_0, k_1), F_1(x) + F_21(x, k_0, k_1) + F_22(x, k_0, k_1) + F_24(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), F_14(x, k_1)*F_20(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), F_23(x, k_0*k_1, k_1))
Eq(F_23(x, k_0, k_1), F_14(x, k_1)*F_19(x, k_0, k_1))
Eq(F_24(x, k_0, k_1), F_25(x, k_0*k_1, k_1))
Eq(F_25(x, k_0, k_1), F_14(x, k_1)*F_26(x, k_0, k_1))
Eq(F_26(x, k_0, k_1), (-k_0*F_27(x, k_0/k_1, k_1) + k_1*F_27(x, 1, k_1))/(-k_0 + k_1))
Eq(F_27(x, k_0, k_1), F_1(x) + F_28(x, k_0, k_1) + F_29(x, k_0, k_1) + F_31(x, k_0, k_1))
Eq(F_28(x, k_0, k_1), F_14(x, k_1)*F_27(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), F_30(x, k_0*k_1, k_1))
Eq(F_30(x, k_0, k_1), F_14(x, k_1)*F_26(x, k_0, k_1))
Eq(F_31(x, k_0, k_1), F_32(x, k_0*k_1, k_1))
Eq(F_32(x, k_0, k_1), F_14(x, k_1)*F_19(x, k_0, k_1))
Eq(F_33(x, k_0, k_1), F_14(x, k_1)*F_34(x, k_0, k_1))
Eq(F_34(x, k_0, k_1), (-k_0*F_26(x, k_0, k_1) + F_26(x, 1, k_1))/(1 - k_0))
Eq(F_35(x, k_0), F_23(x, 1, k_0))
Eq(F_36(x, k_0), F_25(x, 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": false, "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_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, 3, 1, 4], "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": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 0, 1], "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": [[1, 1]]}, {"patt": 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