01234_01243_01324_02134_02143_02413_20134_20143_20413_24013
Counting sequence:
1, 1, 2, 6, 24, 110, 532, 2629, 13135, 66133, 335163, 1708689, 8757982, 45108924, 233368559, 1212191532, 6319744231, 33059587610, 173481063736, 912986225735, 4817768953161, 25487002751457, 135148720610268, 718226606237390, 3824803796368191, 20408058505016737, 109091317475131426, 584157062236869873, 3133130290735999416, 16830545042485381527, 90542632482782823265, 487764402491801306785, 2631105536671523874274, 14210483306168368399005, 76841351637713491678996, 415979209176231093903815, 2254318505228839190595794, 12229367154215926364832764, 66407505046553584108735055, 360940412243767850852052852, 1963545176310047866485275191, 10690950015106784027600747881, 58256676207799895339910781459, 317697678822160222491371977901, 1733832452023904792204572777391, 9469162874920081865558074678440, 51750530628191175254899130252097, 283012021930118540957348436608649, 1548711675657278997549423517030988, 8480105260725508286783723290760793, 46460816836300080633536561852550002, 254693492041802384983185360696107268, 1396964106003826765093619674428168435, 7666206112471241331250748720224876412, 42091603564335348866411320633662123075, 231218452037858686035218242052328131170, 1270732778307448493751693287735826968422, 6986887485126150075164803443175117328411, 38433012516362874010012506172190204907227, 211499804968607503118566756485926825932765, 1164379056611289099966724141769238361084221, 6412862889091269858026002148275989692697871, 35332732729643092287200632218437304050644213, 194744411833301948238651656553524231215105871, 1073767650209623674247092893197542267492045611, 5922545625273980007909101758846163645570753544, 32677947016118447690213997165435327446034810420, 180361991309664207714479572680929539825579021690, 995806669815474827762398590461863326794823043166, 5499722939288553198894987478724458716320469661145, 30383552359650165854373772044027680287594095318635, 167905369836649129914391044986439480007395353519086, 928144109263055028461898931126277679714188023364827, 5132011983701656856086669551925062602828143318646482, 28384294140868325098748584884614531799921711986655707, 157030356034332292859159139449359262194842243048150595, 868962878772054853671249992275951142998342294124192715, 4809811448897716337023633278493737795351313743554666339, 26629397046006736682117874477063320492813876949643892654, 147468209173248271789743263815408504216433612410577359430, 816839456628527666335522661881330970763739200714440478726, 4525575006090198953289987219758087062865227179783593703304, 25078826063735504676560534261980958313989667799820054328510, 139006375559848336941979660356468883193186616318324927646817, 770644530801575410052551780933933402428993872888850386030500, 4273298274287052974605412389381888538110849384223238026120885, 23700634630037435024838046635731285897981594702946534865808859, 131474766841750048640656100608173927096847658468385336535489336, 729471925177951386824693390798518285040309511944967209703623055, 4048150314023229073110402973747138694090756386413812695277564467, 22469052112365741016535803049598238697028793352977844528248847806, 124735824714678183545770464939126007720487013694599439330253372623, 692586938550197117097583684624564308880734857324387874564237538941, 3846204756919213203656403111317157154136003113852233633037274663061, 21363083214217148089536000025576760213217313260013745193551326597692, 118677218555964870695708786880481902059546266919255681367726663357437, 659388239102303848319297923327533112038620954487547742358598598309509, 3664240794479835728742071580813422822314137563364649884752781985949847, 20365467755320790564329444990348269016992282630847865882876832689945593, 113206403866808562555649127427794836566361170892636475346119150639725525, 629379376230437966505719199926750895223838412187562646250108917806250143
Specification 1
Strategy pack name: row_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/24209/
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[22,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,1,k[0]]
F[10,x,k[0],k[1]] = F[11,x,k[0]*k[1],k[1]]
F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[24,x,k[0],k[1]]+F[32,x,k[0],k[1]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[7,x]
F[13,x,k[0],k[1]] = 1/(-1+k[0])*(F[14,x,k[0],k[1]]*k[0]-F[14,x,1,k[1]])
F[14,x,k[0],k[1]] = F[15,x,k[0],k[1]]+F[4,x,k[0]]
F[15,x,k[0],k[1]] = F[16,x,k[0],k[1]]
F[16,x,k[0],k[1]] = F[0,x]*F[17,x,k[0]]*F[22,x,k[1]]
F[17,x,k[0]] = F[1,x]+F[18,x,k[0]]+F[20,x,k[0]]
F[18,x,k[0]] = F[19,x,k[0]]*F[7,x]
F[19,x,k[0]] = 1/(-1+k[0])*(F[17,x,k[0]]*k[0]-F[17,x,1])
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[17,x,k[0]]*F[22,x,k[0]]*F[23,x,k[0]]
F[22,x,k[0]] = k[0]*x
F[23,x,k[0]] = F[1,x]+F[22,x,k[0]]
F[24,x,k[0],k[1]] = F[22,x,k[0]]*F[25,x,k[0],k[1]]
F[25,x,k[0],k[1]] = F[26,x,k[0],k[1]]+F[9,x,k[0]]
F[26,x,k[0],k[1]] = F[27,x,k[0],k[1]]
F[27,x,k[0],k[1]] = F[22,x,k[1]]*F[23,x,k[0]]*F[28,x,k[0]]
F[29,x,k[0],k[1]] = F[28,x,k[0]]+F[31,x,k[0],k[1]]
F[30,x,k[0],k[1]] = F[22,x,k[1]]*F[23,x,k[1]]*F[29,x,k[0],k[1]]
F[30,x,k[0],k[1]] = F[31,x,k[0],k[1]]
F[11,x,k[0],k[1]] = F[31,x,k[0],k[1]]+F[4,x,k[0]]
F[32,x,k[0],k[1]] = F[22,x,k[1]]*F[33,x,k[0],k[1]]
F[33,x,k[0],k[1]] = F[11,x,k[0],k[1]]+F[34,x,k[0],k[1]]
F[34,x,k[0],k[1]] = F[35,x,k[0],k[1]]
F[35,x,k[0],k[1]] = F[22,x,k[1]]*F[29,x,k[0],k[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_{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_{22}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , 1, y\right)
F_{10}\! \left(x , y , z\right) = F_{11}\! \left(x , y z , z\right)
F_{11}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{24}\! \left(x , y , z\right)+F_{32}\! \left(x , y , z\right)
F_{12}\! \left(x , y , z\right) = F_{13}\! \left(x , y , z\right) F_{7}\! \left(x \right)
F_{13}\! \left(x , y , z\right) = \frac{F_{14}\! \left(x , y , z\right) y -F_{14}\! \left(x , 1, z\right)}{-1+y}
F_{14}\! \left(x , y , z\right) = F_{15}\! \left(x , y , z\right)+F_{4}\! \left(x , y\right)
F_{15}\! \left(x , y , z\right) = F_{16}\! \left(x , y , z\right)
F_{16}\! \left(x , y , z\right) = F_{0}\! \left(x \right) F_{17}\! \left(x , y\right) F_{22}\! \left(x , z\right)
F_{17}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{20}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{19}\! \left(x , y\right) = \frac{F_{17}\! \left(x , y\right) y -F_{17}\! \left(x , 1\right)}{-1+y}
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{17}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = y x
F_{23}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{22}\! \left(x , y\right)
F_{24}\! \left(x , y , z\right) = F_{22}\! \left(x , y\right) F_{25}\! \left(x , y , z\right)
F_{25}\! \left(x , y , z\right) = F_{26}\! \left(x , y , z\right)+F_{9}\! \left(x , y\right)
F_{26}\! \left(x , y , z\right) = F_{27}\! \left(x , y , z\right)
F_{27}\! \left(x , y , z\right) = F_{22}\! \left(x , z\right) F_{23}\! \left(x , y\right) F_{28}\! \left(x , y\right)
F_{29}\! \left(x , y , z\right) = F_{28}\! \left(x , y\right)+F_{31}\! \left(x , y , z\right)
F_{30}\! \left(x , y , z\right) = F_{22}\! \left(x , z\right) F_{23}\! \left(x , z\right) F_{29}\! \left(x , y , z\right)
F_{30}\! \left(x , y , z\right) = F_{31}\! \left(x , y , z\right)
F_{11}\! \left(x , y , z\right) = F_{31}\! \left(x , y , z\right)+F_{4}\! \left(x , y\right)
F_{32}\! \left(x , y , z\right) = F_{22}\! \left(x , z\right) F_{33}\! \left(x , y , z\right)
F_{33}\! \left(x , y , z\right) = F_{11}\! \left(x , y , z\right)+F_{34}\! \left(x , y , z\right)
F_{34}\! \left(x , y , z\right) = F_{35}\! \left(x , y , z\right)
F_{35}\! \left(x , y , z\right) = F_{22}\! \left(x , z\right) F_{29}\! \left(x , y , z\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_22(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, 1, k_0))
Eq(F_10(x, k_0, k_1), F_11(x, k_0*k_1, k_1))
Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_24(x, k_0, k_1) + F_32(x, k_0, k_1))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1)*F_7(x))
Eq(F_13(x, k_0, k_1), (k_0*F_14(x, k_0, k_1) - F_14(x, 1, k_1))/(k_0 - 1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0, k_1) + F_4(x, k_0))
Eq(F_15(x, k_0, k_1), F_16(x, k_0, k_1))
Eq(F_16(x, k_0, k_1), F_0(x)*F_17(x, k_0)*F_22(x, k_1))
Eq(F_17(x, k_0), F_1(x) + F_18(x, k_0) + F_20(x, k_0))
Eq(F_18(x, k_0), F_19(x, k_0)*F_7(x))
Eq(F_19(x, k_0), (k_0*F_17(x, k_0) - F_17(x, 1))/(k_0 - 1))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_17(x, k_0)*F_22(x, k_0)*F_23(x, k_0))
Eq(F_22(x, k_0), k_0*x)
Eq(F_23(x, k_0), F_1(x) + F_22(x, k_0))
Eq(F_24(x, k_0, k_1), F_22(x, k_0)*F_25(x, k_0, k_1))
Eq(F_25(x, k_0, k_1), F_26(x, k_0, k_1) + F_9(x, k_0))
Eq(F_26(x, k_0, k_1), F_27(x, k_0, k_1))
Eq(F_27(x, k_0, k_1), F_22(x, k_1)*F_23(x, k_0)*F_28(x, k_0))
Eq(F_29(x, k_0, k_1), F_28(x, k_0) + F_31(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), F_22(x, k_1)*F_23(x, k_1)*F_29(x, k_0, k_1))
Eq(F_30(x, k_0, k_1), F_31(x, k_0, k_1))
Eq(F_11(x, k_0, k_1), F_31(x, k_0, k_1) + F_4(x, k_0))
Eq(F_32(x, k_0, k_1), F_22(x, k_1)*F_33(x, k_0, k_1))
Eq(F_33(x, k_0, k_1), F_11(x, k_0, k_1) + F_34(x, k_0, k_1))
Eq(F_34(x, k_0, k_1), F_35(x, k_0, k_1))
Eq(F_35(x, k_0, k_1), F_22(x, k_1)*F_29(x, k_0, k_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, 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, 1, 3, 4], "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, 4, 1, 3], "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, 4, 1, 3], "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]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": 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