01342_01432_02341_02431_03421_12340_12430_13420_23410
Counting sequence:
1, 1, 2, 6, 24, 111, 546, 2762, 14198, 73842, 387820, 2054640, 10971550, 59009651, 319465794, 1739872602, 9527278470, 52428316878, 289811861916, 1608593714052, 8961924243432, 50100495150294, 280960090205940, 1580150437281540, 8910551182741596, 50370311659214516, 285383899561984016, 1620309588886466772, 9217567449319655050, 52532346646332437403, 299900600277207956674, 1714828561489866752762, 9820057225122334587462, 56314234364447057527062, 323368352647189407943852, 1859171005058262082868772, 10701722256095168169966112, 61669859271907235597776354, 355755623096081002768431356, 2054313191590778566097670444, 11873968275689087420729250900, 68694082037916595921207186428, 397757402118583225941694810824, 2305023286172098672366086050352, 13368240235561350323867430072060, 77588954211543605756315879449806, 450648704116425795014512202600628, 2619242244328142739858217602590628, 15233513608109374908814429470083484, 88654279918191723116645481177739020, 516254150069096777042722015848727320, 3008024022521585472570795291962492520, 17536511404544127578895174769244255280, 102291623858851110805881323939305149324, 596984746008746930944700986658530609704, 3485816161444544568289081948940217832968, 20363669468018835443087462158083086795736, 119017426172824254273405266943821913841080, 695922764948898740878164591732474103962264, 4070997917394967590123391274510514941746140, 23824498565282970913478549043772634922381282, 139483784436383257379252089286576471286039147, 816949181186758102218705757508746342063252674, 4786656919971161127778954758371345736957243450, 28056295409381583664218953763614792249152471110, 164506923646872146095193187880497630213444971238, 964915216763507488446014523613893990025364435148, 5661620405036716082225361053502940884065745056676, 33230330125787668730422613384291567556942973575216, 195104264928141768668349989980841715561274507846698, 1145864143424268540488596438436001714850565612627244, 6731781040384479261930248790838795896962743678472604, 39559764894483455328499101454904933916396245594093028, 232541688727609190489692640795341178000772980518790988, 1367313222350184950731295964641378969987158683848332680, 8041778024896421982574058191658214964402211948184840192, 47309673992233428345001802883783973211587196428164347940, 278393240272428736058750378503101845086759471278316223418, 1638609377032326801906902374984658916653584977185882019516, 9647115447813342504644904783810906484152826668434550214796, 56809658499629789246861036294674754427030382574500634012852, 334616239466357731385495119485808985280827800609743950976996, 1971376361665008153245175552810784824490742218486928704952776, 11616824292001948024813141774561199402012067712245991124524920, 68469692229096363551829932723038819332061474465535657872259056, 403645601184025499454970885926179380217932732873907427104663924, 2380076166665675465961111794963532856455648186936204412417998552, 14036803900071701798955731262380282362017963776578451322964786872, 82800009689266286089784935690610401871048053571054124883424582920, 488512204794432515392667331693127308627037308177355871155496107800, 2882713531064067244653776780724960634098951739260437387088973787968, 17014015110567640991634101384174545640044703249929517034373382377768, 100436063117947758665897001634697014568165324318159967217850500829156, 592991437205584818363145741662217010533655941462245658105702085324286, 3501720077411806177481976146709678345284915825644311509718612462628788, 20681742766849002916913502852746886563307220666743990537539922400561764, 122169846414088355382995168024188915450563007272428816009690118514209564, 721789646007167129315712216088452897255844268532951314642881179523902588, 4265064186315723194635048388926740298533499351012263017514461843308752888, 25206202490703325431082573382097715690202855689731399899585650655878107048, 148989224494354254498829932888882803354777470314740738748268093241502832512
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24193/
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[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[8,x,k[0]]
F[6,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x,k[0]] = F[10,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[11,x,1,k[0]]
F[11,x,k[0],k[1]] = F[1,x]+F[12,x,k[0],k[1]]+F[14,x,k[0],k[1]]+F[21,x,k[1],k[0]]
F[12,x,k[0],k[1]] = F[13,x,k[0],k[1]]*F[3,x]
F[13,x,k[0],k[1]] = 1/(k[0]*k[1]-1)*(F[11,x,k[0],k[1]]*k[0]*k[1]-F[11,x,1/k[1],k[1]])
F[14,x,k[0],k[1]] = F[15,x,k[0]*k[1],k[1]]
F[16,x,k[0],k[1]] = F[1,x]+F[15,x,k[0],k[1]]+F[17,x,k[0],k[1]]+F[19,x,k[1],k[0]]
F[16,x,k[0],k[1]] = (F[5,x,k[0]]*k[0]-F[5,x,k[1]]*k[1])/(-k[1]+k[0])
F[17,x,k[0],k[1]] = F[18,x,k[0],k[1]]*F[3,x]
F[18,x,k[0],k[1]] = 1/(-1+k[0])*(F[16,x,k[0],k[1]]*k[0]-F[16,x,1,k[1]])
F[19,x,k[0],k[1]] = F[20,x,k[1],k[0]]*F[9,x,k[0]]
F[20,x,k[0],k[1]] = (-F[11,x,1,k[1]]*k[1]+F[11,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]
F[22,x,k[0],k[1]] = F[23,x]*F[25,x,k[0]]*F[25,x,k[1]]*F[27,x,k[0]]*F[9,x,k[0]]
F[23,x] = F[1,x]+F[24,x]
F[24,x] = F[23,x]*F[3,x]
F[25,x,k[0]] = F[1,x]+F[26,x,k[0]]
F[26,x,k[0]] = F[25,x,k[0]]*F[9,x,k[0]]
F[27,x,k[0]] = F[1,x]+F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[25,x,k[0]]*F[27,x,k[0]]*F[9,x,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_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = \frac{y F_{5}\! \left(x , y\right)-F_{5}\! \left(x , 1\right)}{-1+y}
F_{8}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = y x
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , 1, y\right)
F_{11}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{14}\! \left(x , y , z\right)+F_{21}\! \left(x , z , y\right)
F_{12}\! \left(x , y , z\right) = F_{13}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{13}\! \left(x , y , z\right) = \frac{y z F_{11}\! \left(x , y , z\right)-F_{11}\! \left(x , \frac{1}{z}, z\right)}{y z -1}
F_{14}\! \left(x , y , z\right) = F_{15}\! \left(x , y z , z\right)
F_{16}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y , z\right)+F_{17}\! \left(x , y , z\right)+F_{19}\! \left(x , z , y\right)
F_{16}\! \left(x , y , z\right) = \frac{y F_{5}\! \left(x , y\right)-z F_{5}\! \left(x , z\right)}{-z +y}
F_{17}\! \left(x , y , z\right) = F_{18}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{18}\! \left(x , y , z\right) = \frac{y F_{16}\! \left(x , y , z\right)-F_{16}\! \left(x , 1, z\right)}{-1+y}
F_{19}\! \left(x , y , z\right) = F_{20}\! \left(x , z , y\right) F_{9}\! \left(x , y\right)
F_{20}\! \left(x , y , z\right) = \frac{-z F_{11}\! \left(x , 1, z\right)+y F_{11}\! \left(x , \frac{y}{z}, z\right)}{-z +y}
F_{21}\! \left(x , y , z\right) = F_{22}\! \left(x , y , z\right)
F_{22}\! \left(x , y , z\right) = F_{23}\! \left(x \right) F_{25}\! \left(x , y\right) F_{25}\! \left(x , z\right) F_{27}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{23}\! \left(x \right) F_{3}\! \left(x \right)
F_{25}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{26}\! \left(x , y\right)
F_{26}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{25}\! \left(x , y\right) F_{27}\! \left(x , y\right) F_{9}\! \left(x , 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_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_8(x, k_0))
Eq(F_6(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x, k_0), F_10(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_11(x, 1, k_0))
Eq(F_11(x, k_0, k_1), F_1(x) + F_12(x, k_0, k_1) + F_14(x, k_0, k_1) + F_21(x, k_1, k_0))
Eq(F_12(x, k_0, k_1), F_13(x, k_0, k_1)*F_3(x))
Eq(F_13(x, k_0, k_1), (k_0*k_1*F_11(x, k_0, k_1) - F_11(x, 1/k_1, k_1))/(k_0*k_1 - 1))
Eq(F_14(x, k_0, k_1), F_15(x, k_0*k_1, k_1))
Eq(F_16(x, k_0, k_1), F_1(x) + F_15(x, k_0, k_1) + F_17(x, k_0, k_1) + F_19(x, k_1, k_0))
Eq(F_16(x, k_0, k_1), (-k_0*F_5(x, k_0) + k_1*F_5(x, k_1))/(-k_0 + k_1))
Eq(F_17(x, k_0, k_1), F_18(x, k_0, k_1)*F_3(x))
Eq(F_18(x, k_0, k_1), (k_0*F_16(x, k_0, k_1) - F_16(x, 1, k_1))/(k_0 - 1))
Eq(F_19(x, k_0, k_1), F_20(x, k_1, k_0)*F_9(x, k_0))
Eq(F_20(x, k_0, k_1), (-k_0*F_11(x, k_0/k_1, k_1) + k_1*F_11(x, 1, k_1))/(-k_0 + k_1))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1))
Eq(F_22(x, k_0, k_1), F_23(x)*F_25(x, k_0)*F_25(x, k_1)*F_27(x, k_0)*F_9(x, k_0))
Eq(F_23(x), F_1(x) + F_24(x))
Eq(F_24(x), F_23(x)*F_3(x))
Eq(F_25(x, k_0), F_1(x) + F_26(x, k_0))
Eq(F_26(x, k_0), F_25(x, k_0)*F_9(x, k_0))
Eq(F_27(x, k_0), F_1(x) + F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_25(x, k_0)*F_27(x, k_0)*F_9(x, k_0))
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, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "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": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 4, 1, 0], "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": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 3]]}]}, {"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[1, 4]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[0, 4]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 3], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 2], [1, 4], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 3], [1, 3], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 2], [1, 3], [1, 3], [1, 3]]}, {"patt": [0, 2, 3, 1], "pos": 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