01342_01432_03142_03412_03421_04132_04312_04321_10342_10432_13042_30142_30412_30421_31042
Counting sequence:
1, 1, 2, 6, 24, 105, 475, 2195, 10343, 49581, 241184, 1187790, 5911018, 29679420, 150172468, 764960279, 3919673191, 20189778058, 104481432098, 542956623611, 2832254961846, 14824775319592, 77839513324167, 409876323374867, 2163938467856689, 11452146053861273, 60743443005487700, 322858183819929282, 1719336234308210285, 9172540553910298965, 49017036480927089192, 262353404880118880424, 1406262975602796841220, 7548284722632183595838, 40569246310751642094227, 218313473981720291491470, 1176168947842885520848506, 6343623963572517576270389, 34249859816529986243244394, 185101866490320959974478863, 1001318232510979349964115312, 5421544323152168627977594380, 29379547114122730831769063453, 159338703229431973228308102546, 864839691382712129275996782212, 4697569453936307685536330482493, 25534075577784517755686928233654, 138887561787372759588401395511550, 755945720741151278256293020642596, 4117090559705224667772788318189789, 22436337362085747214813847144882751, 122339036544147093505510078843407553, 667452099381282328409050960361012758, 3643409978773145143277073640014316959, 19898498887202845418992860986892429695, 108729857991138400653640556411842414724, 594409707644188681019216222503803695219, 3251054626103803461087751944706146692500, 17789225790901960532422212103037361971695, 97381775886297057283627481954256275181845, 533310304241674833341561384206183690394574, 2921850460664815163268385268696811096994047, 16014231005441037616859786366255493588788577, 87804933991349242773906192621431147721724732, 481605419027502074241178263185714219807026805, 2642521567260122771462608698910850352181742899, 14504267037939971479283290225521827070266723919, 79637689421216131756414876116193843557833397515, 437404125685362895237242103826002366362016706739, 2403169398542328669106987018806509452856930912583, 13207459300408331724700401040053332137030165536751, 72607891703197306664984156209774382124348897752957, 399277134205564943949501654798249299806485210920563, 2196279893714793558105180505819134464145201074328372, 12084265759731739666213610405538011289415865272274292, 66507254553435397602174138338925755963542956603531886, 366126279283910584399006754845423278032491443157531672, 2016057850030779340758451491560692102604822483084252882, 11104077186028321716670554780497376485103434131983551368, 61173966814453095860886006179285991536517007789910874393, 337095456593923881419037797821032430631724174599885343423, 1857970145912839829985857706714439135793929616232129714489, 10242871468881906641406396890234203600021299086663912871751, 56480631514863896490075904272074212436332689153073180267815, 311508532431980125516997650702936764922932129644578368286648, 1718425715942516079962575030115005778666662376544104708394573, 9481562238851485413160061031756085182163089682757009738691941, 52325734889263534667284432660274687222189046709059861417640967, 288825224475407688453460747595045711770439886227703555986002105, 1594547137416306446511045452405353940691960266072018443293708420, 8804815095732551083480495961142177885920666202991302891512512904, 48627505145134996910584052275233847585671707283415139898700127679, 268609210384616328983808739264505726587545801160891596316826356750, 1484004858281303003940840065594551390527348023407715699066437221267, 8200185109174101899054090894319923720960012112148359296327677307516, 45319420810801578769789378518620356222471128202447582490699173862933, 250504715516038923132848014542832978072903643211903172737077899449160, 1384895055737027154331496842423449523738529261371185441362301269575236, 7657479062826421588016242365958877319782188386714036287940170920695633, 42346877929340287407741169543930536601838045443849313136761956397737900, 234219081955775852805016976534772024693788218623351835867180351939370499
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/24309/
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[9,x]
F[3,x] = F[1,x]+F[37,x]+F[4,x]
F[4,x] = F[5,x]*F[9,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[24,x,k[0]]+F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,k[0]]*F[9,x]
F[8,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[9,x] = x
F[10,x,k[0]] = F[11,x,k[0]]*F[9,x]
F[11,x,k[0]] = 1/(-1+k[0])*(F[12,x,k[0]]*k[0]-F[12,x,1])
F[12,x,k[0]] = 1/(-1+k[0])*(F[13,x,k[0]]*k[0]-F[13,x,1])
F[13,x,k[0]] = F[1,x]+F[14,x,k[0]]+F[15,x,k[0]]
F[14,x,k[0]] = F[6,x,k[0]]*F[9,x]
F[15,x,k[0]] = F[16,x,k[0]]*F[20,x,k[0]]
F[16,x,k[0]] = F[17,x,1,k[0]]
F[17,x,k[0],k[1]] = F[1,x]+F[14,x,k[1]]+F[18,x,k[0],k[1]]+F[21,x,k[0],k[1]]
F[18,x,k[0],k[1]] = F[19,x,k[0]*k[1],k[1]]
F[19,x,k[0],k[1]] = F[13,x,k[1]]*F[20,x,k[0]]
F[20,x,k[0]] = k[0]*x
F[21,x,k[0],k[1]] = F[22,x,k[0]*k[1],k[1]]
F[22,x,k[0],k[1]] = F[20,x,k[1]]*F[23,x,k[0],k[1]]
F[23,x,k[0],k[1]] = (-F[17,x,1,k[1]]*k[1]+F[17,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[24,x,k[0]] = F[20,x,k[0]]*F[25,x,k[0]]
F[25,x,k[0]] = F[26,x,1,k[0]]
F[26,x,k[0],k[1]] = F[1,x]+F[27,x,k[1]]+F[33,x,k[0],k[1]]+F[35,x,k[0],k[1]]+F[7,x,k[1]]
F[27,x,k[0]] = F[28,x,k[0]]*F[9,x]
F[28,x,k[0]] = 1/(-1+k[0])*(F[29,x,k[0]]*k[0]-F[29,x,1])
F[29,x,k[0]] = F[1,x]+F[14,x,k[0]]+F[30,x,k[0]]+F[31,x,k[0]]
F[30,x,k[0]] = F[13,x,k[0]]*F[9,x]
F[31,x,k[0]] = F[20,x,k[0]]*F[32,x,k[0]]
F[32,x,k[0]] = 1/(-1+k[0])*(F[17,x,1,k[0]]*k[0]-F[17,x,1/k[0],k[0]])
F[33,x,k[0],k[1]] = F[34,x,k[0]*k[1],k[1]]
F[34,x,k[0],k[1]] = F[20,x,k[0]]*F[29,x,k[1]]
F[36,x,k[0],k[1]] = F[1,x]+F[14,x,k[1]]+F[18,x,k[0],k[1]]+F[30,x,k[1]]+F[35,x,k[0],k[1]]
F[36,x,k[0],k[1]] = 1/(k[0]*k[1]-1)*(F[17,x,k[0],k[1]]*k[0]*k[1]-F[17,x,1/k[1],k[1]])
F[37,x] = F[38,x]*F[9,x]
F[38,x] = F[39,x,1]
F[39,x,k[0]] = 1/(-1+k[0])*(F[13,x,k[0]]*k[0]-F[13,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_{3}\! \left(x \right) F_{9}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{37}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{9}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{8}\! \left(x , y\right) = \frac{F_{6}\! \left(x , y\right) y -F_{6}\! \left(x , 1\right)}{-1+y}
F_{9}\! \left(x \right) = x
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{11}\! \left(x , y\right) = \frac{F_{12}\! \left(x , y\right) y -F_{12}\! \left(x , 1\right)}{-1+y}
F_{12}\! \left(x , y\right) = \frac{F_{13}\! \left(x , y\right) y -F_{13}\! \left(x , 1\right)}{-1+y}
F_{13}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{15}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{20}\! \left(x , y\right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , 1, y\right)
F_{17}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , z\right)+F_{18}\! \left(x , y , z\right)+F_{21}\! \left(x , y , z\right)
F_{18}\! \left(x , y , z\right) = F_{19}\! \left(x , y z , z\right)
F_{19}\! \left(x , y , z\right) = F_{13}\! \left(x , z\right) F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = y x
F_{21}\! \left(x , y , z\right) = F_{22}\! \left(x , y z , z\right)
F_{22}\! \left(x , y , z\right) = F_{20}\! \left(x , z\right) F_{23}\! \left(x , y , z\right)
F_{23}\! \left(x , y , z\right) = \frac{-F_{17}\! \left(x , 1, z\right) z +F_{17}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{24}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{26}\! \left(x , 1, y\right)
F_{26}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , z\right)+F_{33}\! \left(x , y , z\right)+F_{35}\! \left(x , y , z\right)+F_{7}\! \left(x , z\right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{28}\! \left(x , y\right) = \frac{F_{29}\! \left(x , y\right) y -F_{29}\! \left(x , 1\right)}{-1+y}
F_{29}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{30}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{13}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{31}\! \left(x , y\right) = F_{20}\! \left(x , y\right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = \frac{F_{17}\! \left(x , 1, y\right) y -F_{17}\! \left(x , \frac{1}{y}, y\right)}{-1+y}
F_{33}\! \left(x , y , z\right) = F_{34}\! \left(x , y z , z\right)
F_{34}\! \left(x , y , z\right) = F_{20}\! \left(x , y\right) F_{29}\! \left(x , z\right)
F_{36}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{14}\! \left(x , z\right)+F_{18}\! \left(x , y , z\right)+F_{30}\! \left(x , z\right)+F_{35}\! \left(x , y , z\right)
F_{36}\! \left(x , y , z\right) = \frac{F_{17}\! \left(x , y , z\right) y z -F_{17}\! \left(x , \frac{1}{z}, z\right)}{y z -1}
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{9}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x , 1\right)
F_{39}\! \left(x , y\right) = \frac{F_{13}\! \left(x , y\right) y -F_{13}\! \left(x , 1\right)}{-1+y}
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_9(x))
Eq(F_3(x), F_1(x) + F_37(x) + F_4(x))
Eq(F_4(x), F_5(x)*F_9(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_10(x, k_0) + F_24(x, k_0) + F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, k_0)*F_9(x))
Eq(F_8(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_9(x), x)
Eq(F_10(x, k_0), F_11(x, k_0)*F_9(x))
Eq(F_11(x, k_0), (k_0*F_12(x, k_0) - F_12(x, 1))/(k_0 - 1))
Eq(F_12(x, k_0), (k_0*F_13(x, k_0) - F_13(x, 1))/(k_0 - 1))
Eq(F_13(x, k_0), F_1(x) + F_14(x, k_0) + F_15(x, k_0))
Eq(F_14(x, k_0), F_6(x, k_0)*F_9(x))
Eq(F_15(x, k_0), F_16(x, k_0)*F_20(x, k_0))
Eq(F_16(x, k_0), F_17(x, 1, k_0))
Eq(F_17(x, k_0, k_1), F_1(x) + F_14(x, k_1) + F_18(x, k_0, k_1) + F_21(x, k_0, k_1))
Eq(F_18(x, k_0, k_1), F_19(x, k_0*k_1, k_1))
Eq(F_19(x, k_0, k_1), F_13(x, k_1)*F_20(x, k_0))
Eq(F_20(x, k_0), k_0*x)
Eq(F_21(x, k_0, k_1), F_22(x, k_0*k_1, k_1))
Eq(F_22(x, k_0, k_1), F_20(x, k_1)*F_23(x, k_0, k_1))
Eq(F_23(x, k_0, k_1), (-k_0*F_17(x, k_0/k_1, k_1) + k_1*F_17(x, 1, k_1))/(-k_0 + k_1))
Eq(F_24(x, k_0), F_20(x, k_0)*F_25(x, k_0))
Eq(F_25(x, k_0), F_26(x, 1, k_0))
Eq(F_26(x, k_0, k_1), F_1(x) + F_27(x, k_1) + F_33(x, k_0, k_1) + F_35(x, k_0, k_1) + F_7(x, k_1))
Eq(F_27(x, k_0), F_28(x, k_0)*F_9(x))
Eq(F_28(x, k_0), (k_0*F_29(x, k_0) - F_29(x, 1))/(k_0 - 1))
Eq(F_29(x, k_0), F_1(x) + F_14(x, k_0) + F_30(x, k_0) + F_31(x, k_0))
Eq(F_30(x, k_0), F_13(x, k_0)*F_9(x))
Eq(F_31(x, k_0), F_20(x, k_0)*F_32(x, k_0))
Eq(F_32(x, k_0), (k_0*F_17(x, 1, k_0) - F_17(x, 1/k_0, k_0))/(k_0 - 1))
Eq(F_33(x, k_0, k_1), F_34(x, k_0*k_1, k_1))
Eq(F_34(x, k_0, k_1), F_20(x, k_0)*F_29(x, k_1))
Eq(F_36(x, k_0, k_1), F_1(x) + F_14(x, k_1) + F_18(x, k_0, k_1) + F_30(x, k_1) + F_35(x, k_0, k_1))
Eq(F_36(x, k_0, k_1), (k_0*k_1*F_17(x, k_0, k_1) - F_17(x, 1/k_1, k_1))/(k_0*k_1 - 1))
Eq(F_37(x), F_38(x)*F_9(x))
Eq(F_38(x), F_39(x, 1))
Eq(F_39(x, k_0), (-k_0*F_13(x, k_0) + F_13(x, 1))/(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, 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, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "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": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 4, "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": [[3, 1]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [3, 1], [3, 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