01342_03142_03412_10342_13042_30142_30412_31042
Counting sequence:
1, 1, 2, 6, 24, 112, 568, 3030, 16726, 94658, 546022, 3197806, 18961792, 113606290, 686660298, 4181824738, 25635871104, 158067216052, 979626159988, 6099075393508, 38128518640934, 239246234752430, 1506262308456858, 9512338689738776, 60241047018122780, 382487533690739466, 2434300977119172268, 15526943417938194860, 99239207176878603688, 635483633378901908684, 4076558068973970877922, 26193946097211495987088, 168570225620940956734026, 1086406185697038554101634, 7011282575536957455047478, 45306686294827342908858366, 293126653107969971780999480, 1898662034478359470832598816, 12311552858837877307035225744, 79914637932698050702404207874, 519236900503686346934459001634, 3376832493831796617014714178238, 21980562397668317982551322706770, 143197461280092846517328088911182, 933645997689280407550824446427830, 6092055650733965107918422036249692, 39780067424213424838095084710235384, 259940214117612678163267120663117532, 1699710167916485614183869916653214260, 11121353534011670448392800892973793334, 72813256671141772147146145612356346194, 477004672149243167330748063257596093652, 3126684999477399140702595530340887173550, 20506213404389784794837990125179905127738, 134560538299374136367184876515331585501488, 883430534219077499553125646432752224377968, 5802852676944589888487123404643728340568850, 38134456288776481428699231237337495375941886, 250722475764289736735348181435932967605263326, 1649156454887568821671067250365940877712305348, 10852176862570773215568663038510555581740163608, 71441757547028212523086890429137820437488158078, 470502364151187649095371866850349318794145638916, 3099847526118961999625192673542392301723905692570, 20430659703176604441601727735210432716095239382180, 134704753637034409006719775975239774294816549631108, 888458400555193196343461067567082273599795432628448, 5861925656498661953646405879550398168356964736219744, 38689056493835210019835836041429482475314159642822562, 255432633308345351903031121841570841520561970556382066, 1686945291646214921968825777188824338216727961480497894, 11144436914926125638666350263659893018869361647838660220, 73645137167321058964952571178722979534558198755119107620, 486805287477797716597450437778938658425325778726084241424, 3218758262121205430006922205192114345103744766174280972552, 21288253474548799369152315539389932364668019009679409478172, 140833886543520813240839287686256350719471279012505250101464, 931937404600719086372813690931278235530955284159447419397530, 6168447475282357213544402933487391915460426761030569210721990, 40838686146761884430776675577530393938386081761209112410668962, 270440501775995778891280468803024692351741518123701232606606722, 1791320117948553651482879584268699874951766882234505642215470618, 11867894734655396143963975376542484764745980925864459243609110934, 78644939524001647387046470419615303059982833157892130933499029566, 521269343539467741108425981350807597785482505978274191674388502474, 3455776613003720057966807537845542393882815991773815263330257183206, 22914957850479411584514235689546250071965838866485461866632439099762, 151977855692805860211936113299922150293318973284660686832252769579646, 1008155225716262641096926598467397237060606334580344152526440678769562, 6688957004701977253199922371276744153060605989559389377207833310980400, 44388598852556906955292770973067373217503296951785954054102328458903720, 294621673120084449640214500289350994979266866875646193434334450374733388, 1955853934687771396910742348949724258772364963844886602133708744831979168, 12986284761634568472704873419506024126530412257945219422541324113328261120, 86239963187462205511253387250079950463846570805800561012869260824192567404, 572803617246693223792215242254281581863098154530114928030834552578314024244, 3805177776608389327793881011864727626930369721794828540413041667358481758584, 25282188862088405142456436722873149052879453189104565428239589486633487071002, 168005486988001606358384069455131868515849001086996519207822732494801769437776, 1116605941855957758776472799093895372105958345073367428560369197866837196956400, 7422372032705835930091264260754999119943339459824494375502208606763032679392556
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24162/
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[31,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[22,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]] = F[1,x]+F[10,x,k[0]]+F[13,x,k[0]]+F[7,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[19,x,k[0]]
F[14,x,k[0]] = 1/(-1+k[0])*(F[15,x,1,k[0]]*k[0]-F[15,x,1/k[0],k[0]])
F[15,x,k[0],k[1]] = F[16,x,k[0]*k[1],k[1]]
F[16,x,k[0],k[1]] = F[1,x]+F[17,x,k[1]]+F[18,x,k[0],k[1]]+F[20,x,k[0],k[1]]
F[17,x,k[0]] = F[6,x,k[0]]*F[9,x]
F[18,x,k[0],k[1]] = F[16,x,k[0],k[1]]*F[19,x,k[0]]
F[19,x,k[0]] = k[0]*x
F[20,x,k[0],k[1]] = F[19,x,k[1]]*F[21,x,k[0],k[1]]
F[21,x,k[0],k[1]] = (-F[15,x,1,k[1]]*k[1]+F[15,x,k[0]/k[1],k[1]]*k[0])/(-k[1]+k[0])
F[22,x,k[0]] = F[19,x,k[0]]*F[23,x,k[0]]
F[23,x,k[0]] = F[24,x,1,k[0]]
F[24,x,k[0],k[1]] = F[1,x]+F[10,x,k[1]]+F[25,x,k[0],k[1]]+F[26,x,k[0],k[1]]+F[7,x,k[1]]
F[25,x,k[0],k[1]] = F[19,x,k[1]]*F[24,x,k[0],k[1]]
F[27,x,k[0],k[1]] = F[1,x]+F[17,x,k[1]]+F[26,x,k[0],k[1]]+F[28,x,k[1]]+F[30,x,k[0],k[1]]
F[27,x,k[0],k[1]] = 1/(k[0]*k[1]-1)*(F[15,x,k[0],k[1]]*k[0]*k[1]-F[15,x,1/k[1],k[1]])
F[28,x,k[0]] = F[29,x,k[0]]*F[9,x]
F[29,x,k[0]] = F[16,x,1,k[0]]
F[30,x,k[0],k[1]] = F[19,x,k[1]]*F[27,x,k[0],k[1]]
F[31,x] = F[32,x]*F[9,x]
F[32,x] = F[12,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_{31}\! \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_{22}\! \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) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{7}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = \frac{F_{15}\! \left(x , 1, y\right) y -F_{15}\! \left(x , \frac{1}{y}, y\right)}{-1+y}
F_{15}\! \left(x , y , z\right) = F_{16}\! \left(x , y z , z\right)
F_{16}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , z\right)+F_{18}\! \left(x , y , z\right)+F_{20}\! \left(x , y , z\right)
F_{17}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{18}\! \left(x , y , z\right) = F_{16}\! \left(x , y , z\right) F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = y x
F_{20}\! \left(x , y , z\right) = F_{19}\! \left(x , z\right) F_{21}\! \left(x , y , z\right)
F_{21}\! \left(x , y , z\right) = \frac{-F_{15}\! \left(x , 1, z\right) z +F_{15}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}
F_{22}\! \left(x , y\right) = F_{19}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x , 1, y\right)
F_{24}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , z\right)+F_{25}\! \left(x , y , z\right)+F_{26}\! \left(x , y , z\right)+F_{7}\! \left(x , z\right)
F_{25}\! \left(x , y , z\right) = F_{19}\! \left(x , z\right) F_{24}\! \left(x , y , z\right)
F_{27}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , z\right)+F_{26}\! \left(x , y , z\right)+F_{28}\! \left(x , z\right)+F_{30}\! \left(x , y , z\right)
F_{27}\! \left(x , y , z\right) = \frac{F_{15}\! \left(x , y , z\right) y z -F_{15}\! \left(x , \frac{1}{z}, z\right)}{y z -1}
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{29}\! \left(x , y\right) = F_{16}\! \left(x , 1, y\right)
F_{30}\! \left(x , y , z\right) = F_{19}\! \left(x , z\right) F_{27}\! \left(x , y , z\right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{9}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \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_3(x)*F_9(x))
Eq(F_3(x), F_1(x) + F_31(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_22(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), F_1(x) + F_10(x, k_0) + F_13(x, k_0) + F_7(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_19(x, k_0))
Eq(F_14(x, k_0), (k_0*F_15(x, 1, k_0) - F_15(x, 1/k_0, k_0))/(k_0 - 1))
Eq(F_15(x, k_0, k_1), F_16(x, k_0*k_1, k_1))
Eq(F_16(x, k_0, k_1), F_1(x) + F_17(x, k_1) + F_18(x, k_0, k_1) + F_20(x, k_0, k_1))
Eq(F_17(x, k_0), F_6(x, k_0)*F_9(x))
Eq(F_18(x, k_0, k_1), F_16(x, k_0, k_1)*F_19(x, k_0))
Eq(F_19(x, k_0), k_0*x)
Eq(F_20(x, k_0, k_1), F_19(x, k_1)*F_21(x, k_0, k_1))
Eq(F_21(x, k_0, k_1), (-k_0*F_15(x, k_0/k_1, k_1) + k_1*F_15(x, 1, k_1))/(-k_0 + k_1))
Eq(F_22(x, k_0), F_19(x, k_0)*F_23(x, k_0))
Eq(F_23(x, k_0), F_24(x, 1, k_0))
Eq(F_24(x, k_0, k_1), F_1(x) + F_10(x, k_1) + F_25(x, k_0, k_1) + F_26(x, k_0, k_1) + F_7(x, k_1))
Eq(F_25(x, k_0, k_1), F_19(x, k_1)*F_24(x, k_0, k_1))
Eq(F_27(x, k_0, k_1), F_1(x) + F_17(x, k_1) + F_26(x, k_0, k_1) + F_28(x, k_1) + F_30(x, k_0, k_1))
Eq(F_27(x, k_0, k_1), (k_0*k_1*F_15(x, k_0, k_1) - F_15(x, 1/k_1, k_1))/(k_0*k_1 - 1))
Eq(F_28(x, k_0), F_29(x, k_0)*F_9(x))
Eq(F_29(x, k_0), F_16(x, 1, k_0))
Eq(F_30(x, k_0, k_1), F_19(x, k_1)*F_27(x, k_0, k_1))
Eq(F_31(x), F_32(x)*F_9(x))
Eq(F_32(x), F_12(x, 1))
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, 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": [1, 0, 3, 4, 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, 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": []}, 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