01234_01243_02134_02143_02413_20134_20143_20413_24013
Counting sequence:
1, 1, 2, 6, 24, 111, 546, 2758, 14121, 72932, 379231, 1983307, 10425256, 55050742, 291892450, 1553447501, 8295426185, 44434876300, 238695586620, 1285601246082, 6941092673295, 37560987868771, 203690041999284, 1106799574233399, 6025360005839814, 32859814347750211, 179503403504655048, 982124877417009223, 5381598144953067362, 29530661696958048473, 162263827876417584015, 892746829308724006678, 4917749027160501841948, 27121330738447968908884, 149740389223496565451950, 827615174172554032037294, 4578877061182250063785615, 25357785486439001615189802, 140561810964740224773586866, 779848002582056365043033032, 4330350703709187990385040223, 24065309107783525077742548503, 133844553630437544712557479123, 744967356249616697511842652794, 4149427516362250995995884100225, 23128172761361217572385870811615, 128998630117897739657798862744989, 719960284778277811372773966129514, 4020695989552680769210030122012218, 22467425049128181673450875063291235, 125619002446776393729687894790686206, 702746063800723566589743504335450500, 3933453770217877900668777836662969394, 22027952967522564771417314549308039625, 123421549187984058704204550977965269799, 691858488617310432511138140108302765812, 3880127441569636468141063869847379255425, 21770603813916173580725070443429296122006, 122203702686801506668324679096838551316909, 686248784233576995003299474278890989070481, 3855283710467515020408696432126321982204925, 21667214757880154710469681013108487953848577, 121819418738732347318153003665511777769722381, 685159336341029004539895402570706290387072900, 3854991361336787234769311324480564212966213678, 21697383593075411146262785029730106561156277016, 122162807823143223014108031399317746370789330807, 688040597575557277869805955910325125607238314870, 3876398847702312247145398389355542762862355939939, 21846318510661054095752039323687814453244158364472, 123157175378102589250900362999310843760478432516405, 694495156025568005774704252840692113235862990055728, 3917448511566274554600044354484314764173507616068641, 22103376232400046870447105223309329048326395845496163, 124747535604179441935689672255276284718312612711405715, 704239358055507806580988806865790967750988486160671405, 3976679648021655516909569539697574607198086762283800809, 22461050444783991533077865685896270825407431740211784659, 126895410724437580998026894922327147092243288333586927854, 717076546364541458205653456225675376186382281935421262231, 4053090678839170137061801073320716747099212727417032031410, 22914261419632656534176835080231291475756342894665517048788, 129575166847099933644770267112946406241355484904208965289677, 732878147152278853254112340295523118278881019730334009703671, 4146041468234200859897090855169514138176402465831218228583323, 23459851173643449294595164939038505700338554389137093393454386, 132771403465576259741717495374448693946527456843454297272037812, 751570164632403839198087298816958725173166734972257096632074097, 4255183420839635707776214763890089149295759155850271588491951712, 24096221527997043892603249074407545620934751041060347302177677506, 136477078786249666159487201852377226380144534484327184468270684916, 773123468641022954497513409004511282270007278637357762307498513273, 4380409153762139998337780054723477117325770696630982189910470583772, 24823073287877435276727617510786027414445995524182341850589091034177, 140692158003116534079533087744813764109492750131691791762984168066769, 797546789585736401224978956591438880083207899147735721281660309296679, 4521816199763140985766598353859951116389930607331114004497787967161673, 25641218217868573687648244788739816746068229600854680087489002481554506, 145422639655414431927795513529492750542081260448738778230833119660841303, 824881679178326634265817441831511522768260597552874368899381197038131499, 4679680942321025448007631777931369984535010138070852063519907587827496366
Specification 1
Strategy pack name: row_and_col_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24185/
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[26,x,k[0],k[1]]+F[34,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[24,x,k[0]]
F[24,x,k[0]] = F[25,x,k[0]]
F[25,x,k[0]] = F[22,x,k[0]]*F[23,x,k[0]]
F[26,x,k[0],k[1]] = F[22,x,k[0]]*F[27,x,k[0],k[1]]
F[27,x,k[0],k[1]] = F[28,x,k[0],k[1]]+F[9,x,k[0]]
F[28,x,k[0],k[1]] = F[29,x,k[0],k[1]]
F[29,x,k[0],k[1]] = F[22,x,k[1]]*F[23,x,k[0]]*F[30,x,k[0]]
F[31,x,k[0],k[1]] = F[30,x,k[0]]+F[33,x,k[0],k[1]]
F[32,x,k[0],k[1]] = F[22,x,k[1]]*F[23,x,k[1]]*F[31,x,k[0],k[1]]
F[32,x,k[0],k[1]] = F[33,x,k[0],k[1]]
F[11,x,k[0],k[1]] = F[33,x,k[0],k[1]]+F[4,x,k[0]]
F[34,x,k[0],k[1]] = F[22,x,k[1]]*F[35,x,k[0],k[1]]
F[35,x,k[0],k[1]] = F[11,x,k[0],k[1]]+F[33,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{y F_{4}\! \left(x , y\right)-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_{26}\! \left(x , y , z\right)+F_{34}\! \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{y F_{14}\! \left(x , y , z\right)-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{y F_{17}\! \left(x , y\right)-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_{24}\! \left(x , y\right)
F_{24}\! \left(x , y\right) = F_{25}\! \left(x , y\right)
F_{25}\! \left(x , y\right) = F_{22}\! \left(x , y\right) F_{23}\! \left(x , y\right)
F_{26}\! \left(x , y , z\right) = F_{22}\! \left(x , y\right) F_{27}\! \left(x , y , z\right)
F_{27}\! \left(x , y , z\right) = F_{28}\! \left(x , y , z\right)+F_{9}\! \left(x , y\right)
F_{28}\! \left(x , y , z\right) = F_{29}\! \left(x , y , z\right)
F_{29}\! \left(x , y , z\right) = F_{22}\! \left(x , z\right) F_{23}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{31}\! \left(x , y , z\right) = F_{30}\! \left(x , y\right)+F_{33}\! \left(x , y , z\right)
F_{32}\! \left(x , y , z\right) = F_{22}\! \left(x , z\right) F_{23}\! \left(x , z\right) F_{31}\! \left(x , y , z\right)
F_{32}\! \left(x , y , z\right) = F_{33}\! \left(x , y , z\right)
F_{11}\! \left(x , y , z\right) = F_{33}\! \left(x , y , z\right)+F_{4}\! \left(x , y\right)
F_{34}\! \left(x , y , z\right) = F_{22}\! \left(x , z\right) F_{35}\! \left(x , y , z\right)
F_{35}\! \left(x , y , z\right) = F_{11}\! \left(x , y , z\right)+F_{33}\! \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_26(x, k_0, k_1) + F_34(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_24(x, k_0))
Eq(F_24(x, k_0), F_25(x, k_0))
Eq(F_25(x, k_0), F_22(x, k_0)*F_23(x, k_0))
Eq(F_26(x, k_0, k_1), F_22(x, k_0)*F_27(x, k_0, k_1))
Eq(F_27(x, k_0, k_1), F_28(x, k_0, k_1) + F_9(x, k_0))
Eq(F_28(x, k_0, k_1), F_29(x, k_0, k_1))
Eq(F_29(x, k_0, k_1), F_22(x, k_1)*F_23(x, k_0)*F_30(x, k_0))
Eq(F_31(x, k_0, k_1), F_30(x, k_0) + F_33(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), F_22(x, k_1)*F_23(x, k_1)*F_31(x, k_0, k_1))
Eq(F_32(x, k_0, k_1), F_33(x, k_0, k_1))
Eq(F_11(x, k_0, k_1), F_33(x, k_0, k_1) + F_4(x, k_0))
Eq(F_34(x, k_0, k_1), F_22(x, k_1)*F_35(x, k_0, k_1))
Eq(F_35(x, k_0, k_1), F_11(x, k_0, k_1) + F_33(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, 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": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": 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