02143_02413_02431_20143_20413_20431_21043_21403_24013_24031_24103
Counting sequence:
1, 1, 2, 6, 24, 109, 522, 2568, 12846, 65017, 331980, 1706894, 8825656, 45848634, 239134024, 1251583062, 6570518886, 34587294736, 182512745056, 965234994495, 5115119832718, 27157739279588, 144440344638422, 769467835728910, 4105403172231248, 21935426356110474, 117361887561002322, 628735812662861259, 3372420813180447372, 18110174221145865626, 97361620504484481682, 523981659122164165389, 2822850767156641073756, 15222468813997362977467, 82165711282775447096932, 443903515185902715925356, 2400291739858735826466740, 12989811790998495847852499, 70354477521354601761331232, 381345000893752515799669224, 2068568098387903701691528638, 11228859412477756744124510266, 60996465894896331787947187930, 331563382870523901684242744711, 1803480430141673368223551161382, 9815893764558057377141305340023, 53458008884898431987647730664752, 291307441409262649045930238776347, 1588319871894679410239055999655198, 8664909179690736502892358660134515, 47295748705531075014729370461223866, 258288420862912900025560833079271255, 1411255030998378574360560191862484894, 7714665027258087720949971509371532874, 42192298482590668484009228788893977096, 230859433922025397809974846323668110729, 1263730391583928725030964536105261284670, 6920665488938438061171786022335266211172, 37915989452496191268209668534383405230952, 207813009251886610911964440583119941623239, 1139446047698370958823381985739615764253710, 6250008213173285532155131282159997073677029, 34294815449125513360179323011727593967692418, 188249080346983539611650314943159438037649569, 1033687792362000666644529072788074896657888966, 5677979561405717814816056044306213110296589832, 31199103403404072082964941596242838711877749490, 171486659196902201991150506351959380252619303241, 942876329223880717420629618877327579380079224340, 5185750992181534553371429076477026404502839952974, 28529726950715242328530641018431668222862233966768, 157003460130566768377636415321901336449975448677959, 864257640745595835337539224499337333398986358155392, 4758789400042225671680850831705719807456717339067114, 26209936339141139332318134083471404519754213520664282, 144393866033072583288076721764926292343254448381167320, 795686514077429091683441675681937950313524771036220550, 4385741184800026826634420079316592857889140248683403359, 24179600307566115848968167909483313363365059239901489574, 133339189351210672060474119643444905282484812153528286507, 735472809276230532799403335709044606206149915614024055616, 4057636854812777311063705655532450085095933859695101142499, 22391087215726272631288497400225748794962339152736306476970, 123586325015857224982404211210230814326165704955877026444204, 682270731356586984097337165952558786456229219323850531458354, 3767316212893565119995212553427912344440177592009228162278510, 20806278684436943507483760118224408736791579535495558967340228, 114932223174763986001324743377923320021058612774154285275212110, 634998036117689056657309286294513320185667768282623233949300774, 3509007638013446026554315904830093114414325706717965749205462308, 19394377176343051288861513181201882283244949925701074808926861314, 107212455897667987160285050104592965368998322008584724149650351763, 592776363753387669416115723480320383054529624303944533635332025254, 3278016487887475589284453778636969378177122799419649938604869730563, 18130277603762010018174284233539365141353546146353084198414931570270, 100292701468545454033152826681182150772418256498620646212259670248741, 554886675818556777749040245633803674010691679205718138175949760663116, 3070491744141047201507152393559685803319990463202141082962534177256300, 16993344564152102629295393108222993352966154064233626032161049782275112, 94062333044559321049879392744728928735809287681244587217261383656103584, 520735617158118895660956331449041208393677203820993826272221774009687844
Specification 1
Strategy pack name: row_and_col_placements_tracked_fusion
Tree: http://permpal.com/tree/24245/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[12,x]*F[3,x]
F[3,x] = F[1,x]+F[39,x]+F[4,x]
F[4,x] = F[12,x]*F[5,x]
F[5,x] = F[1,x]+F[13,x]+F[38,x]+F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[12,x]*F[8,x,k[0]]
F[8,x,k[0]] = F[5,x]+F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]
F[10,x,k[0]] = F[0,x]*F[11,x,k[0]]*F[8,x,k[0]]
F[11,x,k[0]] = k[0]*x
F[12,x] = x
F[13,x] = F[12,x]*F[14,x]
F[14,x] = F[15,x,1]
F[15,x,k[0]] = (F[16,x,k[0]]*k[0]-F[16,x,1])/(-1+k[0])
F[16,x,k[0]] = F[1,x]+F[17,x,k[0]]+F[22,x,k[0]]+F[31,x,k[0]]
F[17,x,k[0]] = F[12,x]*F[18,x,k[0]]
F[18,x,k[0]] = 1/(-1+k[0])*(F[19,x,k[0]]*k[0]-F[19,x,1])
F[19,x,k[0]] = F[20,x,k[0]]+F[3,x]
F[20,x,k[0]] = F[21,x,k[0]]
F[21,x,k[0]] = F[0,x]*F[11,x,k[0]]*F[19,x,k[0]]
F[22,x,k[0]] = F[23,x,1,k[0]]
F[23,x,k[0],k[1]] = F[11,x,k[0]]*F[24,x,k[0],k[1]]
F[24,x,k[0],k[1]] = (F[25,x,k[0],1]*k[0]-F[25,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[25,x,k[0],k[1]] = F[1,x]+F[26,x,k[0],k[1]]+F[29,x,k[0],k[1]]+F[30,x,k[0],k[1]]
F[26,x,k[0],k[1]] = F[27,x,k[0],k[0]*k[1]]
F[27,x,k[0],k[1]] = F[12,x]*F[28,x,k[0],k[1]]
F[28,x,k[0],k[1]] = (F[19,x,k[0]]*k[0]-F[19,x,k[1]]*k[1])/(-k[1]+k[0])
F[29,x,k[0],k[1]] = F[23,x,k[0],k[0]*k[1]]
F[30,x,k[0],k[1]] = F[11,x,k[1]]*F[25,x,k[0],k[1]]
F[31,x,k[0]] = F[11,x,k[0]]*F[32,x,k[0]]
F[32,x,k[0]] = 1/(-1+k[0])*(F[33,x,1,k[0]]*k[0]-F[33,x,1/k[0],k[0]])
F[33,x,k[0],k[1]] = F[1,x]+F[34,x,k[0],k[1]]+F[35,x,k[0],k[1]]+F[36,x,k[0],k[1]]
F[34,x,k[0],k[1]] = F[27,x,k[0]*k[1],k[1]]
F[35,x,k[0],k[1]] = F[23,x,k[0]*k[1],k[1]]
F[36,x,k[0],k[1]] = F[11,x,k[1]]*F[37,x,k[0],k[1]]
F[37,x,k[0],k[1]] = (F[33,x,k[0],k[1]]*k[0]-F[33,x,1,k[1]])/(-1+k[0])
F[38,x] = F[31,x,1]
F[39,x] = F[12,x]*F[40,x]
F[40,x] = F[16,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_{12}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{39}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{12}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)+F_{38}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{5}\! \left(x \right)+F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)
F_{10}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{11}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = y x
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x , 1\right)
F_{15}\! \left(x , y\right) = \frac{F_{16}\! \left(x , y\right) y -F_{16}\! \left(x , 1\right)}{-1+y}
F_{16}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)+F_{22}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{18}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = \frac{F_{19}\! \left(x , y\right) y -F_{19}\! \left(x , 1\right)}{-1+y}
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)+F_{3}\! \left(x \right)
F_{20}\! \left(x , y\right) = F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = F_{0}\! \left(x \right) F_{11}\! \left(x , y\right) F_{19}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , 1, y\right)
F_{23}\! \left(x , y , z\right) = F_{11}\! \left(x , y\right) F_{24}\! \left(x , y , z\right)
F_{24}\! \left(x , y , z\right) = \frac{F_{25}\! \left(x , y , 1\right) y -F_{25}\! \left(x , y , \frac{z}{y}\right) z}{-z +y}
F_{25}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{26}\! \left(x , y , z\right)+F_{29}\! \left(x , y , z\right)+F_{30}\! \left(x , y , z\right)
F_{26}\! \left(x , y , z\right) = F_{27}\! \left(x , y , y z \right)
F_{27}\! \left(x , y , z\right) = F_{12}\! \left(x \right) F_{28}\! \left(x , y , z\right)
F_{28}\! \left(x , y , z\right) = \frac{F_{19}\! \left(x , y\right) y -F_{19}\! \left(x , z\right) z}{-z +y}
F_{29}\! \left(x , y , z\right) = F_{23}\! \left(x , y , y z \right)
F_{30}\! \left(x , y , z\right) = F_{11}\! \left(x , z\right) F_{25}\! \left(x , y , z\right)
F_{31}\! \left(x , y\right) = F_{11}\! \left(x , y\right) F_{32}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = \frac{F_{33}\! \left(x , 1, y\right) y -F_{33}\! \left(x , \frac{1}{y}, y\right)}{-1+y}
F_{33}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{34}\! \left(x , y , z\right)+F_{35}\! \left(x , y , z\right)+F_{36}\! \left(x , y , z\right)
F_{34}\! \left(x , y , z\right) = F_{27}\! \left(x , y z , z\right)
F_{35}\! \left(x , y , z\right) = F_{23}\! \left(x , y z , z\right)
F_{36}\! \left(x , y , z\right) = F_{11}\! \left(x , z\right) F_{37}\! \left(x , y , z\right)
F_{37}\! \left(x , y , z\right) = \frac{F_{33}\! \left(x , y , z\right) y -F_{33}\! \left(x , 1, z\right)}{-1+y}
F_{38}\! \left(x \right) = F_{31}\! \left(x , 1\right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{16}\! \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_12(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_39(x) + F_4(x))
Eq(F_4(x), F_12(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_13(x) + F_38(x) + F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_12(x)*F_8(x, k_0))
Eq(F_8(x, k_0), F_5(x) + F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0))
Eq(F_10(x, k_0), F_0(x)*F_11(x, k_0)*F_8(x, k_0))
Eq(F_11(x, k_0), k_0*x)
Eq(F_12(x), x)
Eq(F_13(x), F_12(x)*F_14(x))
Eq(F_14(x), F_15(x, 1))
Eq(F_15(x, k_0), (-k_0*F_16(x, k_0) + F_16(x, 1))/(1 - k_0))
Eq(F_16(x, k_0), F_1(x) + F_17(x, k_0) + F_22(x, k_0) + F_31(x, k_0))
Eq(F_17(x, k_0), F_12(x)*F_18(x, k_0))
Eq(F_18(x, k_0), (k_0*F_19(x, k_0) - F_19(x, 1))/(k_0 - 1))
Eq(F_19(x, k_0), F_20(x, k_0) + F_3(x))
Eq(F_20(x, k_0), F_21(x, k_0))
Eq(F_21(x, k_0), F_0(x)*F_11(x, k_0)*F_19(x, k_0))
Eq(F_22(x, k_0), F_23(x, 1, k_0))
Eq(F_23(x, k_0, k_1), F_11(x, k_0)*F_24(x, k_0, k_1))
Eq(F_24(x, k_0, k_1), (-k_0*F_25(x, k_0, 1) + k_1*F_25(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_25(x, k_0, k_1), F_1(x) + F_26(x, k_0, k_1) + F_29(x, k_0, k_1) + F_30(x, k_0, k_1))
Eq(F_26(x, k_0, k_1), F_27(x, k_0, k_0*k_1))
Eq(F_27(x, k_0, k_1), F_12(x)*F_28(x, k_0, k_1))
Eq(F_28(x, k_0, k_1), (-k_0*F_19(x, k_0) + k_1*F_19(x, k_1))/(-k_0 + k_1))
Eq(F_29(x, k_0, k_1), F_23(x, k_0, k_0*k_1))
Eq(F_30(x, k_0, k_1), F_11(x, k_1)*F_25(x, k_0, k_1))
Eq(F_31(x, k_0), F_11(x, k_0)*F_32(x, k_0))
Eq(F_32(x, k_0), (k_0*F_33(x, 1, k_0) - F_33(x, 1/k_0, k_0))/(k_0 - 1))
Eq(F_33(x, k_0, k_1), F_1(x) + F_34(x, k_0, k_1) + F_35(x, k_0, k_1) + F_36(x, k_0, k_1))
Eq(F_34(x, k_0, k_1), F_27(x, k_0*k_1, k_1))
Eq(F_35(x, k_0, k_1), F_23(x, k_0*k_1, k_1))
Eq(F_36(x, k_0, k_1), F_11(x, k_1)*F_37(x, k_0, k_1))
Eq(F_37(x, k_0, k_1), (-k_0*F_33(x, k_0, k_1) + F_33(x, 1, k_1))/(1 - k_0))
Eq(F_38(x), F_31(x, 1))
Eq(F_39(x), F_12(x)*F_40(x))
Eq(F_40(x), F_16(x, 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:
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