0132_0231_0321_1203_2031
Counting sequence:
1, 1, 2, 6, 19, 58, 173, 512, 1512, 4461, 13154, 38775, 114290, 336878, 993015, 2927210, 8629001, 25437304, 74986488, 221052377, 651639234, 1920963275, 5662793842, 16693305974, 49210062347, 145065941754, 427638704501, 1260632646832, 3716208708168, 10954981410837, 32294100624642, 95199516739663, 280637881705170, 827290130785694, 2438761853241743, 7189206247267818, 21193002668604081, 62474680326808872, 184168602388624600, 542909126196623585, 1600437400753794082, 4717916406519420995, 13907907431076050578, 40999007282995696870, 120860640360292596931, 356284099453305815354, 1050287001168023487101, 3096132514796952805472, 9127063877323301437352, 26905597426020559562237, 79314791983616868667426, 233811430677264766779879, 689250816249274263217842, 2031836879506699388419534, 5989635423849043655336423, 17656797586692797161227498, 52050330104581992771192217, 153438745089188488978039000, 452320829613190761892054712, 1333392897491711456340745769, 3930698085696765449938017282, 11587272941054688723808147323, 34158027730256988751126001714, 100694172335152088165834456022, 296835532259960043634294740539, 875039053092194986969143610106, 2579520512948271206226754655685, 7604147555708976927825996429584, 22416204778657006013647000118792, 66080547884875388657679786485029, 194798310056610847960758707848386, 574244355041080367763332127154751, 1692810267197466645982284645001746, 4990221628777105315611067695743102, 14710633782687216167309538475410943, 43365357770967310676734263516342122, 127836385731877754456236120838852033, 376847842540580736393085233446968200, 1110906692288290511366323686714141080, 3274832809578883163541078408115699633, 9653853023968647953273615682824202594, 28458514870068425943920658631177418355, 83892624695975061063306913910284752210, 247306386524828606903611449739159223110, 729032486915411046897889264846111907955, 2149108943147772684629749078664314261562, 6335340787157042412967776738464812154189, 18675899617554113892582829692236669956800, 55054532698859850757068491974906667548008, 162294809500950998488494035077218167590797, 478427549917165190939607980829244037411554, 1410352686099923283296221273030791529592663, 4157567221063377359652560528609647862426866, 12256058621379467128107308194249756805816750, 36129535601897167690526666371199980108692439, 106505964367020419688563160293102303913700714, 313968066756810825872498781327103666213578025, 925543912295049543855978427892813642046691640, 2728403376926687662529375949707286514102771064, 8043038140422513131063895578633796846280687481, 23710006766360000027686574433579743932097303618
Generating function in Maple syntax:
(2*x-1)*(x-1)^4/(8*x^5-21*x^4+27*x^3-19*x^2+7*x-1)
Generating function in latex syntax:
\frac{\left(2 x -1\right) \left(x -1\right)^{4}}{8 x^{5}-21 x^{4}+27 x^{3}-19 x^{2}+7 x -1}
Generating function in sympy syntax:
(x - 1)**4*(2*x - 1)/(8*x**5 - 21*x**4 + 27*x**3 - 19*x**2 + 7*x - 1)
Implicit equation for the generating function in Maple syntax:
(8*x^5-21*x^4+27*x^3-19*x^2+7*x-1)*F(x)-(2*x-1)*(x-1)^4 = 0
Implicit equation for the generating function in latex syntax:
\left(8 x^{5}-21 x^{4}+27 x^{3}-19 x^{2}+7 x -1\right) F \! \left(x \right)-\left(2 x -1\right) \left(x -1\right)^{4} = 0
Explicit closed form in Maple syntax:
3056/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+3)+3056/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+3)+3056/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+3)+3056/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+3)+3056/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+3)-9054/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+2)-9054/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+2)-9054/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+2)-9054/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+2)-9054/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+2)+10333/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+1)+10333/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+1)+10333/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+1)+10333/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+1)+10333/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+1)+1487/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n-1)+1487/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n-1)+1487/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n-1)+1487/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n-1)+1487/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n-1)-5704/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n)-5704/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n)-5704/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n)-5704/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n)-5704/4757*RootOf(8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n)+piecewise(n = 0,1/4,0)
Explicit closed form in latex syntax:
\frac{3056 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{4757}+\frac{3056 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{4757}+\frac{3056 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{4757}+\frac{3056 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{4757}+\frac{3056 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{4757}-\frac{9054 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{4757}-\frac{9054 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{4757}-\frac{9054 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{4757}-\frac{9054 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{4757}-\frac{9054 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{4757}+\frac{10333 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{4757}+\frac{10333 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{4757}+\frac{10333 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{4757}+\frac{10333 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{4757}+\frac{10333 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +1}}{4757}+\frac{1487 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{4757}+\frac{1487 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{4757}+\frac{1487 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{4757}+\frac{1487 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{4757}+\frac{1487 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{4757}-\frac{5704 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{4757}-\frac{5704 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{4757}-\frac{5704 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{4757}-\frac{5704 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{4757}-\frac{5704 \mathit{RootOf}\! \left(8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{4757}+\left(\left\{\begin{array}{cc}\frac{1}{4} & n =0 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 58
a(n+5) = 8*a(n)-21*a(n+1)+27*a(n+2)-19*a(n+3)+7*a(n+4), n >= 6
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 19
a \! \left(5\right) = 58
a \! \left(n +5\right) = 8 a \! \left(n \right)-21 a \! \left(n +1\right)+27 a \! \left(n +2\right)-19 a \! \left(n +3\right)+7 a \! \left(n +4\right), \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18663/
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[3,x] = F[12,x]*F[4,x]
F[4,x] = F[18,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[12,x]+F[14,x]
F[14,x] = F[15,x]+F[16,x]+F[17,x]
F[15,x] = 0
F[16,x] = F[10,x]*F[12,x]
F[17,x] = F[12,x]*F[13,x]
F[18,x] = F[19,x]+F[2,x]
F[19,x] = F[15,x]+F[20,x]+F[42,x]
F[20,x] = F[12,x]*F[21,x]
F[21,x] = F[22,x]+F[29,x]
F[22,x] = F[23,x]+F[6,x]
F[23,x] = F[24,x]
F[24,x] = F[12,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[12,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[12,x]*F[26,x]
F[29,x] = F[19,x]+F[30,x]
F[30,x] = 2*F[15,x]+F[31,x]+F[35,x]
F[31,x] = F[12,x]*F[32,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[23,x]
F[34,x] = F[30,x]
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]+F[40,x]
F[38,x] = F[39,x]
F[39,x] = F[12,x]*F[2,x]
F[40,x] = F[41,x]
F[41,x] = F[12,x]*F[37,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[44,x]+F[57,x]
F[44,x] = F[2,x]+F[45,x]
F[45,x] = F[15,x]+F[46,x]+F[56,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[48,x]+F[50,x]
F[48,x] = F[10,x]+F[49,x]
F[49,x] = F[28,x]
F[50,x] = F[45,x]+F[51,x]
F[51,x] = 2*F[15,x]+F[41,x]+F[52,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[54,x]+F[55,x]
F[54,x] = F[49,x]
F[55,x] = F[51,x]
F[56,x] = F[12,x]*F[44,x]
F[57,x] = F[38,x]+F[58,x]
F[58,x] = 2*F[15,x]+F[59,x]+F[60,x]
F[59,x] = F[12,x]*F[45,x]
F[60,x] = F[12,x]*F[57,x]
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_{3}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{18}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
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 \right)+F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{17}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{2}\! \left(x \right)
F_{19}\! \left(x \right) = F_{15}\! \left(x \right)+F_{20}\! \left(x \right)+F_{42}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{29}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{6}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{12}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{29}\! \left(x \right) = F_{19}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{31}\! \left(x \right) = F_{12}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{23}\! \left(x \right)
F_{34}\! \left(x \right) = F_{30}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{40}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{2}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{57}\! \left(x \right)
F_{44}\! \left(x \right) = F_{2}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{15}\! \left(x \right)+F_{46}\! \left(x \right)+F_{56}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{50}\! \left(x \right)
F_{48}\! \left(x \right) = F_{10}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{28}\! \left(x \right)
F_{50}\! \left(x \right) = F_{45}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{41}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{55}\! \left(x \right)
F_{54}\! \left(x \right) = F_{49}\! \left(x \right)
F_{55}\! \left(x \right) = F_{51}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{57}\! \left(x \right) = F_{38}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{59}\! \left(x \right)+F_{60}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \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))
Eq(F_3(x), F_12(x)*F_4(x))
Eq(F_4(x), F_18(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_12(x) + F_14(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_17(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_10(x)*F_12(x))
Eq(F_17(x), F_12(x)*F_13(x))
Eq(F_18(x), F_19(x) + F_2(x))
Eq(F_19(x), F_15(x) + F_20(x) + F_42(x))
Eq(F_20(x), F_12(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_29(x))
Eq(F_22(x), F_23(x) + F_6(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_12(x)*F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_12(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_12(x)*F_26(x))
Eq(F_29(x), F_19(x) + F_30(x))
Eq(F_30(x), 2*F_15(x) + F_31(x) + F_35(x))
Eq(F_31(x), F_12(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_23(x))
Eq(F_34(x), F_30(x))
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x) + F_40(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_12(x)*F_2(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_12(x)*F_37(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_57(x))
Eq(F_44(x), F_2(x) + F_45(x))
Eq(F_45(x), F_15(x) + F_46(x) + F_56(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_50(x))
Eq(F_48(x), F_10(x) + F_49(x))
Eq(F_49(x), F_28(x))
Eq(F_50(x), F_45(x) + F_51(x))
Eq(F_51(x), 2*F_15(x) + F_41(x) + F_52(x))
Eq(F_52(x), F_12(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_55(x))
Eq(F_54(x), F_49(x))
Eq(F_55(x), F_51(x))
Eq(F_56(x), F_12(x)*F_44(x))
Eq(F_57(x), F_38(x) + F_58(x))
Eq(F_58(x), 2*F_15(x) + F_59(x) + F_60(x))
Eq(F_59(x), F_12(x)*F_45(x))
Eq(F_60(x), F_12(x)*F_57(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "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.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "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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1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 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