0123_0132_0321_1302_2130
Counting sequence:
1, 1, 2, 6, 19, 50, 117, 269, 615, 1386, 3090, 6845, 15089, 33118, 72430, 157956, 343662, 746220, 1617639, 3501809, 7571719, 16355593, 35299931, 76132941, 164100198, 353527007, 761283241, 1638733133, 3526406184, 7586453828, 16317172702, 35088537599, 75441859387, 162179854271, 348600431235, 749226589280, 1610123963701, 3459967141881, 7434572474738, 15974067764426, 34320537282557, 73735170571319, 158409032655024, 340307913546315, 731059796933104, 1570450026406439, 3373549553516155, 7246745440190418, 15566567999980311, 33437789916853918, 71825362303260993, 154281655992532920, 331396188800725244, 711832718175708310, 1528994770996748145, 3284218288747419074, 7054338315828865388, 15152317343058278885, 32546219601712026712, 69907045387556116750, 150155209734923541109, 322521788034780158226, 692750781399999473023, 1487970771436216895353, 3196033122933578037117, 6864797180608143018934, 14744966136207963308864, 31670836292718988459757, 68026012089802798210747, 146113471766166086949702, 313837842209628921531760, 674093575101679231967608, 1447887839482874098517900, 3109922227332686008548448, 6679808762302624236978189, 14347572840985976613119945, 30817171053798352680141625, 66192233024384988787829849, 142174345744689277250746997, 305376346606165714225049257, 655917940176871029366858124, 1408846209721463220128203547, 3026060700084792356718454919, 6499675222752524446886190925, 13960650489682499849687760866, 29986075718762624553591010844, 64407077824457294243046064048, 138339927395771399665758056899, 297140246394622398167889159881, 638227340189479779213934852611, 1370848056828633404615244918489, 2944443528866383863544708951720, 6324367985610293671194096013527, 13584104944787163953837200065017, 29177287837650936032247209813692, 62669871953124990853736218328918, 134608564050895730138103900392435, 289125616905544585258957230376643, 621012655789180110278691507745886, 1333872525068313725471669873030843, 2865023584908834257095894064806618
Generating function in Maple syntax:
(3*x^9+8*x^8+11*x^7+5*x^6-4*x^5-6*x^4-x^3+2*x-1)/(x-1)/(x^2+1)/(x^3+2*x^2+x-1)/(x^3+x^2+x-1)
Generating function in latex syntax:
\frac{3 x^{9}+8 x^{8}+11 x^{7}+5 x^{6}-4 x^{5}-6 x^{4}-x^{3}+2 x -1}{\left(x -1\right) \left(x^{2}+1\right) \left(x^{3}+2 x^{2}+x -1\right) \left(x^{3}+x^{2}+x -1\right)}
Generating function in sympy syntax:
(3*x**9 + 8*x**8 + 11*x**7 + 5*x**6 - 4*x**5 - 6*x**4 - x**3 + 2*x - 1)/((x - 1)*(x**2 + 1)*(x**3 + x**2 + x - 1)*(x**3 + 2*x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
(x-1)*(x^2+1)*(x^3+2*x^2+x-1)*(x^3+x^2+x-1)*F(x)-3*x^9-8*x^8-11*x^7-5*x^6+4*x^5+6*x^4+x^3-2*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(x^{2}+1\right) \left(x^{3}+2 x^{2}+x -1\right) \left(x^{3}+x^{2}+x -1\right) F \! \left(x \right)-3 x^{9}-8 x^{8}-11 x^{7}-5 x^{6}+4 x^{5}+6 x^{4}+x^{3}-2 x +1 = 0
Explicit closed form in Maple syntax:
78425/24552*Sum(_alpha^(-n+7),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))+392743/49104*Sum(_alpha^(-n+6),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))+251699/24552*Sum(_alpha^(-n+5),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))+75323/49104*Sum(_alpha^(-n+4),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))-292411/49104*Sum(_alpha^(-n+3),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))-616471/49104*Sum(_alpha^(-n+2),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))-148019/24552*Sum(_alpha^(-n+1),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))-309281/49104*Sum(_alpha^(-n),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))+35147/5456*Sum(_alpha^(-n-1),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))+piecewise(n = 0,3,0)
Explicit closed form in latex syntax:
\frac{78425 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +7}\right)}{24552}+\frac{392743 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +6}\right)}{49104}+\frac{251699 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +5}\right)}{24552}+\frac{75323 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +4}\right)}{49104}-\frac{292411 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +3}\right)}{49104}-\frac{616471 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +2}\right)}{49104}-\frac{148019 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +1}\right)}{24552}-\frac{309281 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n}\right)}{49104}+\frac{35147 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n -1}\right)}{5456}+\left(\left\{\begin{array}{cc}3 & 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) = 50
a(6) = 117
a(7) = 269
a(8) = 615
a(9) = 1386
a(n+8) = -a(n)-3*a(n+1)-5*a(n+2)-4*a(n+3)-2*a(n+4)+a(n+5)+a(n+6)+2*a(n+7)-17, n >= 10
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) = 50
a \! \left(6\right) = 117
a \! \left(7\right) = 269
a \! \left(8\right) = 615
a \! \left(9\right) = 1386
a \! \left(n +8\right) = -a \! \left(n \right)-3 a \! \left(n +1\right)-5 a \! \left(n +2\right)-4 a \! \left(n +3\right)-2 a \! \left(n +4\right)+a \! \left(n +5\right)+a \! \left(n +6\right)+2 a \! \left(n +7\right)-17, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16262/
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[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[19,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = F[1,x]+F[4,x]
F[11,x] = F[12,x]+F[14,x]
F[12,x] = F[13,x]
F[13,x] = F[10,x]*F[4,x]
F[14,x] = F[15,x]+F[16,x]+F[18,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[4,x]
F[18,x] = F[12,x]*F[4,x]
F[19,x] = F[2,x]+F[20,x]
F[20,x] = F[111,x]+F[15,x]+F[21,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[30,x]
F[23,x] = F[24,x]+F[7,x]
F[24,x] = F[15,x]+F[25,x]+F[28,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[17,x]+F[27,x]
F[27,x] = F[16,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[11,x]
F[30,x] = F[31,x]+F[91,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[36,x]
F[34,x] = F[35,x]+F[7,x]
F[35,x] = F[25,x]
F[36,x] = F[31,x]+F[37,x]
F[37,x] = 2*F[15,x]+F[38,x]+F[59,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[44,x]
F[40,x] = F[35,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[27,x]
F[44,x] = F[45,x]+F[50,x]
F[45,x] = F[46,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[48,x]+F[49,x]
F[48,x] = F[35,x]
F[49,x] = F[45,x]
F[50,x] = F[51,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = F[41,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[57,x]+F[58,x]
F[57,x] = F[41,x]
F[58,x] = F[55,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[88,x]
F[61,x] = F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[65,x]+F[67,x]
F[65,x] = F[4,x]+F[66,x]
F[66,x] = F[25,x]
F[67,x] = F[62,x]+F[68,x]
F[68,x] = 2*F[15,x]+F[59,x]+F[69,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[71,x]+F[73,x]
F[71,x] = F[66,x]+F[72,x]
F[72,x] = F[42,x]
F[73,x] = F[74,x]+F[79,x]
F[74,x] = F[75,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = F[66,x]
F[78,x] = F[74,x]
F[79,x] = F[80,x]
F[80,x] = F[4,x]*F[81,x]
F[81,x] = F[82,x]+F[83,x]
F[82,x] = F[72,x]
F[83,x] = F[84,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[72,x]
F[87,x] = F[84,x]
F[88,x] = F[89,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[62,x]
F[91,x] = 2*F[15,x]+F[59,x]+F[92,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[94,x]+F[96,x]
F[94,x] = F[24,x]+F[95,x]
F[95,x] = F[42,x]
F[96,x] = F[102,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[24,x]
F[101,x] = F[97,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[4,x]
F[104,x] = F[105,x]+F[106,x]
F[105,x] = F[95,x]
F[106,x] = F[107,x]
F[107,x] = F[108,x]*F[4,x]
F[108,x] = F[109,x]+F[110,x]
F[109,x] = F[95,x]
F[110,x] = F[107,x]
F[111,x] = F[112,x]*F[4,x]
F[112,x] = F[113,x]+F[141,x]
F[113,x] = F[114,x]+F[2,x]
F[114,x] = F[115,x]+F[140,x]+F[15,x]
F[115,x] = F[116,x]*F[4,x]
F[116,x] = F[117,x]+F[119,x]
F[117,x] = F[118,x]+F[4,x]
F[118,x] = F[15,x]+F[18,x]+F[25,x]
F[119,x] = F[120,x]+F[62,x]
F[120,x] = 2*F[15,x]+F[121,x]+F[59,x]
F[121,x] = F[122,x]*F[4,x]
F[122,x] = F[123,x]+F[125,x]
F[123,x] = F[118,x]+F[124,x]
F[124,x] = F[42,x]
F[125,x] = F[126,x]+F[131,x]
F[126,x] = F[127,x]
F[127,x] = F[128,x]*F[4,x]
F[128,x] = F[129,x]+F[130,x]
F[129,x] = F[118,x]
F[130,x] = F[126,x]
F[131,x] = F[132,x]
F[132,x] = F[133,x]*F[4,x]
F[133,x] = F[134,x]+F[135,x]
F[134,x] = F[124,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]*F[4,x]
F[137,x] = F[138,x]+F[139,x]
F[138,x] = F[124,x]
F[139,x] = F[136,x]
F[140,x] = F[2,x]*F[4,x]
F[141,x] = F[142,x]+F[146,x]
F[142,x] = F[143,x]
F[143,x] = F[144,x]*F[4,x]
F[144,x] = F[145,x]+F[2,x]
F[145,x] = F[140,x]
F[146,x] = 2*F[15,x]+F[147,x]+F[89,x]
F[147,x] = F[142,x]*F[4,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{19}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{14}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{18}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{111}\! \left(x \right)+F_{15}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{30}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{7}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right)+F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{17}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{16}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{91}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{36}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{7}\! \left(x \right)
F_{35}\! \left(x \right) = F_{25}\! \left(x \right)
F_{36}\! \left(x \right) = F_{31}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{38}\! \left(x \right)+F_{59}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{44}\! \left(x \right)
F_{40}\! \left(x \right) = F_{35}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{27}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{50}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{49}\! \left(x \right)
F_{48}\! \left(x \right) = F_{35}\! \left(x \right)
F_{49}\! \left(x \right) = F_{45}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{54}\! \left(x \right)
F_{53}\! \left(x \right) = F_{41}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{58}\! \left(x \right)
F_{57}\! \left(x \right) = F_{41}\! \left(x \right)
F_{58}\! \left(x \right) = F_{55}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{88}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{67}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{25}\! \left(x \right)
F_{67}\! \left(x \right) = F_{62}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{59}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{73}\! \left(x \right)
F_{71}\! \left(x \right) = F_{66}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{42}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{79}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{66}\! \left(x \right)
F_{78}\! \left(x \right) = F_{74}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{83}\! \left(x \right)
F_{82}\! \left(x \right) = F_{72}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{72}\! \left(x \right)
F_{87}\! \left(x \right) = F_{84}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{62}\! \left(x \right)
F_{91}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{59}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{96}\! \left(x \right)
F_{94}\! \left(x \right) = F_{24}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{42}\! \left(x \right)
F_{96}\! \left(x \right) = F_{102}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{24}\! \left(x \right)
F_{101}\! \left(x \right) = F_{97}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{106}\! \left(x \right)
F_{105}\! \left(x \right) = F_{95}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{4}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{95}\! \left(x \right)
F_{110}\! \left(x \right) = F_{107}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{4}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{141}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{2}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{140}\! \left(x \right)+F_{15}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{4}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{119}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{4}\! \left(x \right)
F_{118}\! \left(x \right) = F_{15}\! \left(x \right)+F_{18}\! \left(x \right)+F_{25}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{62}\! \left(x \right)
F_{120}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{121}\! \left(x \right)+F_{59}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{4}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{125}\! \left(x \right)
F_{123}\! \left(x \right) = F_{118}\! \left(x \right)+F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{42}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{131}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{4}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{130}\! \left(x \right)
F_{129}\! \left(x \right) = F_{118}\! \left(x \right)
F_{130}\! \left(x \right) = F_{126}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{4}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{135}\! \left(x \right)
F_{134}\! \left(x \right) = F_{124}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{4}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{139}\! \left(x \right)
F_{138}\! \left(x \right) = F_{124}\! \left(x \right)
F_{139}\! \left(x \right) = F_{136}\! \left(x \right)
F_{140}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{146}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right) F_{4}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{2}\! \left(x \right)
F_{145}\! \left(x \right) = F_{140}\! \left(x \right)
F_{146}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{147}\! \left(x \right)+F_{89}\! \left(x \right)
F_{147}\! \left(x \right) = F_{142}\! \left(x \right) F_{4}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_19(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), F_1(x) + F_4(x))
Eq(F_11(x), F_12(x) + F_14(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_10(x)*F_4(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_18(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_4(x))
Eq(F_18(x), F_12(x)*F_4(x))
Eq(F_19(x), F_2(x) + F_20(x))
Eq(F_20(x), F_111(x) + F_15(x) + F_21(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_30(x))
Eq(F_23(x), F_24(x) + F_7(x))
Eq(F_24(x), F_15(x) + F_25(x) + F_28(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_17(x) + F_27(x))
Eq(F_27(x), F_16(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_11(x))
Eq(F_30(x), F_31(x) + F_91(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_36(x))
Eq(F_34(x), F_35(x) + F_7(x))
Eq(F_35(x), F_25(x))
Eq(F_36(x), F_31(x) + F_37(x))
Eq(F_37(x), 2*F_15(x) + F_38(x) + F_59(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_44(x))
Eq(F_40(x), F_35(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_27(x))
Eq(F_44(x), F_45(x) + F_50(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_49(x))
Eq(F_48(x), F_35(x))
Eq(F_49(x), F_45(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), F_41(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_58(x))
Eq(F_57(x), F_41(x))
Eq(F_58(x), F_55(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_88(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_67(x))
Eq(F_65(x), F_4(x) + F_66(x))
Eq(F_66(x), F_25(x))
Eq(F_67(x), F_62(x) + F_68(x))
Eq(F_68(x), 2*F_15(x) + F_59(x) + F_69(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_73(x))
Eq(F_71(x), F_66(x) + F_72(x))
Eq(F_72(x), F_42(x))
Eq(F_73(x), F_74(x) + F_79(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_66(x))
Eq(F_78(x), F_74(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_4(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_83(x))
Eq(F_82(x), F_72(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_72(x))
Eq(F_87(x), F_84(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_62(x))
Eq(F_91(x), 2*F_15(x) + F_59(x) + F_92(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_96(x))
Eq(F_94(x), F_24(x) + F_95(x))
Eq(F_95(x), F_42(x))
Eq(F_96(x), F_102(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_24(x))
Eq(F_101(x), F_97(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_4(x))
Eq(F_104(x), F_105(x) + F_106(x))
Eq(F_105(x), F_95(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x)*F_4(x))
Eq(F_108(x), F_109(x) + F_110(x))
Eq(F_109(x), F_95(x))
Eq(F_110(x), F_107(x))
Eq(F_111(x), F_112(x)*F_4(x))
Eq(F_112(x), F_113(x) + F_141(x))
Eq(F_113(x), F_114(x) + F_2(x))
Eq(F_114(x), F_115(x) + F_140(x) + F_15(x))
Eq(F_115(x), F_116(x)*F_4(x))
Eq(F_116(x), F_117(x) + F_119(x))
Eq(F_117(x), F_118(x) + F_4(x))
Eq(F_118(x), F_15(x) + F_18(x) + F_25(x))
Eq(F_119(x), F_120(x) + F_62(x))
Eq(F_120(x), F_121(x) + 2*F_15(x) + F_59(x))
Eq(F_121(x), F_122(x)*F_4(x))
Eq(F_122(x), F_123(x) + F_125(x))
Eq(F_123(x), F_118(x) + F_124(x))
Eq(F_124(x), F_42(x))
Eq(F_125(x), F_126(x) + F_131(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_128(x)*F_4(x))
Eq(F_128(x), F_129(x) + F_130(x))
Eq(F_129(x), F_118(x))
Eq(F_130(x), F_126(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_133(x)*F_4(x))
Eq(F_133(x), F_134(x) + F_135(x))
Eq(F_134(x), F_124(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x)*F_4(x))
Eq(F_137(x), F_138(x) + F_139(x))
Eq(F_138(x), F_124(x))
Eq(F_139(x), F_136(x))
Eq(F_140(x), F_2(x)*F_4(x))
Eq(F_141(x), F_142(x) + F_146(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_144(x)*F_4(x))
Eq(F_144(x), F_145(x) + F_2(x))
Eq(F_145(x), F_140(x))
Eq(F_146(x), F_147(x) + 2*F_15(x) + F_89(x))
Eq(F_147(x), F_142(x)*F_4(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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