0123_0132_0321_2130_3102
Counting sequence:
1, 1, 2, 6, 19, 46, 79, 139, 279, 576, 1205, 2536, 5356, 11341, 24066, 51159, 108910, 232140, 495332, 1057895, 2261169, 4836383, 10350585, 22163087, 47477306, 101743303, 218105507, 467679864, 1003078407, 2151842854, 4617033449, 9907894955, 21264555265, 45643580526, 97981635896, 210351354594, 451623461118, 969692112710, 2082157952669, 4471082763086, 9601259774688, 20618536934127, 44279179044654, 95093675159849, 204226726134238, 438612613719898, 942011417792772, 2023190562183653, 4345324237171837, 9332793872476089, 20044935418647213, 43052725229241977, 92469647370271250, 198609471016775757, 426582064015663115, 916234921649220894, 1967942799725534155, 4226873827326688264, 9078772015971972997, 19500053537211139725, 41883719251174074801, 89961214930665879676, 193226162480875278328, 415027631547821075088, 891432563494425135818, 1914698156590220260688, 4112561794654796890817, 8833337110431033152216, 18973060342479400778552, 40752115162774093445461, 87531239688191681814694, 188007917377173406199791, 403821384472090583121874, 867366385221370687558956, 1863013257426180726788192, 4001560397086969481883751, 8594940394096855496883405, 18461050713262541324944919, 39652448247790898608821421, 85169409782162233575190775, 182935209321569211883106446, 392926205527244291035459415, 843965534390416698354937135, 1812752235928468595445514408, 3893607820229971849698624179, 8363074718070617158566992302, 17963036877207740542676485357, 38582783617914374784906002723, 82871912749077903613112006821, 178000481287875963474550177614, 382327024972720573894312823668, 821199779950763833198393536514, 1763854089831830371361020021978, 3788580267575815895702071559710, 8137487478360940611313775792561, 17478500726032589624719611887926, 37542053417058911017431130280180, 80636537688072542142897968702399, 173199136678227276192216248205914, 372014249708751729424275457047385, 799049031761191115534888309227178
Generating function in Maple syntax:
(x^17+5*x^16+19*x^15+37*x^14+35*x^13-11*x^12-66*x^11-87*x^10-53*x^9-8*x^8+31*x^7+31*x^6-6*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{x^{17}+5 x^{16}+19 x^{15}+37 x^{14}+35 x^{13}-11 x^{12}-66 x^{11}-87 x^{10}-53 x^{9}-8 x^{8}+31 x^{7}+31 x^{6}-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:
(x**17 + 5*x**16 + 19*x**15 + 37*x**14 + 35*x**13 - 11*x**12 - 66*x**11 - 87*x**10 - 53*x**9 - 8*x**8 + 31*x**7 + 31*x**6 - 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)+x^17+5*x^16+19*x^15+37*x^14+35*x^13-11*x^12-66*x^11-87*x^10-53*x^9-8*x^8+31*x^7+31*x^6-6*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)+x^{17}+5 x^{16}+19 x^{15}+37 x^{14}+35 x^{13}-11 x^{12}-66 x^{11}-87 x^{10}-53 x^{9}-8 x^{8}+31 x^{7}+31 x^{6}-6 x^{4}-x^{3}+2 x -1 = 0
Explicit closed form in Maple syntax:
15269/24552*Sum(_alpha^(7-n),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))+42767/24552*Sum(_alpha^(6-n),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))+68755/24552*Sum(_alpha^(5-n),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))+24203/12276*Sum(_alpha^(4-n),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))+995/1364*Sum(_alpha^(3-n),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))-2839/2728*Sum(_alpha^(2-n),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))-4787/8184*Sum(_alpha^(1-n),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))-13549/12276*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))+21215/24552*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))+piecewise(n = 0,-6,Or(n = 1,n = 2,n = 3),-7,n = 4,-2,n = 5,10,n = 6,11,n = 7,3,n = 8,1,0)
Explicit closed form in latex syntax:
\frac{15269 \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^{7-n}\right)}{24552}+\frac{42767 \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^{6-n}\right)}{24552}+\frac{68755 \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^{5-n}\right)}{24552}+\frac{24203 \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^{4-n}\right)}{12276}+\frac{995 \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^{3-n}\right)}{1364}-\frac{2839 \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^{2-n}\right)}{2728}-\frac{4787 \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^{1-n}\right)}{8184}-\frac{13549 \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)}{12276}+\frac{21215 \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}+\left(\left\{\begin{array}{cc}-6 & n =0 \\ -7 & n =1\text{ or } n =2\text{ or } n =3 \\ -2 & n =4 \\ 10 & n =5 \\ 11 & n =6 \\ 3 & n =7 \\ 1 & n =8 \\ 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) = 46
a(6) = 79
a(7) = 139
a(8) = 279
a(9) = 576
a(10) = 1205
a(11) = 2536
a(12) = 5356
a(13) = 11341
a(14) = 24066
a(15) = 51159
a(16) = 108910
a(17) = 232140
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)+72, n >= 18
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) = 46
a \! \left(6\right) = 79
a \! \left(7\right) = 139
a \! \left(8\right) = 279
a \! \left(9\right) = 576
a \! \left(10\right) = 1205
a \! \left(11\right) = 2536
a \! \left(12\right) = 5356
a \! \left(13\right) = 11341
a \! \left(14\right) = 24066
a \! \left(15\right) = 51159
a \! \left(16\right) = 108910
a \! \left(17\right) = 232140
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)+72, \quad n \geq 18
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16286/
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[20,x]+F[41,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[29,x]
F[23,x] = F[1,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[10,x]+F[27,x]
F[27,x] = F[12,x]+F[28,x]
F[28,x] = F[18,x]
F[29,x] = F[20,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[33,x]+F[36,x]
F[33,x] = F[20,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[20,x]*F[4,x]
F[36,x] = F[37,x]+F[39,x]
F[37,x] = F[38,x]
F[38,x] = F[33,x]*F[4,x]
F[39,x] = F[40,x]
F[40,x] = F[37,x]*F[4,x]
F[41,x] = F[15,x]+F[42,x]+F[76,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[55,x]
F[44,x] = F[45,x]+F[7,x]
F[45,x] = F[15,x]+F[46,x]+F[49,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[17,x]+F[48,x]
F[48,x] = F[16,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[11,x]+F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[16,x]
F[53,x] = F[54,x]
F[54,x] = F[4,x]*F[52,x]
F[55,x] = F[56,x]+F[75,x]
F[56,x] = F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[59,x]+F[61,x]
F[59,x] = F[60,x]+F[7,x]
F[60,x] = F[46,x]
F[61,x] = F[56,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[73,x]
F[65,x] = F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[71,x]
F[69,x] = F[4,x]+F[70,x]
F[70,x] = F[46,x]
F[71,x] = F[66,x]+F[72,x]
F[72,x] = F[63,x]
F[73,x] = F[74,x]
F[74,x] = F[4,x]*F[65,x]
F[75,x] = F[63,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[78,x]+F[86,x]
F[78,x] = F[20,x]+F[79,x]
F[79,x] = F[15,x]+F[35,x]+F[80,x]
F[80,x] = F[4,x]*F[81,x]
F[81,x] = F[82,x]+F[84,x]
F[82,x] = F[4,x]+F[83,x]
F[83,x] = F[15,x]+F[18,x]+F[46,x]
F[84,x] = F[66,x]+F[85,x]
F[85,x] = F[63,x]
F[86,x] = F[87,x]+F[95,x]
F[87,x] = F[15,x]+F[38,x]+F[88,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[90,x]
F[90,x] = F[12,x]+F[91,x]
F[91,x] = F[15,x]+F[92,x]+F[94,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[17,x]
F[94,x] = F[27,x]*F[4,x]
F[95,x] = F[102,x]+F[15,x]+F[74,x]+F[96,x]
F[96,x] = F[4,x]*F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[14,x]+F[99,x]
F[99,x] = F[100,x]+F[101,x]+F[15,x]+F[54,x]
F[100,x] = 0
F[101,x] = F[4,x]*F[48,x]
F[102,x] = F[4,x]*F[87,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_{20}\! \left(x \right)+F_{41}\! \left(x \right)
F_{20}\! \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_{29}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{10}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{12}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{18}\! \left(x \right)
F_{29}\! \left(x \right) = F_{20}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{36}\! \left(x \right)
F_{33}\! \left(x \right) = F_{20}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{39}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{41}\! \left(x \right) = F_{15}\! \left(x \right)+F_{42}\! \left(x \right)+F_{76}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{55}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{7}\! \left(x \right)
F_{45}\! \left(x \right) = F_{15}\! \left(x \right)+F_{46}\! \left(x \right)+F_{49}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{17}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{16}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{11}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{16}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{75}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{61}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{7}\! \left(x \right)
F_{60}\! \left(x \right) = F_{46}\! \left(x \right)
F_{61}\! \left(x \right) = F_{56}\! \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_{73}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{71}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{46}\! \left(x \right)
F_{71}\! \left(x \right) = F_{66}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{63}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{75}\! \left(x \right) = F_{63}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{86}\! \left(x \right)
F_{78}\! \left(x \right) = F_{20}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{15}\! \left(x \right)+F_{35}\! \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_{84}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{15}\! \left(x \right)+F_{18}\! \left(x \right)+F_{46}\! \left(x \right)
F_{84}\! \left(x \right) = F_{66}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{63}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{95}\! \left(x \right)
F_{87}\! \left(x \right) = F_{15}\! \left(x \right)+F_{38}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{15}\! \left(x \right)+F_{92}\! \left(x \right)+F_{94}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{17}\! \left(x \right)
F_{94}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{95}\! \left(x \right) = F_{102}\! \left(x \right)+F_{15}\! \left(x \right)+F_{74}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{4}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{14}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)+F_{15}\! \left(x \right)+F_{54}\! \left(x \right)
F_{100}\! \left(x \right) = 0
F_{101}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{102}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \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_20(x) + F_41(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_29(x))
Eq(F_23(x), F_1(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_10(x) + F_27(x))
Eq(F_27(x), F_12(x) + F_28(x))
Eq(F_28(x), F_18(x))
Eq(F_29(x), F_20(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_36(x))
Eq(F_33(x), F_20(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_20(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_39(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_33(x)*F_4(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_37(x)*F_4(x))
Eq(F_41(x), F_15(x) + F_42(x) + F_76(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_55(x))
Eq(F_44(x), F_45(x) + F_7(x))
Eq(F_45(x), F_15(x) + F_46(x) + F_49(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_17(x) + F_48(x))
Eq(F_48(x), F_16(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_11(x) + F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_16(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_4(x)*F_52(x))
Eq(F_55(x), F_56(x) + F_75(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_61(x))
Eq(F_59(x), F_60(x) + F_7(x))
Eq(F_60(x), F_46(x))
Eq(F_61(x), F_56(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_73(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_71(x))
Eq(F_69(x), F_4(x) + F_70(x))
Eq(F_70(x), F_46(x))
Eq(F_71(x), F_66(x) + F_72(x))
Eq(F_72(x), F_63(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_4(x)*F_65(x))
Eq(F_75(x), F_63(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_86(x))
Eq(F_78(x), F_20(x) + F_79(x))
Eq(F_79(x), F_15(x) + F_35(x) + F_80(x))
Eq(F_80(x), F_4(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_84(x))
Eq(F_82(x), F_4(x) + F_83(x))
Eq(F_83(x), F_15(x) + F_18(x) + F_46(x))
Eq(F_84(x), F_66(x) + F_85(x))
Eq(F_85(x), F_63(x))
Eq(F_86(x), F_87(x) + F_95(x))
Eq(F_87(x), F_15(x) + F_38(x) + F_88(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_12(x) + F_91(x))
Eq(F_91(x), F_15(x) + F_92(x) + F_94(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_17(x))
Eq(F_94(x), F_27(x)*F_4(x))
Eq(F_95(x), F_102(x) + F_15(x) + F_74(x) + F_96(x))
Eq(F_96(x), F_4(x)*F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_14(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_101(x) + F_15(x) + F_54(x))
Eq(F_100(x), 0)
Eq(F_101(x), F_4(x)*F_48(x))
Eq(F_102(x), F_4(x)*F_87(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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "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], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": 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