0123_0231_0321_2130_3021

Counting sequence:
1, 1, 2, 6, 19, 50, 100, 191, 365, 696, 1324, 2509, 4737, 8914, 16724, 31295, 58429, 108876, 202536, 376217, 697953, 1293418, 2394636, 4429779, 8188665, 15127696, 27931600, 51548049, 95092905, 175358214, 323270400, 595778423, 1097735185, 2022169072, 3724395904, 6858398461, 12627774973, 23247479186, 42793374016, 78765259431, 144962465297, 266774082676, 490911144012, 903310012537, 1662066896397, 3058022030682, 5626204574536, 10350833114283, 19042404967101, 35031327516200, 64443795705476, 118548643156961, 218074111454725, 401148010361446, 737902570093516, 1357337957074367, 2496733607814405, 4592532470432056, 8447507441055684, 15538235260486781, 28580640318894025, 52570209908540642, 96695277522945116, 177856146673507615, 327137845063144885, 601715499140876972, 1106751931716960352, 2035673946641692457, 3744252489059670921, 6886858149699175130, 12667075479241531060, 23298656794122221075, 42853351993025763793, 78820316512474196432, 144974319115669698344, 266651213683301856129, 490451069189625465521, 902085047928908932182, 1659200996620327880648, 3051759225497665817367, 5613081047624197796041, 10324099159078290198928, 18989033099113547683064, 34926364862065528253645, 64239742343420252581989, 118155537084011707540674, 217322286292072753844648, 399718604501492358457639, 735198108662139729801641, 1352241719022255396552948, 2487162832537000949219940, 4574609780139060094431273, 8414025851967093923468629, 15475817104829596469241066, 28464482897390969472526672, 52354374654829320352743307, 96294753618146765767403701, 177113738932105595553073288, 325763073927917101106512572, 599171900962743421820681457, 1102049255030175497307251501

Generating function in Maple syntax:
-(4*x^11+14*x^10+17*x^9+3*x^8-18*x^7-19*x^6+3*x^5+6*x^4+3*x^3-2*x+1)/(x-1)/(x^2+x-1)/(x^3+x^2+x-1)

Generating function in latex syntax:
-\frac{4 x^{11}+14 x^{10}+17 x^{9}+3 x^{8}-18 x^{7}-19 x^{6}+3 x^{5}+6 x^{4}+3 x^{3}-2 x +1}{\left(x -1\right) \left(x^{2}+x -1\right) \left(x^{3}+x^{2}+x -1\right)}

Generating function in sympy syntax:
(-4*x**11 - 14*x**10 - 17*x**9 - 3*x**8 + 18*x**7 + 19*x**6 - 3*x**5 - 6*x**4 - 3*x**3 + 2*x - 1)/((x - 1)*(x**2 + x - 1)*(x**3 + x**2 + x - 1))

Implicit equation for the generating function in Maple syntax:
(x-1)*(x^2+x-1)*(x^3+x^2+x-1)*F(x)+4*x^11+14*x^10+17*x^9+3*x^8-18*x^7-19*x^6+3*x^5+6*x^4+3*x^3-2*x+1 = 0

Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(x^{2}+x -1\right) \left(x^{3}+x^{2}+x -1\right) F \! \left(x \right)+4 x^{11}+14 x^{10}+17 x^{9}+3 x^{8}-18 x^{7}-19 x^{6}+3 x^{5}+6 x^{4}+3 x^{3}-2 x +1 = 0

Explicit closed form in Maple syntax:
1159/55*Sum(_alpha^(4-n),_alpha = RootOf(_Z^6+_Z^5-_Z^4-2*_Z^3-_Z^2+3*_Z-1))+1917/55*Sum(_alpha^(3-n),_alpha = RootOf(_Z^6+_Z^5-_Z^4-2*_Z^3-_Z^2+3*_Z-1))+41/22*Sum(_alpha^(2-n),_alpha = RootOf(_Z^6+_Z^5-_Z^4-2*_Z^3-_Z^2+3*_Z-1))-2213/55*Sum(_alpha^(1-n),_alpha = RootOf(_Z^6+_Z^5-_Z^4-2*_Z^3-_Z^2+3*_Z-1))-510/11*Sum(_alpha^(-n),_alpha = RootOf(_Z^6+_Z^5-_Z^4-2*_Z^3-_Z^2+3*_Z-1))+3829/110*Sum(_alpha^(-n-1),_alpha = RootOf(_Z^6+_Z^5-_Z^4-2*_Z^3-_Z^2+3*_Z-1))-piecewise(n = 0,4,n = 1,7,n = 2,10,n = 3,11,n = 4,10,n = 5,4,0)

Explicit closed form in latex syntax:
\frac{1159 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{4-n}\right)}{55}+\frac{1917 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{3-n}\right)}{55}+\frac{41 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{2-n}\right)}{22}-\frac{2213 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{1-n}\right)}{55}-\frac{510 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n}\right)}{11}+\frac{3829 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{6}+\textit{\_Z}^{5}-\textit{\_Z}^{4}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n -1}\right)}{110}-\left(\left\{\begin{array}{cc}4 & n =0 \\ 7 & n =1 \\ 10 & n =2 \\ 11 & n =3 \\ 10 & n =4 \\ 4 & n =5 \\ 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) = 100
a(7) = 191
a(8) = 365
a(9) = 696
a(10) = 1324
a(11) = 2509
a(n+5) = -a(n)-2*a(n+1)-a(n+2)+a(n+3)+2*a(n+4)+12, n >= 12

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) = 100
a \! \left(7\right) = 191
a \! \left(8\right) = 365
a \! \left(9\right) = 696
a \! \left(10\right) = 1324
a \! \left(11\right) = 2509
a \! \left(n +5\right) = -a \! \left(n \right)-2 a \! \left(n +1\right)-a \! \left(n +2\right)+a \! \left(n +3\right)+2 a \! \left(n +4\right)+12, \quad n \geq 12

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/17173/
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[20,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[14,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[4,x]
F[14,x] = F[15,x]+F[17,x]
F[15,x] = F[16,x]
F[16,x] = F[13,x]*F[4,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[4,x]
F[19,x] = F[11,x]
F[20,x] = F[21,x]+F[58,x]
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[24,x]+F[25,x]
F[24,x] = F[1,x]+F[15,x]
F[25,x] = F[21,x]+F[26,x]
F[26,x] = F[27,x]+F[28,x]+F[54,x]
F[27,x] = 0
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[30,x]+F[34,x]
F[30,x] = F[15,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[4,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[28,x]
F[36,x] = 2*F[27,x]+F[37,x]+F[41,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[39,x]+F[40,x]
F[39,x] = F[31,x]
F[40,x] = F[37,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[48,x]
F[46,x] = F[4,x]+F[47,x]
F[47,x] = F[32,x]
F[48,x] = F[43,x]+F[49,x]
F[49,x] = 2*F[27,x]+F[41,x]+F[50,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[47,x]
F[53,x] = F[50,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[21,x]+F[56,x]
F[56,x] = F[27,x]+F[44,x]+F[57,x]
F[57,x] = F[21,x]*F[4,x]
F[58,x] = F[125,x]+F[27,x]+F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[71,x]
F[61,x] = F[62,x]+F[7,x]
F[62,x] = F[27,x]+F[63,x]+F[68,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[11,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[4,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[14,x]+F[70,x]
F[70,x] = F[31,x]
F[71,x] = F[72,x]+F[95,x]
F[72,x] = F[73,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[75,x]+F[77,x]
F[75,x] = F[7,x]+F[76,x]
F[76,x] = F[18,x]
F[77,x] = F[72,x]+F[78,x]
F[78,x] = 2*F[27,x]+F[79,x]+F[83,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[81,x]+F[82,x]
F[81,x] = F[76,x]
F[82,x] = F[79,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[85,x]
F[85,x] = F[86,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[11,x]+F[17,x]
F[89,x] = F[85,x]+F[90,x]
F[90,x] = 2*F[27,x]+F[83,x]+F[91,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[93,x]+F[94,x]
F[93,x] = F[17,x]
F[94,x] = F[91,x]
F[95,x] = 2*F[27,x]+F[122,x]+F[96,x]
F[96,x] = F[4,x]*F[97,x]
F[97,x] = F[102,x]+F[98,x]
F[98,x] = F[62,x]+F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[4,x]
F[101,x] = F[65,x]
F[102,x] = F[103,x]+F[104,x]
F[103,x] = F[96,x]
F[104,x] = 3*F[27,x]+F[105,x]+F[109,x]
F[105,x] = F[106,x]*F[4,x]
F[106,x] = F[107,x]+F[108,x]
F[107,x] = F[99,x]
F[108,x] = F[105,x]
F[109,x] = F[110,x]*F[4,x]
F[110,x] = F[111,x]
F[111,x] = F[112,x]
F[112,x] = F[113,x]*F[4,x]
F[113,x] = F[114,x]+F[116,x]
F[114,x] = F[115,x]+F[65,x]
F[115,x] = F[100,x]
F[116,x] = F[111,x]+F[117,x]
F[117,x] = 3*F[27,x]+F[109,x]+F[118,x]
F[118,x] = F[119,x]*F[4,x]
F[119,x] = F[120,x]+F[121,x]
F[120,x] = F[115,x]
F[121,x] = F[118,x]
F[122,x] = F[123,x]*F[4,x]
F[123,x] = F[124,x]+F[85,x]
F[124,x] = F[112,x]
F[125,x] = F[126,x]*F[4,x]
F[126,x] = F[127,x]+F[149,x]
F[127,x] = F[128,x]+F[21,x]
F[128,x] = F[129,x]+F[148,x]+F[27,x]
F[129,x] = F[130,x]*F[4,x]
F[130,x] = F[131,x]+F[135,x]
F[131,x] = F[11,x]+F[132,x]
F[132,x] = F[133,x]+F[27,x]+F[63,x]
F[133,x] = F[134,x]*F[4,x]
F[134,x] = F[15,x]+F[47,x]
F[135,x] = F[136,x]+F[85,x]
F[136,x] = 2*F[27,x]+F[122,x]+F[137,x]
F[137,x] = F[138,x]*F[4,x]
F[138,x] = F[139,x]+F[141,x]
F[139,x] = F[132,x]+F[140,x]
F[140,x] = F[100,x]
F[141,x] = F[142,x]+F[143,x]
F[142,x] = F[137,x]
F[143,x] = 3*F[27,x]+F[109,x]+F[144,x]
F[144,x] = F[145,x]*F[4,x]
F[145,x] = F[146,x]+F[147,x]
F[146,x] = F[140,x]
F[147,x] = F[144,x]
F[148,x] = F[4,x]*F[55,x]
F[149,x] = F[150,x]+F[26,x]
F[150,x] = 2*F[27,x]+F[151,x]+F[83,x]
F[151,x] = F[152,x]*F[4,x]
F[152,x] = F[153,x]+F[154,x]
F[153,x] = F[17,x]
F[154,x] = F[91,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_{20}\! \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_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{17}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{11}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{58}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)
F_{24}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{25}\! \left(x \right) = F_{21}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)+F_{54}\! \left(x \right)
F_{27}\! \left(x \right) = 0
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{34}\! \left(x \right)
F_{30}\! \left(x \right) = F_{15}\! \left(x \right)+F_{31}\! \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_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{28}\! \left(x \right)
F_{36}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{37}\! \left(x \right)+F_{41}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)
F_{39}\! \left(x \right) = F_{31}\! \left(x \right)
F_{40}\! \left(x \right) = F_{37}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{48}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{32}\! \left(x \right)
F_{48}\! \left(x \right) = F_{43}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{41}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \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_{47}\! \left(x \right)
F_{53}\! \left(x \right) = F_{50}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{21}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{27}\! \left(x \right)+F_{44}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{58}\! \left(x \right) = F_{125}\! \left(x \right)+F_{27}\! \left(x \right)+F_{59}\! \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_{71}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{7}\! \left(x \right)
F_{62}\! \left(x \right) = F_{27}\! \left(x \right)+F_{63}\! \left(x \right)+F_{68}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{11}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{14}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{31}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{95}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{77}\! \left(x \right)
F_{75}\! \left(x \right) = F_{7}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{18}\! \left(x \right)
F_{77}\! \left(x \right) = F_{72}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{79}\! \left(x \right)+F_{83}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{82}\! \left(x \right)
F_{81}\! \left(x \right) = F_{76}\! \left(x \right)
F_{82}\! \left(x \right) = F_{79}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{89}\! \left(x \right)
F_{88}\! \left(x \right) = F_{11}\! \left(x \right)+F_{17}\! \left(x \right)
F_{89}\! \left(x \right) = F_{85}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{83}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{94}\! \left(x \right)
F_{93}\! \left(x \right) = F_{17}\! \left(x \right)
F_{94}\! \left(x \right) = F_{91}\! \left(x \right)
F_{95}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{122}\! \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_{102}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{62}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{4}\! \left(x \right)
F_{101}\! \left(x \right) = F_{65}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{104}\! \left(x \right)
F_{103}\! \left(x \right) = F_{96}\! \left(x \right)
F_{104}\! \left(x \right) = 3 F_{27}\! \left(x \right)+F_{105}\! \left(x \right)+F_{109}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{4}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{108}\! \left(x \right)
F_{107}\! \left(x \right) = F_{99}\! \left(x \right)
F_{108}\! \left(x \right) = F_{105}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{4}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{116}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{65}\! \left(x \right)
F_{115}\! \left(x \right) = F_{100}\! \left(x \right)
F_{116}\! \left(x \right) = F_{111}\! \left(x \right)+F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = 3 F_{27}\! \left(x \right)+F_{109}\! \left(x \right)+F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{4}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{121}\! \left(x \right)
F_{120}\! \left(x \right) = F_{115}\! \left(x \right)
F_{121}\! \left(x \right) = F_{118}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{4}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{85}\! \left(x \right)
F_{124}\! \left(x \right) = F_{112}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{4}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{149}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{21}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{148}\! \left(x \right)+F_{27}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{4}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{135}\! \left(x \right)
F_{131}\! \left(x \right) = F_{11}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{27}\! \left(x \right)+F_{63}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{4}\! \left(x \right)
F_{134}\! \left(x \right) = F_{15}\! \left(x \right)+F_{47}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{85}\! \left(x \right)
F_{136}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{122}\! \left(x \right)+F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right) F_{4}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{141}\! \left(x \right)
F_{139}\! \left(x \right) = F_{132}\! \left(x \right)+F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{100}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{143}\! \left(x \right)
F_{142}\! \left(x \right) = F_{137}\! \left(x \right)
F_{143}\! \left(x \right) = 3 F_{27}\! \left(x \right)+F_{109}\! \left(x \right)+F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right) F_{4}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{147}\! \left(x \right)
F_{146}\! \left(x \right) = F_{140}\! \left(x \right)
F_{147}\! \left(x \right) = F_{144}\! \left(x \right)
F_{148}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{26}\! \left(x \right)
F_{150}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{151}\! \left(x \right)+F_{83}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{4}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{154}\! \left(x \right)
F_{153}\! \left(x \right) = F_{17}\! \left(x \right)
F_{154}\! \left(x \right) = F_{91}\! \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_20(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_14(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_4(x))
Eq(F_14(x), F_15(x) + F_17(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_13(x)*F_4(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_11(x))
Eq(F_20(x), F_21(x) + F_58(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_24(x) + F_25(x))
Eq(F_24(x), F_1(x) + F_15(x))
Eq(F_25(x), F_21(x) + F_26(x))
Eq(F_26(x), F_27(x) + F_28(x) + F_54(x))
Eq(F_27(x), 0)
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_30(x) + F_34(x))
Eq(F_30(x), F_15(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_4(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_28(x))
Eq(F_36(x), 2*F_27(x) + F_37(x) + F_41(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_39(x) + F_40(x))
Eq(F_39(x), F_31(x))
Eq(F_40(x), F_37(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_48(x))
Eq(F_46(x), F_4(x) + F_47(x))
Eq(F_47(x), F_32(x))
Eq(F_48(x), F_43(x) + F_49(x))
Eq(F_49(x), 2*F_27(x) + F_41(x) + F_50(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_47(x))
Eq(F_53(x), F_50(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_21(x) + F_56(x))
Eq(F_56(x), F_27(x) + F_44(x) + F_57(x))
Eq(F_57(x), F_21(x)*F_4(x))
Eq(F_58(x), F_125(x) + F_27(x) + F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_71(x))
Eq(F_61(x), F_62(x) + F_7(x))
Eq(F_62(x), F_27(x) + F_63(x) + F_68(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_11(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_4(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_14(x) + F_70(x))
Eq(F_70(x), F_31(x))
Eq(F_71(x), F_72(x) + F_95(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_77(x))
Eq(F_75(x), F_7(x) + F_76(x))
Eq(F_76(x), F_18(x))
Eq(F_77(x), F_72(x) + F_78(x))
Eq(F_78(x), 2*F_27(x) + F_79(x) + F_83(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_82(x))
Eq(F_81(x), F_76(x))
Eq(F_82(x), F_79(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_89(x))
Eq(F_88(x), F_11(x) + F_17(x))
Eq(F_89(x), F_85(x) + F_90(x))
Eq(F_90(x), 2*F_27(x) + F_83(x) + F_91(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_94(x))
Eq(F_93(x), F_17(x))
Eq(F_94(x), F_91(x))
Eq(F_95(x), F_122(x) + 2*F_27(x) + F_96(x))
Eq(F_96(x), F_4(x)*F_97(x))
Eq(F_97(x), F_102(x) + F_98(x))
Eq(F_98(x), F_62(x) + F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_4(x))
Eq(F_101(x), F_65(x))
Eq(F_102(x), F_103(x) + F_104(x))
Eq(F_103(x), F_96(x))
Eq(F_104(x), F_105(x) + F_109(x) + 3*F_27(x))
Eq(F_105(x), F_106(x)*F_4(x))
Eq(F_106(x), F_107(x) + F_108(x))
Eq(F_107(x), F_99(x))
Eq(F_108(x), F_105(x))
Eq(F_109(x), F_110(x)*F_4(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_113(x)*F_4(x))
Eq(F_113(x), F_114(x) + F_116(x))
Eq(F_114(x), F_115(x) + F_65(x))
Eq(F_115(x), F_100(x))
Eq(F_116(x), F_111(x) + F_117(x))
Eq(F_117(x), F_109(x) + F_118(x) + 3*F_27(x))
Eq(F_118(x), F_119(x)*F_4(x))
Eq(F_119(x), F_120(x) + F_121(x))
Eq(F_120(x), F_115(x))
Eq(F_121(x), F_118(x))
Eq(F_122(x), F_123(x)*F_4(x))
Eq(F_123(x), F_124(x) + F_85(x))
Eq(F_124(x), F_112(x))
Eq(F_125(x), F_126(x)*F_4(x))
Eq(F_126(x), F_127(x) + F_149(x))
Eq(F_127(x), F_128(x) + F_21(x))
Eq(F_128(x), F_129(x) + F_148(x) + F_27(x))
Eq(F_129(x), F_130(x)*F_4(x))
Eq(F_130(x), F_131(x) + F_135(x))
Eq(F_131(x), F_11(x) + F_132(x))
Eq(F_132(x), F_133(x) + F_27(x) + F_63(x))
Eq(F_133(x), F_134(x)*F_4(x))
Eq(F_134(x), F_15(x) + F_47(x))
Eq(F_135(x), F_136(x) + F_85(x))
Eq(F_136(x), F_122(x) + F_137(x) + 2*F_27(x))
Eq(F_137(x), F_138(x)*F_4(x))
Eq(F_138(x), F_139(x) + F_141(x))
Eq(F_139(x), F_132(x) + F_140(x))
Eq(F_140(x), F_100(x))
Eq(F_141(x), F_142(x) + F_143(x))
Eq(F_142(x), F_137(x))
Eq(F_143(x), F_109(x) + F_144(x) + 3*F_27(x))
Eq(F_144(x), F_145(x)*F_4(x))
Eq(F_145(x), F_146(x) + F_147(x))
Eq(F_146(x), F_140(x))
Eq(F_147(x), F_144(x))
Eq(F_148(x), F_4(x)*F_55(x))
Eq(F_149(x), F_150(x) + F_26(x))
Eq(F_150(x), F_151(x) + 2*F_27(x) + F_83(x))
Eq(F_151(x), F_152(x)*F_4(x))
Eq(F_152(x), F_153(x) + F_154(x))
Eq(F_153(x), F_17(x))
Eq(F_154(x), F_91(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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