0132_0213_1230_2130

Counting sequence:
1, 1, 2, 6, 20, 64, 189, 518, 1342, 3342, 8105, 19326, 45618, 107104, 250935, 587940, 1379446, 3243504, 7645923, 18071910, 42826788, 101741414, 242247663, 577961454, 1381375592, 3306727896, 7926223965, 19020929812, 45689924316, 109841763704, 264251061433, 636092052054, 1531920085322, 3690883601230, 8895560177301, 21445701411598, 51714279727198, 124728767818016, 300880624588579, 725907304274164, 1751529271853762, 4226633058412816, 10200128406709231, 24617553638068342, 59416559542678576, 143413314500641542, 346168462483319131, 835600771788488350, 2017071045530150868, 4869144901058452216, 11754164858163791689, 28375082531786896388, 68499545578004131816, 165364604721160495992, 399209616635352892229, 963745560491051186566, 2326624181433251576982, 5616840809075702868302, 13559999567924936811265, 32736227476596673873502, 79031229576355000196234, 190796236726665164847648, 460618803203181891281807, 1112024043445686709775876, 2684647290664315055428110, 6481279425823945169327984, 15647127744266015170908539, 37775378118028257003797318, 91197570387286307182310972, 220169891705912304333612262, 531536099424736873756076615, 1283239581805024936592658446, 3098010245531454577345227328, 7479250037857046781934725464, 18056490251216940613271985845, 43592190400222657073191434420, 105240790771507824100432633076, 254073611382900499287562786744, 613387692416586377245873320273, 1480848353974552584795193238390, 3575083115882527597286584062178, 8631012016773081490562820242574, 20837102011495316999513509427693, 50305205763896448940798586462574, 121447492987552841391246721945782, 293200150635530024960288832152416, 707847712051666477610261257473915, 1708895410324966592818853079942612, 4125638203873801128389662141229146, 9960171160416962459788346058891024, 24045979209396498188119082159102343, 58052126948587478716011135933321174, 140150227845326455899562165401538632, 338352572116750327193107819507568390, 816855351033846880280304800242143411, 1972063232094483460500484431945711678, 4760981731042892276171102998627546028, 11494026525820424524776357429078174456, 27749034445964053641141455498014548129, 66992094744309155291598855679934142244, 161733222587703609338672956981378301952

Generating function in Maple syntax:
(x^10-8*x^8-2*x^7+18*x^6-13*x^5-15*x^4+35*x^3-25*x^2+8*x-1)/(2*x-1)/(x^2+x-1)/(x^2+2*x-1)/(x-1)^4

Generating function in latex syntax:
\frac{x^{10}-8 x^{8}-2 x^{7}+18 x^{6}-13 x^{5}-15 x^{4}+35 x^{3}-25 x^{2}+8 x -1}{\left(2 x -1\right) \left(x^{2}+x -1\right) \left(x^{2}+2 x -1\right) \left(x -1\right)^{4}}

Generating function in sympy syntax:
(x**10 - 8*x**8 - 2*x**7 + 18*x**6 - 13*x**5 - 15*x**4 + 35*x**3 - 25*x**2 + 8*x - 1)/((x - 1)**4*(2*x - 1)*(x**2 + x - 1)*(x**2 + 2*x - 1))

Implicit equation for the generating function in Maple syntax:
-(2*x-1)*(x^2+x-1)*(x^2+2*x-1)*(x-1)^4*F(x)+x^10-8*x^8-2*x^7+18*x^6-13*x^5-15*x^4+35*x^3-25*x^2+8*x-1 = 0

Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right) \left(x^{2}+x -1\right) \left(x^{2}+2 x -1\right) \left(x -1\right)^{4} F \! \left(x \right)+x^{10}-8 x^{8}-2 x^{7}+18 x^{6}-13 x^{5}-15 x^{4}+35 x^{3}-25 x^{2}+8 x -1 = 0

Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/60*(216*5^(1/2)-480)*(-1/2*5^(1/2)-1/2)^(-n)+1/60*(-216*5^(1/2)-480)*(1/2*5^(1/2)-1/2)^(-n)+1/60*(-15*2^(1/2)+30)*(-1-2^(1/2))^(-n)+1/60*(15*2^(1/2)+30)*(2^(1/2)-1)^(-n)-1/6*n^3+n^2+25/6*n+17/4*2^n+11)

Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{\left(216 \sqrt{5}-480\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{60}+\frac{\left(-216 \sqrt{5}-480\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{60}+\\\frac{\left(-15 \sqrt{2}+30\right) \left(-1-\sqrt{2}\right)^{-n}}{60}+\frac{\left(15 \sqrt{2}+30\right) \left(\sqrt{2}-1\right)^{-n}}{60}-\frac{n^{3}}{6}+n^{2}+\\\frac{25 n}{6}+\frac{17 \,2^{n}}{4}+11 & \mathit{\text{otherwise}} \end{array}\right.

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 64
a(6) = 189
a(7) = 518
a(8) = 1342
a(9) = 3342
a(10) = 8105
a(n+5) = 1/3*n^3-4*n^2+5*a(n+4)+2*a(n)+5*a(n+1)-3*a(n+2)-6*a(n+3)-10/3*n+3, n >= 11

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) = 20
a \! \left(5\right) = 64
a \! \left(6\right) = 189
a \! \left(7\right) = 518
a \! \left(8\right) = 1342
a \! \left(9\right) = 3342
a \! \left(10\right) = 8105
a \! \left(n +5\right) = \frac{n^{3}}{3}-4 n^{2}+5 a \! \left(n +4\right)+2 a \! \left(n \right)+5 a \! \left(n +1\right)-3 a \! \left(n +2\right)-6 a \! \left(n +3\right)-\frac{10 n}{3}+3, \quad n \geq 11

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15279/
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[23,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[14,x]+F[21,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[12,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]*F[14,x]
F[21,x] = F[22,x]
F[22,x] = F[12,x]*F[13,x]
F[23,x] = F[24,x]+F[33,x]
F[24,x] = F[25,x]
F[25,x] = F[12,x]*F[26,x]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[1,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[12,x]*F[27,x]
F[30,x] = F[24,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[12,x]*F[30,x]
F[33,x] = F[34,x]+F[35,x]+F[94,x]
F[34,x] = 0
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[37,x]+F[60,x]
F[37,x] = F[38,x]+F[6,x]
F[38,x] = F[34,x]+F[39,x]+F[44,x]
F[39,x] = F[12,x]*F[40,x]
F[40,x] = F[10,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[28,x]+F[41,x]
F[44,x] = F[12,x]*F[45,x]
F[45,x] = F[43,x]+F[46,x]
F[46,x] = F[47,x]+F[58,x]
F[47,x] = F[34,x]+F[48,x]+F[52,x]
F[48,x] = F[12,x]*F[49,x]
F[49,x] = F[12,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[12,x]*F[28,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[54,x]+F[55,x]
F[54,x] = F[28,x]+F[50,x]
F[55,x] = F[47,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[12,x]*F[47,x]
F[58,x] = F[59,x]
F[59,x] = F[12,x]*F[46,x]
F[60,x] = F[33,x]+F[61,x]
F[61,x] = 2*F[34,x]+F[62,x]+F[76,x]
F[62,x] = F[12,x]*F[63,x]
F[63,x] = F[64,x]+F[73,x]
F[64,x] = F[34,x]+F[65,x]+F[74,x]
F[65,x] = F[12,x]*F[66,x]
F[66,x] = F[67,x]+F[69,x]
F[67,x] = F[10,x]+F[68,x]
F[68,x] = F[34,x]+F[39,x]+F[42,x]
F[69,x] = F[64,x]+F[70,x]
F[70,x] = 2*F[34,x]+F[62,x]+F[71,x]
F[71,x] = F[12,x]*F[72,x]
F[72,x] = F[31,x]+F[73,x]
F[73,x] = F[71,x]
F[74,x] = F[12,x]*F[75,x]
F[75,x] = F[24,x]+F[64,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[72,x]+F[78,x]
F[78,x] = F[79,x]+F[92,x]
F[79,x] = 2*F[34,x]+F[80,x]+F[86,x]
F[80,x] = F[12,x]*F[81,x]
F[81,x] = F[82,x]+F[84,x]
F[82,x] = F[83,x]
F[83,x] = F[12,x]*F[24,x]
F[84,x] = F[85,x]
F[85,x] = F[12,x]*F[31,x]
F[86,x] = F[12,x]*F[87,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[31,x]+F[84,x]
F[89,x] = F[79,x]+F[90,x]
F[90,x] = F[91,x]
F[91,x] = F[12,x]*F[79,x]
F[92,x] = F[93,x]
F[93,x] = F[12,x]*F[78,x]
F[94,x] = F[12,x]*F[95,x]
F[95,x] = F[75,x]+F[96,x]
F[96,x] = F[114,x]+F[97,x]
F[97,x] = F[108,x]+F[34,x]+F[98,x]
F[98,x] = F[12,x]*F[99,x]
F[99,x] = F[100,x]+F[104,x]
F[100,x] = F[101,x]+F[28,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]*F[12,x]
F[103,x] = F[101,x]+F[28,x]
F[104,x] = F[105,x]+F[31,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[12,x]
F[107,x] = F[105,x]+F[31,x]
F[108,x] = F[109,x]*F[12,x]
F[109,x] = F[110,x]+F[111,x]
F[110,x] = F[24,x]+F[82,x]
F[111,x] = F[112,x]+F[97,x]
F[112,x] = F[113,x]
F[113,x] = F[12,x]*F[97,x]
F[114,x] = 2*F[34,x]+F[115,x]+F[127,x]
F[115,x] = F[116,x]*F[12,x]
F[116,x] = F[117,x]+F[122,x]
F[117,x] = F[118,x]+F[41,x]
F[118,x] = F[119,x]
F[119,x] = F[12,x]*F[120,x]
F[120,x] = F[101,x]+F[121,x]
F[121,x] = F[119,x]
F[122,x] = F[123,x]+F[73,x]
F[123,x] = F[124,x]
F[124,x] = F[12,x]*F[125,x]
F[125,x] = F[105,x]+F[126,x]
F[126,x] = F[124,x]
F[127,x] = F[12,x]*F[96,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_{23}\! \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_{14}\! \left(x \right)+F_{21}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{33}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{24}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)+F_{94}\! \left(x \right)
F_{34}\! \left(x \right) = 0
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_{60}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{6}\! \left(x \right)
F_{38}\! \left(x \right) = F_{34}\! \left(x \right)+F_{39}\! \left(x \right)+F_{44}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{10}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{28}\! \left(x \right)+F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{58}\! \left(x \right)
F_{47}\! \left(x \right) = F_{34}\! \left(x \right)+F_{48}\! \left(x \right)+F_{52}\! \left(x \right)
F_{48}\! \left(x \right) = F_{12}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \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_{28}\! \left(x \right)+F_{50}\! \left(x \right)
F_{55}\! \left(x \right) = F_{47}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{46}\! \left(x \right)
F_{60}\! \left(x \right) = F_{33}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{62}\! \left(x \right)+F_{76}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{73}\! \left(x \right)
F_{64}\! \left(x \right) = F_{34}\! \left(x \right)+F_{65}\! \left(x \right)+F_{74}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{69}\! \left(x \right)
F_{67}\! \left(x \right) = F_{10}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{34}\! \left(x \right)+F_{39}\! \left(x \right)+F_{42}\! \left(x \right)
F_{69}\! \left(x \right) = F_{64}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{62}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{12}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{31}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{71}\! \left(x \right)
F_{74}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{24}\! \left(x \right)+F_{64}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{72}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{92}\! \left(x \right)
F_{79}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{80}\! \left(x \right)+F_{86}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \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_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{86}\! \left(x \right) = F_{12}\! \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_{31}\! \left(x \right)+F_{84}\! \left(x \right)
F_{89}\! \left(x \right) = F_{79}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{79}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{94}\! \left(x \right) = F_{12}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{75}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{114}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{108}\! \left(x \right)+F_{34}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{12}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{104}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{28}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{12}\! \left(x \right)
F_{103}\! \left(x \right) = F_{101}\! \left(x \right)+F_{28}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{31}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{12}\! \left(x \right)
F_{107}\! \left(x \right) = F_{105}\! \left(x \right)+F_{31}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{12}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{111}\! \left(x \right)
F_{110}\! \left(x \right) = F_{24}\! \left(x \right)+F_{82}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{97}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{12}\! \left(x \right) F_{97}\! \left(x \right)
F_{114}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{115}\! \left(x \right)+F_{127}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{12}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{122}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{41}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{12}\! \left(x \right) F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{101}\! \left(x \right)+F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{119}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{73}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{12}\! \left(x \right) F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{105}\! \left(x \right)+F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{124}\! \left(x \right)
F_{127}\! \left(x \right) = F_{12}\! \left(x \right) F_{96}\! \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_23(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_14(x) + F_21(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_12(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x)*F_14(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_12(x)*F_13(x))
Eq(F_23(x), F_24(x) + F_33(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_12(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_1(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_12(x)*F_27(x))
Eq(F_30(x), F_24(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_12(x)*F_30(x))
Eq(F_33(x), F_34(x) + F_35(x) + F_94(x))
Eq(F_34(x), 0)
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_60(x))
Eq(F_37(x), F_38(x) + F_6(x))
Eq(F_38(x), F_34(x) + F_39(x) + F_44(x))
Eq(F_39(x), F_12(x)*F_40(x))
Eq(F_40(x), F_10(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_28(x) + F_41(x))
Eq(F_44(x), F_12(x)*F_45(x))
Eq(F_45(x), F_43(x) + F_46(x))
Eq(F_46(x), F_47(x) + F_58(x))
Eq(F_47(x), F_34(x) + F_48(x) + F_52(x))
Eq(F_48(x), F_12(x)*F_49(x))
Eq(F_49(x), F_12(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_12(x)*F_28(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_28(x) + F_50(x))
Eq(F_55(x), F_47(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_12(x)*F_47(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_12(x)*F_46(x))
Eq(F_60(x), F_33(x) + F_61(x))
Eq(F_61(x), 2*F_34(x) + F_62(x) + F_76(x))
Eq(F_62(x), F_12(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_73(x))
Eq(F_64(x), F_34(x) + F_65(x) + F_74(x))
Eq(F_65(x), F_12(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_69(x))
Eq(F_67(x), F_10(x) + F_68(x))
Eq(F_68(x), F_34(x) + F_39(x) + F_42(x))
Eq(F_69(x), F_64(x) + F_70(x))
Eq(F_70(x), 2*F_34(x) + F_62(x) + F_71(x))
Eq(F_71(x), F_12(x)*F_72(x))
Eq(F_72(x), F_31(x) + F_73(x))
Eq(F_73(x), F_71(x))
Eq(F_74(x), F_12(x)*F_75(x))
Eq(F_75(x), F_24(x) + F_64(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_72(x) + F_78(x))
Eq(F_78(x), F_79(x) + F_92(x))
Eq(F_79(x), 2*F_34(x) + F_80(x) + F_86(x))
Eq(F_80(x), F_12(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_84(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_12(x)*F_24(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_12(x)*F_31(x))
Eq(F_86(x), F_12(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_89(x))
Eq(F_88(x), F_31(x) + F_84(x))
Eq(F_89(x), F_79(x) + F_90(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_12(x)*F_79(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_12(x)*F_78(x))
Eq(F_94(x), F_12(x)*F_95(x))
Eq(F_95(x), F_75(x) + F_96(x))
Eq(F_96(x), F_114(x) + F_97(x))
Eq(F_97(x), F_108(x) + F_34(x) + F_98(x))
Eq(F_98(x), F_12(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_104(x))
Eq(F_100(x), F_101(x) + F_28(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x)*F_12(x))
Eq(F_103(x), F_101(x) + F_28(x))
Eq(F_104(x), F_105(x) + F_31(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_12(x))
Eq(F_107(x), F_105(x) + F_31(x))
Eq(F_108(x), F_109(x)*F_12(x))
Eq(F_109(x), F_110(x) + F_111(x))
Eq(F_110(x), F_24(x) + F_82(x))
Eq(F_111(x), F_112(x) + F_97(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_12(x)*F_97(x))
Eq(F_114(x), F_115(x) + F_127(x) + 2*F_34(x))
Eq(F_115(x), F_116(x)*F_12(x))
Eq(F_116(x), F_117(x) + F_122(x))
Eq(F_117(x), F_118(x) + F_41(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_12(x)*F_120(x))
Eq(F_120(x), F_101(x) + F_121(x))
Eq(F_121(x), F_119(x))
Eq(F_122(x), F_123(x) + F_73(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_12(x)*F_125(x))
Eq(F_125(x), F_105(x) + F_126(x))
Eq(F_126(x), F_124(x))
Eq(F_127(x), F_12(x)*F_96(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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"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]]}]]}], "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": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], 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