0123_0231_1230_1320_3021

Counting sequence:
1, 1, 2, 6, 19, 53, 125, 271, 565, 1161, 2381, 4899, 10125, 21005, 43685, 90967, 189477, 394513, 820765, 1705803, 3541149, 7342613, 15207349, 31460735, 65015669, 134222233, 276829165, 570431091, 1174411565, 2415926301, 4966063941, 10200556199, 20937975365, 42949683745, 88046841405, 180388639387, 369367201597, 755914259493, 1546188243285, 3161095947983, 6459630832789, 13194139554473, 26938034903309, 54975581413315, 112150186059469, 228698418605613, 466192930207205, 949978046430711, 1935140464920165, 3940649673985841, 8022036836292701, 16325548649259499, 33214047251901405, 67553994410604085, 137359788634849525, 279223176897023007, 567453553048737717, 1152921504606905273, 2341871806232719405, 4755801206503308563, 9655717601082411629, 19599665578316470333, 39775791908936296069, 80704505322479367495, 163714853654172353669, 332041393326772016193, 673306158690398725245, 1365059061454506915131, 2767011611056432842365, 5607810198407703795781, 11363194349405083904661, 23021536603989520530799, 46633369018337746604245, 94447329657392904398025, 191255842556220631284045, 387234051595310907657827, 783912836156361105613837, 1586715138244200791947853, 3211209208351358745465125, 6497976280428631814203543, 13147068288309092275093669, 26596368031521841843706193, 53797198972850998274601629, 108803323765316625723739275, 220024499169862509796714269, 444884701618183536292069973, 899440809793284105981599285, 1818224432700402278758300351, 3675134491628472691106994165, 7427640235712281649394972121, 15010022976335235833152115821, 30329530962491816735028786099, 61278031944626323607506899885, 123794003928538027489912681565, 250063887935646815529623360965, 505079536028435152158842959847, 1020062592371153346516878645957, 2059932225370872777432143003233, 4159478531998877723661057696445, 8398185226512019784915659048923, 16954826778052568245018405694909

Generating function in Maple syntax:
(4*x^9-18*x^8+23*x^7-3*x^6-10*x^5+20*x^4-28*x^3+20*x^2-7*x+1)/(2*x-1)^2/(x-1)^4

Generating function in latex syntax:
\frac{4 x^{9}-18 x^{8}+23 x^{7}-3 x^{6}-10 x^{5}+20 x^{4}-28 x^{3}+20 x^{2}-7 x +1}{\left(2 x -1\right)^{2} \left(x -1\right)^{4}}

Generating function in sympy syntax:
(4*x**9 - 18*x**8 + 23*x**7 - 3*x**6 - 10*x**5 + 20*x**4 - 28*x**3 + 20*x**2 - 7*x + 1)/((x - 1)**4*(2*x - 1)**2)

Implicit equation for the generating function in Maple syntax:
-(2*x-1)^2*(x-1)^4*F(x)+4*x^9-18*x^8+23*x^7-3*x^6-10*x^5+20*x^4-28*x^3+20*x^2-7*x+1 = 0

Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right)^{2} \left(x -1\right)^{4} F \! \left(x \right)+4 x^{9}-18 x^{8}+23 x^{7}-3 x^{6}-10 x^{5}+20 x^{4}-28 x^{3}+20 x^{2}-7 x +1 = 0

Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,n = 3,6,5-10/3*n+1/3*n^3-n^2+1/8*2^n*n+7/8*2^n)

Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ 6 & n =3 \\ 5-\frac{10 n}{3}+\frac{n^{3}}{3}-n^{2}+\frac{2^{n} n}{8}+\frac{7 \,2^{n}}{8} & \mathit{\text{otherwise}} \end{array}\right.

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 53
a(6) = 125
a(7) = 271
a(8) = 565
a(9) = 1161
a(n+2) = 1/3*n^3-3*n^2-4*a(n)+4*a(n+1)+2/3*n+13, 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) = 53
a \! \left(6\right) = 125
a \! \left(7\right) = 271
a \! \left(8\right) = 565
a \! \left(9\right) = 1161
a \! \left(n +2\right) = \frac{n^{3}}{3}-3 n^{2}-4 a \! \left(n \right)+4 a \! \left(n +1\right)+\frac{2 n}{3}+13, \quad n \geq 10

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/17375/
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[29,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[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[24,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[4,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[4,x]
F[23,x] = F[19,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[11,x]
F[28,x] = F[24,x]
F[29,x] = F[30,x]+F[65,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[1,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[17,x]*F[4,x]
F[36,x] = F[30,x]+F[37,x]
F[37,x] = F[38,x]+F[39,x]+F[63,x]
F[38,x] = 0
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[41,x]+F[44,x]
F[41,x] = F[34,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[22,x]*F[4,x]
F[44,x] = F[37,x]+F[45,x]
F[45,x] = 2*F[38,x]+F[46,x]+F[50,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[48,x]+F[49,x]
F[48,x] = F[42,x]
F[49,x] = F[45,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]+F[57,x]
F[55,x] = F[4,x]+F[56,x]
F[56,x] = F[43,x]
F[57,x] = F[52,x]+F[58,x]
F[58,x] = 2*F[38,x]+F[50,x]+F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[56,x]
F[62,x] = F[58,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[30,x]+F[52,x]
F[65,x] = F[149,x]+F[38,x]+F[66,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[81,x]
F[68,x] = F[69,x]+F[7,x]
F[69,x] = F[38,x]+F[70,x]+F[75,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[11,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[4,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[77,x]+F[80,x]
F[77,x] = F[34,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[27,x]*F[4,x]
F[80,x] = F[43,x]
F[81,x] = F[65,x]+F[82,x]
F[82,x] = F[119,x]+F[133,x]+F[38,x]+F[83,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[85,x]+F[91,x]
F[85,x] = F[69,x]+F[86,x]
F[86,x] = 2*F[38,x]+F[87,x]+F[89,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[72,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[42,x]
F[91,x] = F[82,x]+F[92,x]
F[92,x] = 2*F[38,x]+F[114,x]+F[93,x]+F[97,x]
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[95,x]+F[96,x]
F[95,x] = F[86,x]
F[96,x] = F[92,x]
F[97,x] = F[4,x]*F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[4,x]
F[101,x] = F[102,x]+F[106,x]
F[102,x] = F[103,x]+F[72,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[4,x]
F[105,x] = F[72,x]
F[106,x] = F[107,x]+F[99,x]
F[107,x] = 3*F[38,x]+F[108,x]+F[112,x]
F[108,x] = F[109,x]*F[4,x]
F[109,x] = F[110,x]+F[111,x]
F[110,x] = F[103,x]
F[111,x] = F[107,x]
F[112,x] = F[113,x]*F[4,x]
F[113,x] = F[99,x]
F[114,x] = F[115,x]*F[4,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[4,x]
F[117,x] = F[118,x]+F[48,x]
F[118,x] = F[116,x]
F[119,x] = F[120,x]*F[4,x]
F[120,x] = F[121,x]+F[99,x]
F[121,x] = F[122,x]
F[122,x] = F[123,x]*F[4,x]
F[123,x] = F[124,x]+F[125,x]
F[124,x] = F[11,x]+F[78,x]
F[125,x] = F[121,x]+F[126,x]
F[126,x] = 2*F[38,x]+F[127,x]+F[131,x]
F[127,x] = F[128,x]*F[4,x]
F[128,x] = F[129,x]+F[130,x]
F[129,x] = F[78,x]
F[130,x] = F[126,x]
F[131,x] = F[132,x]*F[4,x]
F[132,x] = F[121,x]
F[133,x] = F[134,x]*F[4,x]
F[134,x] = F[135,x]+F[148,x]
F[135,x] = F[136,x]+F[144,x]
F[136,x] = F[137,x]
F[137,x] = F[138,x]*F[4,x]
F[138,x] = F[139,x]+F[41,x]
F[139,x] = F[136,x]+F[140,x]
F[140,x] = 2*F[38,x]+F[141,x]+F[50,x]
F[141,x] = F[142,x]*F[4,x]
F[142,x] = F[143,x]+F[48,x]
F[143,x] = F[140,x]
F[144,x] = F[145,x]
F[145,x] = F[146,x]*F[4,x]
F[146,x] = F[129,x]+F[147,x]
F[147,x] = F[144,x]
F[148,x] = F[116,x]
F[149,x] = F[150,x]*F[4,x]
F[150,x] = F[151,x]+F[152,x]
F[151,x] = F[121,x]+F[30,x]
F[152,x] = F[153,x]+F[154,x]
F[153,x] = F[137,x]
F[154,x] = F[145,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_{29}\! \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_{13}\! \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_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{24}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \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_{4}\! \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_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \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_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{11}\! \left(x \right)
F_{28}\! \left(x \right) = F_{24}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{65}\! \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_{1}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)+F_{63}\! \left(x \right)
F_{38}\! \left(x \right) = 0
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{41}\! \left(x \right) = F_{34}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{44}\! \left(x \right) = F_{37}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{46}\! \left(x \right)+F_{50}\! \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_{42}\! \left(x \right)
F_{49}\! \left(x \right) = F_{45}\! \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_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{57}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{43}\! \left(x \right)
F_{57}\! \left(x \right) = F_{52}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{50}\! \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_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{56}\! \left(x \right)
F_{62}\! \left(x \right) = F_{58}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{30}\! \left(x \right)+F_{52}\! \left(x \right)
F_{65}\! \left(x \right) = F_{149}\! \left(x \right)+F_{38}\! \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_{68}\! \left(x \right)+F_{81}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{7}\! \left(x \right)
F_{69}\! \left(x \right) = F_{38}\! \left(x \right)+F_{70}\! \left(x \right)+F_{75}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{11}\! \left(x \right)+F_{72}\! \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_{4}\! \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_{80}\! \left(x \right)
F_{77}\! \left(x \right) = F_{34}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{80}\! \left(x \right) = F_{43}\! \left(x \right)
F_{81}\! \left(x \right) = F_{65}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{119}\! \left(x \right)+F_{133}\! \left(x \right)+F_{38}\! \left(x \right)+F_{83}\! \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_{91}\! \left(x \right)
F_{85}\! \left(x \right) = F_{69}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{87}\! \left(x \right)+F_{89}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{72}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{42}\! \left(x \right)
F_{91}\! \left(x \right) = F_{82}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{114}\! \left(x \right)+F_{93}\! \left(x \right)+F_{97}\! \left(x \right)
F_{93}\! \left(x \right) = F_{4}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)+F_{96}\! \left(x \right)
F_{95}\! \left(x \right) = F_{86}\! \left(x \right)
F_{96}\! \left(x \right) = F_{92}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \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_{102}\! \left(x \right)+F_{106}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{72}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{4}\! \left(x \right)
F_{105}\! \left(x \right) = F_{72}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{99}\! \left(x \right)
F_{107}\! \left(x \right) = 3 F_{38}\! \left(x \right)+F_{108}\! \left(x \right)+F_{112}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{111}\! \left(x \right)
F_{110}\! \left(x \right) = F_{103}\! \left(x \right)
F_{111}\! \left(x \right) = F_{107}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{99}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{4}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{4}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{48}\! \left(x \right)
F_{118}\! \left(x \right) = F_{116}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{4}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{99}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \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_{125}\! \left(x \right)
F_{124}\! \left(x \right) = F_{11}\! \left(x \right)+F_{78}\! \left(x \right)
F_{125}\! \left(x \right) = F_{121}\! \left(x \right)+F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{127}\! \left(x \right)+F_{131}\! \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_{78}\! \left(x \right)
F_{130}\! \left(x \right) = F_{126}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right) F_{4}\! \left(x \right)
F_{132}\! \left(x \right) = F_{121}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{4}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{148}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{144}\! \left(x \right)
F_{136}\! \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_{41}\! \left(x \right)
F_{139}\! \left(x \right) = F_{136}\! \left(x \right)+F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{141}\! \left(x \right)+F_{50}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right) F_{4}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{48}\! \left(x \right)
F_{143}\! \left(x \right) = F_{140}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right) F_{4}\! \left(x \right)
F_{146}\! \left(x \right) = F_{129}\! \left(x \right)+F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{144}\! \left(x \right)
F_{148}\! \left(x \right) = F_{116}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{4}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{152}\! \left(x \right)
F_{151}\! \left(x \right) = F_{121}\! \left(x \right)+F_{30}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{154}\! \left(x \right)
F_{153}\! \left(x \right) = F_{137}\! \left(x \right)
F_{154}\! \left(x \right) = F_{145}\! \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_29(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_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_24(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_4(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_4(x))
Eq(F_23(x), F_19(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_11(x))
Eq(F_28(x), F_24(x))
Eq(F_29(x), F_30(x) + F_65(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_1(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_17(x)*F_4(x))
Eq(F_36(x), F_30(x) + F_37(x))
Eq(F_37(x), F_38(x) + F_39(x) + F_63(x))
Eq(F_38(x), 0)
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_44(x))
Eq(F_41(x), F_34(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_22(x)*F_4(x))
Eq(F_44(x), F_37(x) + F_45(x))
Eq(F_45(x), 2*F_38(x) + F_46(x) + F_50(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_42(x))
Eq(F_49(x), F_45(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_57(x))
Eq(F_55(x), F_4(x) + F_56(x))
Eq(F_56(x), F_43(x))
Eq(F_57(x), F_52(x) + F_58(x))
Eq(F_58(x), 2*F_38(x) + F_50(x) + F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_56(x))
Eq(F_62(x), F_58(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_30(x) + F_52(x))
Eq(F_65(x), F_149(x) + F_38(x) + F_66(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_81(x))
Eq(F_68(x), F_69(x) + F_7(x))
Eq(F_69(x), F_38(x) + F_70(x) + F_75(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_11(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_4(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_80(x))
Eq(F_77(x), F_34(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_27(x)*F_4(x))
Eq(F_80(x), F_43(x))
Eq(F_81(x), F_65(x) + F_82(x))
Eq(F_82(x), F_119(x) + F_133(x) + F_38(x) + F_83(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_91(x))
Eq(F_85(x), F_69(x) + F_86(x))
Eq(F_86(x), 2*F_38(x) + F_87(x) + F_89(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_72(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_42(x))
Eq(F_91(x), F_82(x) + F_92(x))
Eq(F_92(x), F_114(x) + 2*F_38(x) + F_93(x) + F_97(x))
Eq(F_93(x), F_4(x)*F_94(x))
Eq(F_94(x), F_95(x) + F_96(x))
Eq(F_95(x), F_86(x))
Eq(F_96(x), F_92(x))
Eq(F_97(x), F_4(x)*F_98(x))
Eq(F_98(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_102(x) + F_106(x))
Eq(F_102(x), F_103(x) + F_72(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_4(x))
Eq(F_105(x), F_72(x))
Eq(F_106(x), F_107(x) + F_99(x))
Eq(F_107(x), F_108(x) + F_112(x) + 3*F_38(x))
Eq(F_108(x), F_109(x)*F_4(x))
Eq(F_109(x), F_110(x) + F_111(x))
Eq(F_110(x), F_103(x))
Eq(F_111(x), F_107(x))
Eq(F_112(x), F_113(x)*F_4(x))
Eq(F_113(x), F_99(x))
Eq(F_114(x), F_115(x)*F_4(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_4(x))
Eq(F_117(x), F_118(x) + F_48(x))
Eq(F_118(x), F_116(x))
Eq(F_119(x), F_120(x)*F_4(x))
Eq(F_120(x), F_121(x) + F_99(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x)*F_4(x))
Eq(F_123(x), F_124(x) + F_125(x))
Eq(F_124(x), F_11(x) + F_78(x))
Eq(F_125(x), F_121(x) + F_126(x))
Eq(F_126(x), F_127(x) + F_131(x) + 2*F_38(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_78(x))
Eq(F_130(x), F_126(x))
Eq(F_131(x), F_132(x)*F_4(x))
Eq(F_132(x), F_121(x))
Eq(F_133(x), F_134(x)*F_4(x))
Eq(F_134(x), F_135(x) + F_148(x))
Eq(F_135(x), F_136(x) + F_144(x))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_138(x)*F_4(x))
Eq(F_138(x), F_139(x) + F_41(x))
Eq(F_139(x), F_136(x) + F_140(x))
Eq(F_140(x), F_141(x) + 2*F_38(x) + F_50(x))
Eq(F_141(x), F_142(x)*F_4(x))
Eq(F_142(x), F_143(x) + F_48(x))
Eq(F_143(x), F_140(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_146(x)*F_4(x))
Eq(F_146(x), F_129(x) + F_147(x))
Eq(F_147(x), F_144(x))
Eq(F_148(x), F_116(x))
Eq(F_149(x), F_150(x)*F_4(x))
Eq(F_150(x), F_151(x) + F_152(x))
Eq(F_151(x), F_121(x) + F_30(x))
Eq(F_152(x), F_153(x) + F_154(x))
Eq(F_153(x), F_137(x))
Eq(F_154(x), F_145(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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "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, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": 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