0132_0213_0231_2310

Counting sequence:
1, 1, 2, 6, 20, 64, 184, 477, 1142, 2585, 5636, 11998, 25176, 52398, 108584, 224539, 463850, 957703, 1976564, 4077636, 8407964, 17327028, 35684696, 73442665, 151048414, 310445253, 637616708, 1308723866, 2684477216, 5503074634, 11274465960, 23085659367, 47244888530, 96637055827, 197568836468, 403727322208, 824634179684, 1683627708912, 3435974443928, 7009387321365, 14293651952198, 29137059034417, 59373628916740, 120946280202774, 246290605912808, 501377303714342, 1020346792197032, 2075877955050355, 4222124652674490, 8584986791913183, 17451448558541684, 35465847068287036, 72057594040957484, 146366987892878956, 297237575410123352, 603482350071675777, 1224979098649190318, 2485986994313344221, 5044031582660231492, 10232178353391520594, 20752587082929510832, 42081634918156727106, 85316191340914073384, 172938225691035067583, 350488137400490167202, 710199646837827132331, 1438846037749355175156, 2914585563646120105944, 5902958103587068318964, 11953490159763802152232, 24202128224706945382808, 48994552259772583769005, 99169696140262565238038, 200700575521959938467785, 406123517526789506463236, 821691768019318286535246, 1662273001970115135909752, 3362324935803187414249630, 6800207735332289131305256, 13751531198116406887429323, 27805293851136471045033866, 56215050612080256652359095, 113639027043775142452720628, 229695905726779543226423092, 464227514732017603121425596, 938126436020952239608349220, 1895595685155738545977845080, 3829876996539145225510036633, 7737125245533626718162816638, 15628992995977925970647265781, 31567471001777197009976139332, 63753912023197084157356139274, 128745764085679548589563056192, 259967408249929857728873248314, 524886576657001236557288990120, 1059676673628285515313713950615, 2139160387885137115025753711986, 4317934857027406398848215931139, 8715097876569077135289908911220, 17588652078166682945766835241552, 35494216806390423241907772071300

Generating function in Maple syntax:
-(2*x^9+2*x^8-4*x^7-29*x^6+77*x^5-97*x^4+75*x^3-35*x^2+9*x-1)/(2*x-1)^2/(-1+x)^6

Generating function in latex syntax:
-\frac{2 x^{9}+2 x^{8}-4 x^{7}-29 x^{6}+77 x^{5}-97 x^{4}+75 x^{3}-35 x^{2}+9 x -1}{\left(2 x -1\right)^{2} \left(-1+x \right)^{6}}

Generating function in sympy syntax:
(-2*x**9 - 2*x**8 + 4*x**7 + 29*x**6 - 77*x**5 + 97*x**4 - 75*x**3 + 35*x**2 - 9*x + 1)/((x - 1)**6*(2*x - 1)**2)

Implicit equation for the generating function in Maple syntax:
(2*x-1)^2*(-1+x)^6*F(x)+2*x^9+2*x^8-4*x^7-29*x^6+77*x^5-97*x^4+75*x^3-35*x^2+9*x-1 = 0

Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{2} \left(-1+x \right)^{6} F \! \left(x \right)+2 x^{9}+2 x^{8}-4 x^{7}-29 x^{6}+77 x^{5}-97 x^{4}+75 x^{3}-35 x^{2}+9 x -1 = 0

Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,2-269/30*n+3*n^2-25/24*n^3+1/120*n^5+1/4*2^n*n+3*2^n)

Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2-\frac{269 n}{30}+3 n^{2}-\frac{25 n^{3}}{24}+\frac{n^{5}}{120}+\frac{2^{n} n}{4}+3 \,2^{n} & \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) = 184
a(7) = 477
a(8) = 1142
a(9) = 2585
a(n+2) = 1/120*n^5-1/12*n^4-25/24*n^3+115/12*n^2-4*a(n)+4*a(n+1)-307/15*n+16, 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) = 20
a \! \left(5\right) = 64
a \! \left(6\right) = 184
a \! \left(7\right) = 477
a \! \left(8\right) = 1142
a \! \left(9\right) = 2585
a \! \left(n +2\right) = \frac{n^{5}}{120}-\frac{n^{4}}{12}-\frac{25 n^{3}}{24}+\frac{115 n^{2}}{12}-4 a \! \left(n \right)+4 a \! \left(n +1\right)-\frac{307 n}{15}+16, \quad n \geq 10

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15248/
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[19,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[17,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[1,x]+F[14,x]
F[17,x] = F[18,x]
F[18,x] = F[12,x]*F[13,x]
F[19,x] = F[20,x]+F[41,x]
F[20,x] = F[21,x]
F[21,x] = F[12,x]*F[22,x]
F[22,x] = F[23,x]+F[5,x]
F[23,x] = F[14,x]+F[24,x]
F[24,x] = F[25,x]+F[26,x]+F[28,x]
F[25,x] = 0
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[24,x]+F[6,x]
F[28,x] = F[12,x]*F[29,x]
F[29,x] = F[30,x]+F[35,x]
F[30,x] = F[14,x]+F[31,x]
F[31,x] = F[25,x]+F[32,x]+F[34,x]
F[32,x] = F[12,x]*F[33,x]
F[33,x] = F[10,x]+F[31,x]
F[34,x] = F[12,x]*F[30,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[37,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[14,x]+F[36,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[35,x]
F[41,x] = F[25,x]+F[42,x]+F[99,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[44,x]+F[59,x]
F[44,x] = F[45,x]+F[6,x]
F[45,x] = F[25,x]+F[46,x]+F[54,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[48,x]+F[51,x]
F[48,x] = F[10,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[12,x]*F[48,x]
F[51,x] = F[17,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[12,x]*F[51,x]
F[54,x] = F[12,x]*F[55,x]
F[55,x] = F[13,x]+F[56,x]
F[56,x] = F[36,x]+F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[12,x]*F[56,x]
F[59,x] = F[60,x]+F[73,x]
F[60,x] = F[25,x]+F[61,x]+F[63,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[6,x]+F[60,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[30,x]+F[65,x]
F[65,x] = F[66,x]+F[69,x]
F[66,x] = F[25,x]+F[37,x]+F[67,x]
F[67,x] = F[12,x]*F[68,x]
F[68,x] = F[14,x]+F[66,x]
F[69,x] = 2*F[25,x]+F[70,x]+F[72,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[17,x]+F[69,x]
F[72,x] = F[12,x]*F[65,x]
F[73,x] = F[25,x]+F[74,x]+F[76,x]+F[86,x]
F[74,x] = F[12,x]*F[75,x]
F[75,x] = F[45,x]+F[73,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[78,x]+F[83,x]
F[78,x] = F[31,x]+F[79,x]
F[79,x] = 2*F[25,x]+F[80,x]+F[82,x]
F[80,x] = F[12,x]*F[81,x]
F[81,x] = F[49,x]+F[79,x]
F[82,x] = F[12,x]*F[78,x]
F[83,x] = F[39,x]+F[84,x]
F[84,x] = F[85,x]
F[85,x] = F[12,x]*F[83,x]
F[86,x] = F[12,x]*F[87,x]
F[87,x] = F[65,x]+F[88,x]
F[88,x] = F[89,x]+F[95,x]
F[89,x] = 2*F[25,x]+F[90,x]+F[92,x]
F[90,x] = F[12,x]*F[91,x]
F[91,x] = F[36,x]+F[89,x]
F[92,x] = F[12,x]*F[93,x]
F[93,x] = F[36,x]+F[94,x]
F[94,x] = F[92,x]
F[95,x] = 3*F[25,x]+F[96,x]+F[98,x]
F[96,x] = F[12,x]*F[97,x]
F[97,x] = F[57,x]+F[95,x]
F[98,x] = F[12,x]*F[88,x]
F[99,x] = F[100,x]*F[12,x]
F[100,x] = F[101,x]+F[112,x]
F[101,x] = F[102,x]+F[20,x]
F[102,x] = F[103,x]+F[111,x]+F[25,x]
F[103,x] = F[104,x]*F[12,x]
F[104,x] = F[105,x]+F[107,x]
F[105,x] = F[10,x]+F[106,x]
F[106,x] = F[18,x]+F[25,x]+F[46,x]
F[107,x] = F[108,x]+F[31,x]
F[108,x] = F[109,x]+F[25,x]+F[72,x]+F[76,x]
F[109,x] = F[110,x]*F[12,x]
F[110,x] = F[106,x]+F[108,x]
F[111,x] = F[101,x]*F[12,x]
F[112,x] = F[113,x]+F[147,x]
F[113,x] = F[114,x]+F[25,x]+F[37,x]
F[114,x] = F[115,x]*F[12,x]
F[115,x] = F[116,x]+F[128,x]
F[116,x] = F[117,x]+F[14,x]
F[117,x] = F[118,x]+F[25,x]+F[37,x]
F[118,x] = F[119,x]*F[12,x]
F[119,x] = F[120,x]+F[123,x]
F[120,x] = F[12,x]+F[121,x]
F[121,x] = F[122,x]
F[122,x] = F[12,x]*F[120,x]
F[123,x] = F[124,x]+F[126,x]
F[124,x] = F[125,x]
F[125,x] = F[12,x]*F[14,x]
F[126,x] = F[127,x]
F[127,x] = F[12,x]*F[123,x]
F[128,x] = F[129,x]+F[66,x]
F[129,x] = F[130,x]+F[132,x]+F[25,x]+F[92,x]
F[130,x] = F[12,x]*F[131,x]
F[131,x] = F[117,x]+F[129,x]
F[132,x] = F[12,x]*F[133,x]
F[133,x] = F[134,x]+F[142,x]
F[134,x] = F[135,x]+F[138,x]
F[135,x] = F[125,x]+F[136,x]+F[25,x]
F[136,x] = F[12,x]*F[137,x]
F[137,x] = F[12,x]+F[135,x]
F[138,x] = 2*F[25,x]+F[139,x]+F[141,x]
F[139,x] = F[12,x]*F[140,x]
F[140,x] = F[121,x]+F[138,x]
F[141,x] = F[12,x]*F[134,x]
F[142,x] = F[143,x]+F[145,x]
F[143,x] = F[144,x]
F[144,x] = F[12,x]*F[36,x]
F[145,x] = F[146,x]
F[146,x] = F[12,x]*F[142,x]
F[147,x] = 2*F[25,x]+F[148,x]+F[157,x]
F[148,x] = F[12,x]*F[149,x]
F[149,x] = F[150,x]+F[152,x]
F[150,x] = F[151,x]+F[17,x]
F[151,x] = F[58,x]
F[152,x] = F[153,x]+F[69,x]
F[153,x] = 2*F[25,x]+F[154,x]+F[156,x]+F[98,x]
F[154,x] = F[12,x]*F[155,x]
F[155,x] = F[151,x]+F[153,x]
F[156,x] = 0
F[157,x] = F[112,x]*F[12,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_{19}\! \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_{17}\! \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_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \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_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{5}\! \left(x \right)
F_{23}\! \left(x \right) = F_{14}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{28}\! \left(x \right)
F_{25}\! \left(x \right) = 0
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{24}\! \left(x \right)+F_{6}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{35}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{25}\! \left(x \right)+F_{32}\! \left(x \right)+F_{34}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{10}\! \left(x \right)+F_{31}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{14}\! \left(x \right)+F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{41}\! \left(x \right) = F_{25}\! \left(x \right)+F_{42}\! \left(x \right)+F_{99}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{59}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{6}\! \left(x \right)
F_{45}\! \left(x \right) = F_{25}\! \left(x \right)+F_{46}\! \left(x \right)+F_{54}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{51}\! \left(x \right)
F_{48}\! \left(x \right) = F_{10}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = F_{17}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{51}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{13}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{36}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{73}\! \left(x \right)
F_{60}\! \left(x \right) = F_{25}\! \left(x \right)+F_{61}\! \left(x \right)+F_{63}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{6}\! \left(x \right)+F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{30}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{69}\! \left(x \right)
F_{66}\! \left(x \right) = F_{25}\! \left(x \right)+F_{37}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{14}\! \left(x \right)+F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{70}\! \left(x \right)+F_{72}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{17}\! \left(x \right)+F_{69}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{73}\! \left(x \right) = F_{25}\! \left(x \right)+F_{74}\! \left(x \right)+F_{76}\! \left(x \right)+F_{86}\! \left(x \right)
F_{74}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{45}\! \left(x \right)+F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{83}\! \left(x \right)
F_{78}\! \left(x \right) = F_{31}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{80}\! \left(x \right)+F_{82}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{49}\! \left(x \right)+F_{79}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{83}\! \left(x \right) = F_{39}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{12}\! \left(x \right) F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{12}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{65}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{95}\! \left(x \right)
F_{89}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{90}\! \left(x \right)+F_{92}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{36}\! \left(x \right)+F_{89}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{36}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{92}\! \left(x \right)
F_{95}\! \left(x \right) = 3 F_{25}\! \left(x \right)+F_{96}\! \left(x \right)+F_{98}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{57}\! \left(x \right)+F_{95}\! \left(x \right)
F_{98}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{12}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{112}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{20}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{111}\! \left(x \right)+F_{25}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{12}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{107}\! \left(x \right)
F_{105}\! \left(x \right) = F_{10}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{18}\! \left(x \right)+F_{25}\! \left(x \right)+F_{46}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{31}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{25}\! \left(x \right)+F_{72}\! \left(x \right)+F_{76}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{12}\! \left(x \right)
F_{110}\! \left(x \right) = F_{106}\! \left(x \right)+F_{108}\! \left(x \right)
F_{111}\! \left(x \right) = F_{101}\! \left(x \right) F_{12}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{147}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{25}\! \left(x \right)+F_{37}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{12}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{128}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{14}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{25}\! \left(x \right)+F_{37}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{12}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{123}\! \left(x \right)
F_{120}\! \left(x \right) = F_{12}\! \left(x \right)+F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{12}\! \left(x \right) F_{120}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{126}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{12}\! \left(x \right) F_{123}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{66}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{132}\! \left(x \right)+F_{25}\! \left(x \right)+F_{92}\! \left(x \right)
F_{130}\! \left(x \right) = F_{12}\! \left(x \right) F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{117}\! \left(x \right)+F_{129}\! \left(x \right)
F_{132}\! \left(x \right) = F_{12}\! \left(x \right) F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{142}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{138}\! \left(x \right)
F_{135}\! \left(x \right) = F_{125}\! \left(x \right)+F_{136}\! \left(x \right)+F_{25}\! \left(x \right)
F_{136}\! \left(x \right) = F_{12}\! \left(x \right) F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{12}\! \left(x \right)+F_{135}\! \left(x \right)
F_{138}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{139}\! \left(x \right)+F_{141}\! \left(x \right)
F_{139}\! \left(x \right) = F_{12}\! \left(x \right) F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{121}\! \left(x \right)+F_{138}\! \left(x \right)
F_{141}\! \left(x \right) = F_{12}\! \left(x \right) F_{134}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{145}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{12}\! \left(x \right) F_{142}\! \left(x \right)
F_{147}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{148}\! \left(x \right)+F_{157}\! \left(x \right)
F_{148}\! \left(x \right) = F_{12}\! \left(x \right) F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{152}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{17}\! \left(x \right)
F_{151}\! \left(x \right) = F_{58}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{69}\! \left(x \right)
F_{153}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{154}\! \left(x \right)+F_{156}\! \left(x \right)+F_{98}\! \left(x \right)
F_{154}\! \left(x \right) = F_{12}\! \left(x \right) F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{151}\! \left(x \right)+F_{153}\! \left(x \right)
F_{156}\! \left(x \right) = 0
F_{157}\! \left(x \right) = F_{112}\! \left(x \right) F_{12}\! \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_19(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_17(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_1(x) + F_14(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_12(x)*F_13(x))
Eq(F_19(x), F_20(x) + F_41(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_12(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_5(x))
Eq(F_23(x), F_14(x) + F_24(x))
Eq(F_24(x), F_25(x) + F_26(x) + F_28(x))
Eq(F_25(x), 0)
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_24(x) + F_6(x))
Eq(F_28(x), F_12(x)*F_29(x))
Eq(F_29(x), F_30(x) + F_35(x))
Eq(F_30(x), F_14(x) + F_31(x))
Eq(F_31(x), F_25(x) + F_32(x) + F_34(x))
Eq(F_32(x), F_12(x)*F_33(x))
Eq(F_33(x), F_10(x) + F_31(x))
Eq(F_34(x), F_12(x)*F_30(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_14(x) + F_36(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_35(x))
Eq(F_41(x), F_25(x) + F_42(x) + F_99(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_59(x))
Eq(F_44(x), F_45(x) + F_6(x))
Eq(F_45(x), F_25(x) + F_46(x) + F_54(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_51(x))
Eq(F_48(x), F_10(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_12(x)*F_48(x))
Eq(F_51(x), F_17(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_12(x)*F_51(x))
Eq(F_54(x), F_12(x)*F_55(x))
Eq(F_55(x), F_13(x) + F_56(x))
Eq(F_56(x), F_36(x) + F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_12(x)*F_56(x))
Eq(F_59(x), F_60(x) + F_73(x))
Eq(F_60(x), F_25(x) + F_61(x) + F_63(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_6(x) + F_60(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_30(x) + F_65(x))
Eq(F_65(x), F_66(x) + F_69(x))
Eq(F_66(x), F_25(x) + F_37(x) + F_67(x))
Eq(F_67(x), F_12(x)*F_68(x))
Eq(F_68(x), F_14(x) + F_66(x))
Eq(F_69(x), 2*F_25(x) + F_70(x) + F_72(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_17(x) + F_69(x))
Eq(F_72(x), F_12(x)*F_65(x))
Eq(F_73(x), F_25(x) + F_74(x) + F_76(x) + F_86(x))
Eq(F_74(x), F_12(x)*F_75(x))
Eq(F_75(x), F_45(x) + F_73(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_83(x))
Eq(F_78(x), F_31(x) + F_79(x))
Eq(F_79(x), 2*F_25(x) + F_80(x) + F_82(x))
Eq(F_80(x), F_12(x)*F_81(x))
Eq(F_81(x), F_49(x) + F_79(x))
Eq(F_82(x), F_12(x)*F_78(x))
Eq(F_83(x), F_39(x) + F_84(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_12(x)*F_83(x))
Eq(F_86(x), F_12(x)*F_87(x))
Eq(F_87(x), F_65(x) + F_88(x))
Eq(F_88(x), F_89(x) + F_95(x))
Eq(F_89(x), 2*F_25(x) + F_90(x) + F_92(x))
Eq(F_90(x), F_12(x)*F_91(x))
Eq(F_91(x), F_36(x) + F_89(x))
Eq(F_92(x), F_12(x)*F_93(x))
Eq(F_93(x), F_36(x) + F_94(x))
Eq(F_94(x), F_92(x))
Eq(F_95(x), 3*F_25(x) + F_96(x) + F_98(x))
Eq(F_96(x), F_12(x)*F_97(x))
Eq(F_97(x), F_57(x) + F_95(x))
Eq(F_98(x), F_12(x)*F_88(x))
Eq(F_99(x), F_100(x)*F_12(x))
Eq(F_100(x), F_101(x) + F_112(x))
Eq(F_101(x), F_102(x) + F_20(x))
Eq(F_102(x), F_103(x) + F_111(x) + F_25(x))
Eq(F_103(x), F_104(x)*F_12(x))
Eq(F_104(x), F_105(x) + F_107(x))
Eq(F_105(x), F_10(x) + F_106(x))
Eq(F_106(x), F_18(x) + F_25(x) + F_46(x))
Eq(F_107(x), F_108(x) + F_31(x))
Eq(F_108(x), F_109(x) + F_25(x) + F_72(x) + F_76(x))
Eq(F_109(x), F_110(x)*F_12(x))
Eq(F_110(x), F_106(x) + F_108(x))
Eq(F_111(x), F_101(x)*F_12(x))
Eq(F_112(x), F_113(x) + F_147(x))
Eq(F_113(x), F_114(x) + F_25(x) + F_37(x))
Eq(F_114(x), F_115(x)*F_12(x))
Eq(F_115(x), F_116(x) + F_128(x))
Eq(F_116(x), F_117(x) + F_14(x))
Eq(F_117(x), F_118(x) + F_25(x) + F_37(x))
Eq(F_118(x), F_119(x)*F_12(x))
Eq(F_119(x), F_120(x) + F_123(x))
Eq(F_120(x), F_12(x) + F_121(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_12(x)*F_120(x))
Eq(F_123(x), F_124(x) + F_126(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_12(x)*F_14(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_12(x)*F_123(x))
Eq(F_128(x), F_129(x) + F_66(x))
Eq(F_129(x), F_130(x) + F_132(x) + F_25(x) + F_92(x))
Eq(F_130(x), F_12(x)*F_131(x))
Eq(F_131(x), F_117(x) + F_129(x))
Eq(F_132(x), F_12(x)*F_133(x))
Eq(F_133(x), F_134(x) + F_142(x))
Eq(F_134(x), F_135(x) + F_138(x))
Eq(F_135(x), F_125(x) + F_136(x) + F_25(x))
Eq(F_136(x), F_12(x)*F_137(x))
Eq(F_137(x), F_12(x) + F_135(x))
Eq(F_138(x), F_139(x) + F_141(x) + 2*F_25(x))
Eq(F_139(x), F_12(x)*F_140(x))
Eq(F_140(x), F_121(x) + F_138(x))
Eq(F_141(x), F_12(x)*F_134(x))
Eq(F_142(x), F_143(x) + F_145(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_12(x)*F_36(x))
Eq(F_145(x), F_146(x))
Eq(F_146(x), F_12(x)*F_142(x))
Eq(F_147(x), F_148(x) + F_157(x) + 2*F_25(x))
Eq(F_148(x), F_12(x)*F_149(x))
Eq(F_149(x), F_150(x) + F_152(x))
Eq(F_150(x), F_151(x) + F_17(x))
Eq(F_151(x), F_58(x))
Eq(F_152(x), F_153(x) + F_69(x))
Eq(F_153(x), F_154(x) + F_156(x) + 2*F_25(x) + F_98(x))
Eq(F_154(x), F_12(x)*F_155(x))
Eq(F_155(x), F_151(x) + F_153(x))
Eq(F_156(x), 0)
Eq(F_157(x), F_112(x)*F_12(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": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 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": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 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": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 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, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 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