0123_2301_3120
Counting sequence:
1, 1, 2, 6, 21, 71, 212, 554, 1289, 2725, 5326, 9758, 16941, 28107, 44864, 69266, 103889, 151913, 217210, 304438, 419141, 567855, 758220, 999098, 1300697, 1674701, 2134406, 2694862, 3373021, 4187891, 5160696, 6315042, 7677089, 9275729, 11142770, 13313126, 15825013, 18720151, 22043972, 25845834, 30179241, 35102069, 40676798, 46970750, 54056333, 62011291, 70918960, 80868530, 91955313, 104281017, 117954026, 133089686, 149810597, 168246911, 188536636, 210825946, 235269497, 262030749, 291282294, 323206190, 357994301, 395848643, 436981736, 481616962, 529988929, 582343841, 638939874, 700047558, 765950165, 836944103, 913339316, 995459690, 1083643465, 1178243653, 1279628462, 1388181726, 1504303341, 1628409707, 1760934176, 1902327506, 2053058321, 2213613577, 2384499034, 2566239734, 2759380485, 2964486351, 3182143148, 3412957946, 3657559577, 3916599149, 4190750566, 4480711054, 4787201693, 5110967955, 5452780248, 5813434466, 6193752545, 6594583025, 7016801618, 7461311782, 7929045301
Generating function in Maple syntax:
-(2*x^6-6*x^5+21*x^4-22*x^3+16*x^2-6*x+1)/(x-1)^7
Generating function in latex syntax:
-\frac{2 x^{6}-6 x^{5}+21 x^{4}-22 x^{3}+16 x^{2}-6 x +1}{\left(x -1\right)^{7}}
Generating function in sympy syntax:
(-2*x**6 + 6*x**5 - 21*x**4 + 22*x**3 - 16*x**2 + 6*x - 1)/(x - 1)**7
Implicit equation for the generating function in Maple syntax:
(x-1)^7*F(x)+2*x^6-6*x^5+21*x^4-22*x^3+16*x^2-6*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right)^{7} F \! \left(x \right)+2 x^{6}-6 x^{5}+21 x^{4}-22 x^{3}+16 x^{2}-6 x +1 = 0
Explicit closed form in Maple syntax:
1+1/120*n^6-1/24*n^5+1/8*n^4-1/8*n^3+11/30*n^2-1/3*n
Explicit closed form in latex syntax:
1+\frac{1}{120} n^{6}-\frac{1}{24} n^{5}+\frac{1}{8} n^{4}-\frac{1}{8} n^{3}+\frac{11}{30} n^{2}-\frac{1}{3} n
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 71
a(6) = 212
a(n) = 1+1/120*n^6-1/24*n^5+1/8*n^4-1/8*n^3+11/30*n^2-1/3*n, n >= 7
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) = 21
a \! \left(5\right) = 71
a \! \left(6\right) = 212
a \! \left(n \right) = 1+\frac{1}{120} n^{6}-\frac{1}{24} n^{5}+\frac{1}{8} n^{4}-\frac{1}{8} n^{3}+\frac{11}{30} n^{2}-\frac{1}{3} n, \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14687/
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[43,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[23,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[10,x]+F[17,x]
F[17,x] = F[14,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[22,x]
F[21,x] = F[11,x]
F[22,x] = F[18,x]
F[23,x] = F[24,x]+F[25,x]+F[37,x]
F[24,x] = 0
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[27,x]+F[31,x]
F[27,x] = F[11,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[11,x]+F[28,x]
F[31,x] = F[23,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[28,x]
F[36,x] = F[32,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[11,x]+F[39,x]
F[39,x] = F[24,x]+F[37,x]+F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[11,x]+F[42,x]
F[42,x] = F[40,x]
F[43,x] = F[44,x]+F[60,x]
F[44,x] = F[45,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[1,x]+F[14,x]
F[48,x] = F[44,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]+F[54,x]
F[52,x] = F[14,x]+F[53,x]
F[53,x] = F[19,x]
F[54,x] = F[49,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[59,x]
F[58,x] = F[53,x]
F[59,x] = F[55,x]
F[60,x] = F[113,x]+F[24,x]+F[61,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[101,x]+F[63,x]
F[63,x] = F[64,x]+F[7,x]
F[64,x] = F[24,x]+F[25,x]+F[65,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[67,x]+F[71,x]
F[67,x] = F[11,x]+F[68,x]
F[68,x] = F[24,x]+F[37,x]+F[69,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[11,x]+F[68,x]
F[71,x] = F[72,x]+F[82,x]
F[72,x] = F[24,x]+F[40,x]+F[73,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[75,x]+F[76,x]
F[75,x] = F[11,x]+F[42,x]
F[76,x] = F[72,x]+F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[80,x]+F[81,x]
F[80,x] = F[42,x]
F[81,x] = F[77,x]
F[82,x] = F[24,x]+F[83,x]+F[86,x]+F[95,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[28,x]+F[85,x]
F[85,x] = F[83,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[68,x]+F[85,x]
F[89,x] = F[82,x]+F[90,x]
F[90,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[85,x]
F[94,x] = F[90,x]
F[95,x] = F[4,x]*F[96,x]
F[96,x] = F[28,x]+F[97,x]
F[97,x] = 2*F[24,x]+F[95,x]+F[98,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]+F[42,x]
F[100,x] = F[98,x]
F[101,x] = F[102,x]+F[60,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[4,x]
F[104,x] = F[105,x]+F[107,x]
F[105,x] = F[106,x]+F[64,x]
F[106,x] = F[33,x]
F[107,x] = F[102,x]+F[108,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]*F[4,x]
F[110,x] = F[111,x]+F[112,x]
F[111,x] = F[106,x]
F[112,x] = F[108,x]
F[113,x] = F[114,x]*F[4,x]
F[114,x] = F[115,x]+F[67,x]
F[115,x] = F[116,x]+F[130,x]
F[116,x] = F[117,x]+F[120,x]+F[24,x]
F[117,x] = F[118,x]*F[4,x]
F[118,x] = F[119,x]+F[14,x]
F[119,x] = F[117,x]
F[120,x] = F[121,x]*F[4,x]
F[121,x] = F[122,x]+F[75,x]
F[122,x] = F[116,x]+F[123,x]
F[123,x] = 2*F[24,x]+F[124,x]+F[127,x]
F[124,x] = F[125,x]*F[4,x]
F[125,x] = F[126,x]+F[18,x]
F[126,x] = F[124,x]
F[127,x] = F[128,x]*F[4,x]
F[128,x] = F[129,x]+F[80,x]
F[129,x] = F[123,x]
F[130,x] = F[131,x]+F[134,x]+F[24,x]+F[95,x]
F[131,x] = F[132,x]*F[4,x]
F[132,x] = F[133,x]+F[23,x]
F[133,x] = F[131,x]
F[134,x] = F[135,x]*F[4,x]
F[135,x] = F[136,x]+F[88,x]
F[136,x] = F[130,x]+F[137,x]
F[137,x] = 2*F[24,x]+F[138,x]+F[141,x]+F[144,x]
F[138,x] = F[139,x]*F[4,x]
F[139,x] = F[140,x]+F[32,x]
F[140,x] = F[138,x]
F[141,x] = F[142,x]*F[4,x]
F[142,x] = F[143,x]+F[93,x]
F[143,x] = F[137,x]
F[144,x] = 0
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_{43}\! \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_{23}\! \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_{10}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)+F_{37}\! \left(x \right)
F_{24}\! \left(x \right) = 0
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_{31}\! \left(x \right)
F_{27}\! \left(x \right) = F_{11}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{11}\! \left(x \right)+F_{28}\! \left(x \right)
F_{31}\! \left(x \right) = F_{23}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \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) = F_{32}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{11}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{24}\! \left(x \right)+F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{11}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{60}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{48}\! \left(x \right) = F_{44}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \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_{54}\! \left(x \right)
F_{52}\! \left(x \right) = F_{14}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{19}\! \left(x \right)
F_{54}\! \left(x \right) = F_{49}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{53}\! \left(x \right)
F_{59}\! \left(x \right) = F_{55}\! \left(x \right)
F_{60}\! \left(x \right) = F_{113}\! \left(x \right)+F_{24}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{101}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{7}\! \left(x \right)
F_{64}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{71}\! \left(x \right)
F_{67}\! \left(x \right) = F_{11}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{24}\! \left(x \right)+F_{37}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{11}\! \left(x \right)+F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{82}\! \left(x \right)
F_{72}\! \left(x \right) = F_{24}\! \left(x \right)+F_{40}\! \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_{76}\! \left(x \right)
F_{75}\! \left(x \right) = F_{11}\! \left(x \right)+F_{42}\! \left(x \right)
F_{76}\! \left(x \right) = F_{72}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{81}\! \left(x \right)
F_{80}\! \left(x \right) = F_{42}\! \left(x \right)
F_{81}\! \left(x \right) = F_{77}\! \left(x \right)
F_{82}\! \left(x \right) = F_{24}\! \left(x \right)+F_{83}\! \left(x \right)+F_{86}\! \left(x \right)+F_{95}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{28}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{83}\! \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_{68}\! \left(x \right)+F_{85}\! \left(x \right)
F_{89}\! \left(x \right) = F_{82}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \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_{85}\! \left(x \right)
F_{94}\! \left(x \right) = F_{90}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{28}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{95}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{42}\! \left(x \right)
F_{100}\! \left(x \right) = F_{98}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{60}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{107}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{64}\! \left(x \right)
F_{106}\! \left(x \right) = F_{33}\! \left(x \right)
F_{107}\! \left(x \right) = F_{102}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \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_{112}\! \left(x \right)
F_{111}\! \left(x \right) = F_{106}\! \left(x \right)
F_{112}\! \left(x \right) = F_{108}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{4}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{67}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{130}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{120}\! \left(x \right)+F_{24}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{4}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{14}\! \left(x \right)
F_{119}\! \left(x \right) = F_{117}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{75}\! \left(x \right)
F_{122}\! \left(x \right) = F_{116}\! \left(x \right)+F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{124}\! \left(x \right)+F_{127}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{4}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{18}\! \left(x \right)
F_{126}\! \left(x \right) = F_{124}\! \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_{80}\! \left(x \right)
F_{129}\! \left(x \right) = F_{123}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{134}\! \left(x \right)+F_{24}\! \left(x \right)+F_{95}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right) F_{4}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{23}\! \left(x \right)
F_{133}\! \left(x \right) = F_{131}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{4}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{88}\! \left(x \right)
F_{136}\! \left(x \right) = F_{130}\! \left(x \right)+F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{138}\! \left(x \right)+F_{141}\! \left(x \right)+F_{144}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{4}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{32}\! \left(x \right)
F_{140}\! \left(x \right) = F_{138}\! \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_{93}\! \left(x \right)
F_{143}\! \left(x \right) = F_{137}\! \left(x \right)
F_{144}\! \left(x \right) = 0
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_43(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_23(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_10(x) + F_17(x))
Eq(F_17(x), F_14(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_22(x))
Eq(F_21(x), F_11(x))
Eq(F_22(x), F_18(x))
Eq(F_23(x), F_24(x) + F_25(x) + F_37(x))
Eq(F_24(x), 0)
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_27(x) + F_31(x))
Eq(F_27(x), F_11(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_11(x) + F_28(x))
Eq(F_31(x), F_23(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(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), F_32(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_11(x) + F_39(x))
Eq(F_39(x), F_24(x) + F_37(x) + F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_11(x) + F_42(x))
Eq(F_42(x), F_40(x))
Eq(F_43(x), F_44(x) + F_60(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_1(x) + F_14(x))
Eq(F_48(x), F_44(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_54(x))
Eq(F_52(x), F_14(x) + F_53(x))
Eq(F_53(x), F_19(x))
Eq(F_54(x), F_49(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_59(x))
Eq(F_58(x), F_53(x))
Eq(F_59(x), F_55(x))
Eq(F_60(x), F_113(x) + F_24(x) + F_61(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_101(x) + F_63(x))
Eq(F_63(x), F_64(x) + F_7(x))
Eq(F_64(x), F_24(x) + F_25(x) + F_65(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_71(x))
Eq(F_67(x), F_11(x) + F_68(x))
Eq(F_68(x), F_24(x) + F_37(x) + F_69(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_11(x) + F_68(x))
Eq(F_71(x), F_72(x) + F_82(x))
Eq(F_72(x), F_24(x) + F_40(x) + F_73(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_76(x))
Eq(F_75(x), F_11(x) + F_42(x))
Eq(F_76(x), F_72(x) + F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_81(x))
Eq(F_80(x), F_42(x))
Eq(F_81(x), F_77(x))
Eq(F_82(x), F_24(x) + F_83(x) + F_86(x) + F_95(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_28(x) + F_85(x))
Eq(F_85(x), F_83(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_68(x) + F_85(x))
Eq(F_89(x), F_82(x) + F_90(x))
Eq(F_90(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_85(x))
Eq(F_94(x), F_90(x))
Eq(F_95(x), F_4(x)*F_96(x))
Eq(F_96(x), F_28(x) + F_97(x))
Eq(F_97(x), 2*F_24(x) + F_95(x) + F_98(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_42(x))
Eq(F_100(x), F_98(x))
Eq(F_101(x), F_102(x) + F_60(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_4(x))
Eq(F_104(x), F_105(x) + F_107(x))
Eq(F_105(x), F_106(x) + F_64(x))
Eq(F_106(x), F_33(x))
Eq(F_107(x), F_102(x) + F_108(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x)*F_4(x))
Eq(F_110(x), F_111(x) + F_112(x))
Eq(F_111(x), F_106(x))
Eq(F_112(x), F_108(x))
Eq(F_113(x), F_114(x)*F_4(x))
Eq(F_114(x), F_115(x) + F_67(x))
Eq(F_115(x), F_116(x) + F_130(x))
Eq(F_116(x), F_117(x) + F_120(x) + F_24(x))
Eq(F_117(x), F_118(x)*F_4(x))
Eq(F_118(x), F_119(x) + F_14(x))
Eq(F_119(x), F_117(x))
Eq(F_120(x), F_121(x)*F_4(x))
Eq(F_121(x), F_122(x) + F_75(x))
Eq(F_122(x), F_116(x) + F_123(x))
Eq(F_123(x), F_124(x) + F_127(x) + 2*F_24(x))
Eq(F_124(x), F_125(x)*F_4(x))
Eq(F_125(x), F_126(x) + F_18(x))
Eq(F_126(x), F_124(x))
Eq(F_127(x), F_128(x)*F_4(x))
Eq(F_128(x), F_129(x) + F_80(x))
Eq(F_129(x), F_123(x))
Eq(F_130(x), F_131(x) + F_134(x) + F_24(x) + F_95(x))
Eq(F_131(x), F_132(x)*F_4(x))
Eq(F_132(x), F_133(x) + F_23(x))
Eq(F_133(x), F_131(x))
Eq(F_134(x), F_135(x)*F_4(x))
Eq(F_135(x), F_136(x) + F_88(x))
Eq(F_136(x), F_130(x) + F_137(x))
Eq(F_137(x), F_138(x) + F_141(x) + F_144(x) + 2*F_24(x))
Eq(F_138(x), F_139(x)*F_4(x))
Eq(F_139(x), F_140(x) + F_32(x))
Eq(F_140(x), F_138(x))
Eq(F_141(x), F_142(x)*F_4(x))
Eq(F_142(x), F_143(x) + F_93(x))
Eq(F_143(x), F_137(x))
Eq(F_144(x), 0)
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": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 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], "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": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [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": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 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, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [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": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], 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