0132_0213_1230_2130_2310
Counting sequence:
1, 1, 2, 6, 19, 53, 125, 260, 497, 901, 1587, 2768, 4851, 8629, 15665, 29060, 54989, 105773, 206023, 404928, 800831, 1590381, 3166837, 6316676, 12612809, 25201013, 50372795, 100711120, 201381867, 402716741, 805379097, 1610695588, 3221319461, 6442557149, 12885021455, 25769937920, 51539757559, 103079382333, 206158616093, 412317066468, 824633948641, 1649267692901, 3298535159747, 6597070070096, 13194139865699, 26388279429973, 52776558529665, 105553116698180, 211106233002237, 422212465575181, 844424930683607, 1688849860860608, 3377699721172271, 6755399441750669, 13510798882859845, 27021597765027780, 54043195529310329, 108086391057819093, 216172782114777163, 432345564228630608, 864691128456271451, 1729382256911483621, 3458764513821834857, 6917529027642460516, 13835058055283631189, 27670116110565887933, 55340232221130312735, 110680464442259069440, 221360928884516485607, 442721857769031216221, 885443715538060571117, 1770887431076119169828, 3541774862152236251281, 7083549724304470293189, 14167099448608938250835, 28334198897217874034640, 56668397794435745465299, 113336795588871488184053, 226673591177742973473233, 453347182355485943897348, 906694364710971884585261, 1813388729421943765794541, 3626777458843887528040167, 7253554917687775052351936, 14507109835375550100789279, 29014219670751100197470893, 58028439341502200390634005, 116056878683004400776752900, 232113757366008801548775977, 464227514732017603092599861, 928455029464035206180017627, 1856910058928070412354615248, 3713820117856140824703564491, 7427640235712281649401208709, 14855280471424563298796234425, 29710560942849126597586014500, 59421121885698253195165294469, 118842243771396506390323565213, 237684487542793012780639808303, 475368975085586025561271986688, 950737950171172051122536026071
Generating function in Maple syntax:
(5*x^7-5*x^6-6*x^5+12*x^4-18*x^3+15*x^2-6*x+1)/(2*x-1)/(x-1)^5
Generating function in latex syntax:
\frac{5 x^{7}-5 x^{6}-6 x^{5}+12 x^{4}-18 x^{3}+15 x^{2}-6 x +1}{\left(2 x -1\right) \left(x -1\right)^{5}}
Generating function in sympy syntax:
(5*x**7 - 5*x**6 - 6*x**5 + 12*x**4 - 18*x**3 + 15*x**2 - 6*x + 1)/((x - 1)**5*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
-(2*x-1)*(x-1)^5*F(x)+5*x^7-5*x^6-6*x^5+12*x^4-18*x^3+15*x^2-6*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right) \left(x -1\right)^{5} F \! \left(x \right)+5 x^{7}-5 x^{6}-6 x^{5}+12 x^{4}-18 x^{3}+15 x^{2}-6 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,-11+3/4*2^n+1/3*n^3-55/12*n^2+73/6*n+1/12*n^4)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ -11+\frac{3 \,2^{n}}{4}+\frac{n^{3}}{3}-\frac{55 n^{2}}{12}+\frac{73 n}{6}+\frac{n^{4}}{12} & \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) = 260
a(n+1) = -1/12*n^4+73/12*n^2+2*a(n)-20*n+19, n >= 8
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) = 260
a \! \left(n +1\right) = -\frac{n^{4}}{12}+\frac{73 n^{2}}{12}+2 a \! \left(n \right)-20 n +19, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18486/
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[26,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[24,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[19,x]+F[22,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]*F[21,x]
F[21,x] = F[1,x]+F[19,x]
F[22,x] = F[23,x]
F[23,x] = F[12,x]*F[19,x]
F[24,x] = F[25,x]
F[25,x] = F[12,x]*F[13,x]
F[26,x] = F[27,x]+F[33,x]
F[27,x] = F[28,x]
F[28,x] = F[12,x]*F[29,x]
F[29,x] = F[21,x]+F[30,x]
F[30,x] = F[19,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[98,x]
F[34,x] = 0
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[37,x]+F[57,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[19,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[55,x]
F[47,x] = F[34,x]+F[48,x]+F[50,x]
F[48,x] = F[12,x]*F[49,x]
F[49,x] = F[12,x]+F[22,x]
F[50,x] = F[12,x]*F[51,x]
F[51,x] = F[18,x]+F[52,x]
F[52,x] = F[31,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[12,x]*F[31,x]
F[55,x] = F[56,x]
F[56,x] = F[12,x]*F[46,x]
F[57,x] = F[58,x]+F[79,x]
F[58,x] = F[34,x]+F[59,x]+F[61,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = F[58,x]+F[6,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[63,x]+F[68,x]
F[63,x] = F[19,x]+F[64,x]
F[64,x] = F[34,x]+F[65,x]+F[67,x]
F[65,x] = F[12,x]*F[66,x]
F[66,x] = F[10,x]+F[64,x]
F[67,x] = F[12,x]*F[63,x]
F[68,x] = F[69,x]+F[72,x]
F[69,x] = F[34,x]+F[50,x]+F[70,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[19,x]+F[31,x]
F[72,x] = 2*F[34,x]+F[73,x]+F[78,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[41,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[31,x]+F[75,x]
F[78,x] = F[12,x]*F[68,x]
F[79,x] = 2*F[34,x]+F[80,x]+F[82,x]
F[80,x] = F[12,x]*F[81,x]
F[81,x] = F[64,x]+F[75,x]
F[82,x] = F[12,x]*F[83,x]
F[83,x] = F[77,x]+F[84,x]
F[84,x] = F[85,x]+F[96,x]
F[85,x] = 2*F[34,x]+F[86,x]+F[88,x]
F[86,x] = F[12,x]*F[87,x]
F[87,x] = F[22,x]+F[53,x]
F[88,x] = F[12,x]*F[89,x]
F[89,x] = F[52,x]+F[90,x]
F[90,x] = F[91,x]+F[94,x]
F[91,x] = F[92,x]
F[92,x] = F[12,x]*F[93,x]
F[93,x] = F[31,x]+F[91,x]
F[94,x] = F[95,x]
F[95,x] = F[12,x]*F[91,x]
F[96,x] = F[97,x]
F[97,x] = F[12,x]*F[84,x]
F[98,x] = F[12,x]*F[99,x]
F[99,x] = F[100,x]+F[109,x]
F[100,x] = F[101,x]+F[27,x]
F[101,x] = F[102,x]+F[108,x]+F[34,x]
F[102,x] = F[103,x]*F[12,x]
F[103,x] = F[104,x]+F[106,x]
F[104,x] = F[10,x]+F[105,x]
F[105,x] = F[34,x]+F[39,x]+F[42,x]
F[106,x] = F[107,x]+F[64,x]
F[107,x] = 2*F[34,x]+F[76,x]+F[80,x]
F[108,x] = F[100,x]*F[12,x]
F[109,x] = F[110,x]+F[114,x]
F[110,x] = F[111,x]+F[34,x]+F[50,x]
F[111,x] = F[112,x]*F[12,x]
F[112,x] = F[113,x]+F[71,x]
F[113,x] = F[31,x]+F[91,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[121,x]+F[31,x]
F[121,x] = F[119,x]
F[122,x] = F[123,x]+F[75,x]
F[123,x] = F[124,x]
F[124,x] = F[12,x]*F[125,x]
F[125,x] = F[126,x]+F[91,x]
F[126,x] = F[124,x]
F[127,x] = F[109,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_{26}\! \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_{24}\! \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_{19}\! \left(x \right)+F_{22}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{33}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{21}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{19}\! \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_{98}\! \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_{57}\! \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_{19}\! \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_{55}\! \left(x \right)
F_{47}\! \left(x \right) = F_{34}\! \left(x \right)+F_{48}\! \left(x \right)+F_{50}\! \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_{22}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{18}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{31}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{46}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{79}\! \left(x \right)
F_{58}\! \left(x \right) = F_{34}\! \left(x \right)+F_{59}\! \left(x \right)+F_{61}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{58}\! \left(x \right)+F_{6}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{68}\! \left(x \right)
F_{63}\! \left(x \right) = F_{19}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{34}\! \left(x \right)+F_{65}\! \left(x \right)+F_{67}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{10}\! \left(x \right)+F_{64}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{63}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{72}\! \left(x \right)
F_{69}\! \left(x \right) = F_{34}\! \left(x \right)+F_{50}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{19}\! \left(x \right)+F_{31}\! \left(x \right)
F_{72}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{73}\! \left(x \right)+F_{78}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{41}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{31}\! \left(x \right)+F_{75}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right)
F_{79}\! \left(x \right) = 2 F_{34}\! \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_{64}\! \left(x \right)+F_{75}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{77}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{96}\! \left(x \right)
F_{85}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{86}\! \left(x \right)+F_{88}\! \left(x \right)
F_{86}\! \left(x \right) = F_{12}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{22}\! \left(x \right)+F_{53}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{52}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{94}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{31}\! \left(x \right)+F_{91}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{12}\! \left(x \right) F_{91}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{12}\! \left(x \right) F_{84}\! \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_{109}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{27}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{108}\! \left(x \right)+F_{34}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{12}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{106}\! \left(x \right)
F_{104}\! \left(x \right) = F_{10}\! \left(x \right)+F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{34}\! \left(x \right)+F_{39}\! \left(x \right)+F_{42}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{64}\! \left(x \right)
F_{107}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{76}\! \left(x \right)+F_{80}\! \left(x \right)
F_{108}\! \left(x \right) = F_{100}\! \left(x \right) F_{12}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{114}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{34}\! \left(x \right)+F_{50}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{12}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{71}\! \left(x \right)
F_{113}\! \left(x \right) = F_{31}\! \left(x \right)+F_{91}\! \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_{121}\! \left(x \right)+F_{31}\! \left(x \right)
F_{121}\! \left(x \right) = F_{119}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{75}\! \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_{126}\! \left(x \right)+F_{91}\! \left(x \right)
F_{126}\! \left(x \right) = F_{124}\! \left(x \right)
F_{127}\! \left(x \right) = F_{109}\! \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_26(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_24(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_19(x) + F_22(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x)*F_21(x))
Eq(F_21(x), F_1(x) + F_19(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_12(x)*F_19(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_12(x)*F_13(x))
Eq(F_26(x), F_27(x) + F_33(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_12(x)*F_29(x))
Eq(F_29(x), F_21(x) + F_30(x))
Eq(F_30(x), F_19(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_98(x))
Eq(F_34(x), 0)
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_57(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_19(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_55(x))
Eq(F_47(x), F_34(x) + F_48(x) + F_50(x))
Eq(F_48(x), F_12(x)*F_49(x))
Eq(F_49(x), F_12(x) + F_22(x))
Eq(F_50(x), F_12(x)*F_51(x))
Eq(F_51(x), F_18(x) + F_52(x))
Eq(F_52(x), F_31(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_12(x)*F_31(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_12(x)*F_46(x))
Eq(F_57(x), F_58(x) + F_79(x))
Eq(F_58(x), F_34(x) + F_59(x) + F_61(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_58(x) + F_6(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_68(x))
Eq(F_63(x), F_19(x) + F_64(x))
Eq(F_64(x), F_34(x) + F_65(x) + F_67(x))
Eq(F_65(x), F_12(x)*F_66(x))
Eq(F_66(x), F_10(x) + F_64(x))
Eq(F_67(x), F_12(x)*F_63(x))
Eq(F_68(x), F_69(x) + F_72(x))
Eq(F_69(x), F_34(x) + F_50(x) + F_70(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_19(x) + F_31(x))
Eq(F_72(x), 2*F_34(x) + F_73(x) + F_78(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_41(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_31(x) + F_75(x))
Eq(F_78(x), F_12(x)*F_68(x))
Eq(F_79(x), 2*F_34(x) + F_80(x) + F_82(x))
Eq(F_80(x), F_12(x)*F_81(x))
Eq(F_81(x), F_64(x) + F_75(x))
Eq(F_82(x), F_12(x)*F_83(x))
Eq(F_83(x), F_77(x) + F_84(x))
Eq(F_84(x), F_85(x) + F_96(x))
Eq(F_85(x), 2*F_34(x) + F_86(x) + F_88(x))
Eq(F_86(x), F_12(x)*F_87(x))
Eq(F_87(x), F_22(x) + F_53(x))
Eq(F_88(x), F_12(x)*F_89(x))
Eq(F_89(x), F_52(x) + F_90(x))
Eq(F_90(x), F_91(x) + F_94(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_12(x)*F_93(x))
Eq(F_93(x), F_31(x) + F_91(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_12(x)*F_91(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_12(x)*F_84(x))
Eq(F_98(x), F_12(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_109(x))
Eq(F_100(x), F_101(x) + F_27(x))
Eq(F_101(x), F_102(x) + F_108(x) + F_34(x))
Eq(F_102(x), F_103(x)*F_12(x))
Eq(F_103(x), F_104(x) + F_106(x))
Eq(F_104(x), F_10(x) + F_105(x))
Eq(F_105(x), F_34(x) + F_39(x) + F_42(x))
Eq(F_106(x), F_107(x) + F_64(x))
Eq(F_107(x), 2*F_34(x) + F_76(x) + F_80(x))
Eq(F_108(x), F_100(x)*F_12(x))
Eq(F_109(x), F_110(x) + F_114(x))
Eq(F_110(x), F_111(x) + F_34(x) + F_50(x))
Eq(F_111(x), F_112(x)*F_12(x))
Eq(F_112(x), F_113(x) + F_71(x))
Eq(F_113(x), F_31(x) + F_91(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_121(x) + F_31(x))
Eq(F_121(x), F_119(x))
Eq(F_122(x), F_123(x) + F_75(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_12(x)*F_125(x))
Eq(F_125(x), F_126(x) + F_91(x))
Eq(F_126(x), F_124(x))
Eq(F_127(x), F_109(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": [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]]}, {"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": [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]]}, {"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": [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]]}, {"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, 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": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 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]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 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": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 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]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[2, 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]]}, {"patt": [2, 3, 1, 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": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 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, 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