0123_0321_1032_2310
Counting sequence:
1, 1, 2, 6, 20, 57, 124, 212, 309, 423, 554, 702, 867, 1049, 1248, 1464, 1697, 1947, 2214, 2498, 2799, 3117, 3452, 3804, 4173, 4559, 4962, 5382, 5819, 6273, 6744, 7232, 7737, 8259, 8798, 9354, 9927, 10517, 11124, 11748, 12389, 13047, 13722, 14414, 15123, 15849, 16592, 17352, 18129, 18923, 19734, 20562, 21407, 22269, 23148, 24044, 24957, 25887, 26834, 27798, 28779, 29777, 30792, 31824, 32873, 33939, 35022, 36122, 37239, 38373, 39524, 40692, 41877, 43079, 44298, 45534, 46787, 48057, 49344, 50648, 51969, 53307, 54662, 56034, 57423, 58829, 60252, 61692, 63149, 64623, 66114, 67622, 69147, 70689, 72248, 73824, 75417, 77027, 78654, 80298, 81959
Generating function in Maple syntax:
-(8*x^9-12*x^8-9*x^7+7*x^6+13*x^5+7*x^4+2*x^3+2*x^2-2*x+1)/(x-1)^3
Generating function in latex syntax:
-\frac{8 x^{9}-12 x^{8}-9 x^{7}+7 x^{6}+13 x^{5}+7 x^{4}+2 x^{3}+2 x^{2}-2 x +1}{\left(x -1\right)^{3}}
Generating function in sympy syntax:
(-8*x**9 + 12*x**8 + 9*x**7 - 7*x**6 - 13*x**5 - 7*x**4 - 2*x**3 - 2*x**2 + 2*x - 1)/(x - 1)**3
Implicit equation for the generating function in Maple syntax:
(x-1)^3*F(x)+8*x^9-12*x^8-9*x^7+7*x^6+13*x^5+7*x^4+2*x^3+2*x^2-2*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right)^{3} F \! \left(x \right)+8 x^{9}-12 x^{8}-9 x^{7}+7 x^{6}+13 x^{5}+7 x^{4}+2 x^{3}+2 x^{2}-2 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,n = 3,6,n = 4,20,n = 5,57,n = 6,124,9+17/2*n^2-61/2*n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ 6 & n =3 \\ 20 & n =4 \\ 57 & n =5 \\ 124 & n =6 \\ 9+\frac{17}{2} n^{2}-\frac{61}{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) = 57
a(6) = 124
a(7) = 212
a(8) = 309
a(9) = 423
a(n) = 9+17/2*n^2-61/2*n, 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) = 57
a \! \left(6\right) = 124
a \! \left(7\right) = 212
a \! \left(8\right) = 309
a \! \left(9\right) = 423
a \! \left(n \right) = 9+\frac{17}{2} n^{2}-\frac{61}{2} n, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15098/
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[28,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[14,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[4,x]
F[14,x] = F[15,x]+F[17,x]
F[15,x] = F[16,x]
F[16,x] = F[13,x]*F[4,x]
F[17,x] = F[18,x]+F[19,x]+F[23,x]
F[18,x] = 0
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[4,x]
F[21,x] = F[22,x]
F[22,x] = x^2
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[15,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[4,x]
F[28,x] = F[2,x]+F[29,x]
F[29,x] = F[101,x]+F[18,x]+F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[45,x]
F[32,x] = F[15,x]+F[33,x]
F[33,x] = F[18,x]+F[34,x]+F[43,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[36,x]+F[38,x]
F[36,x] = F[37,x]+F[4,x]
F[37,x] = F[22,x]
F[38,x] = F[39,x]+F[41,x]
F[39,x] = F[18,x]+F[19,x]+F[40,x]
F[40,x] = F[15,x]*F[4,x]
F[41,x] = F[42,x]
F[42,x] = F[25,x]*F[4,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[15,x]+F[39,x]
F[45,x] = F[46,x]+F[56,x]
F[46,x] = F[18,x]+F[30,x]+F[47,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[49,x]+F[52,x]
F[49,x] = F[50,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[1,x]+F[15,x]
F[52,x] = F[18,x]+F[53,x]+F[55,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[39,x]+F[4,x]
F[55,x] = F[4,x]*F[49,x]
F[56,x] = F[18,x]+F[57,x]+F[78,x]+F[99,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[59,x]+F[64,x]
F[59,x] = F[60,x]+F[61,x]
F[60,x] = F[26,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[39,x]
F[64,x] = F[65,x]+F[68,x]
F[65,x] = 2*F[18,x]+F[57,x]+F[66,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[52,x]
F[68,x] = F[69,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[71,x]
F[71,x] = 2*F[18,x]+F[72,x]+F[74,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[25,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[15,x]+F[60,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[80,x]+F[86,x]
F[80,x] = F[52,x]+F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[25,x]+F[4,x]
F[86,x] = F[87,x]+F[94,x]
F[87,x] = F[18,x]+F[74,x]+F[88,x]+F[91,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[25,x]+F[90,x]
F[90,x] = F[62,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[52,x]+F[93,x]
F[93,x] = F[82,x]
F[94,x] = F[95,x]
F[95,x] = F[4,x]*F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[4,x]*F[98,x]
F[98,x] = F[25,x]
F[99,x] = F[100,x]*F[4,x]
F[100,x] = F[71,x]+F[75,x]
F[101,x] = F[102,x]*F[4,x]
F[102,x] = F[103,x]+F[106,x]
F[103,x] = F[104,x]+F[49,x]
F[104,x] = F[105,x]+F[18,x]+F[53,x]
F[105,x] = F[4,x]*F[48,x]
F[106,x] = F[107,x]+F[111,x]
F[107,x] = F[108,x]+F[18,x]+F[47,x]
F[108,x] = F[109,x]*F[4,x]
F[109,x] = F[110,x]+F[15,x]
F[110,x] = F[18,x]+F[19,x]+F[43,x]
F[111,x] = F[112,x]+F[18,x]+F[88,x]+F[91,x]
F[112,x] = F[113,x]*F[4,x]
F[113,x] = F[114,x]+F[75,x]
F[114,x] = F[72,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_{28}\! \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_{14}\! \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_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{17}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{23}\! \left(x \right)
F_{18}\! \left(x \right) = 0
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_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = x^{2}
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{2}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{101}\! \left(x \right)+F_{18}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{45}\! \left(x \right)
F_{32}\! \left(x \right) = F_{15}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18}\! \left(x \right)+F_{34}\! \left(x \right)+F_{43}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{38}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{22}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{41}\! \left(x \right)
F_{39}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{15}\! \left(x \right)+F_{39}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{56}\! \left(x \right)
F_{46}\! \left(x \right) = F_{18}\! \left(x \right)+F_{30}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{52}\! \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_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{52}\! \left(x \right) = F_{18}\! \left(x \right)+F_{53}\! \left(x \right)+F_{55}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{39}\! \left(x \right)+F_{4}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{56}\! \left(x \right) = F_{18}\! \left(x \right)+F_{57}\! \left(x \right)+F_{78}\! \left(x \right)+F_{99}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{64}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{61}\! \left(x \right)
F_{60}\! \left(x \right) = F_{26}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{39}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{68}\! \left(x \right)
F_{65}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{57}\! \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_{52}\! \left(x \right)
F_{68}\! \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_{71}\! \left(x \right)
F_{71}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{72}\! \left(x \right)+F_{74}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{25}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{15}\! \left(x \right)+F_{60}\! \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_{86}\! \left(x \right)
F_{80}\! \left(x \right) = F_{52}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{25}\! \left(x \right)+F_{4}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{94}\! \left(x \right)
F_{87}\! \left(x \right) = F_{18}\! \left(x \right)+F_{74}\! \left(x \right)+F_{88}\! \left(x \right)+F_{91}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{25}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{62}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{52}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{82}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{25}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{4}\! \left(x \right)
F_{100}\! \left(x \right) = F_{71}\! \left(x \right)+F_{75}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{4}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{106}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{49}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{18}\! \left(x \right)+F_{53}\! \left(x \right)
F_{105}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{111}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{18}\! \left(x \right)+F_{47}\! \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_{15}\! \left(x \right)
F_{110}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{43}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{18}\! \left(x \right)+F_{88}\! \left(x \right)+F_{91}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{75}\! \left(x \right)
F_{114}\! \left(x \right) = F_{72}\! \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_28(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_14(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_4(x))
Eq(F_14(x), F_15(x) + F_17(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_13(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_23(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_4(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), x**2)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_15(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_4(x))
Eq(F_28(x), F_2(x) + F_29(x))
Eq(F_29(x), F_101(x) + F_18(x) + F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_45(x))
Eq(F_32(x), F_15(x) + F_33(x))
Eq(F_33(x), F_18(x) + F_34(x) + F_43(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_36(x) + F_38(x))
Eq(F_36(x), F_37(x) + F_4(x))
Eq(F_37(x), F_22(x))
Eq(F_38(x), F_39(x) + F_41(x))
Eq(F_39(x), F_18(x) + F_19(x) + F_40(x))
Eq(F_40(x), F_15(x)*F_4(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_25(x)*F_4(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_15(x) + F_39(x))
Eq(F_45(x), F_46(x) + F_56(x))
Eq(F_46(x), F_18(x) + F_30(x) + F_47(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_52(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_1(x) + F_15(x))
Eq(F_52(x), F_18(x) + F_53(x) + F_55(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_39(x) + F_4(x))
Eq(F_55(x), F_4(x)*F_49(x))
Eq(F_56(x), F_18(x) + F_57(x) + F_78(x) + F_99(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_64(x))
Eq(F_59(x), F_60(x) + F_61(x))
Eq(F_60(x), F_26(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_39(x))
Eq(F_64(x), F_65(x) + F_68(x))
Eq(F_65(x), 2*F_18(x) + F_57(x) + F_66(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_52(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), 2*F_18(x) + F_72(x) + F_74(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_25(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_15(x) + F_60(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_86(x))
Eq(F_80(x), F_52(x) + F_81(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_25(x) + F_4(x))
Eq(F_86(x), F_87(x) + F_94(x))
Eq(F_87(x), F_18(x) + F_74(x) + F_88(x) + F_91(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_25(x) + F_90(x))
Eq(F_90(x), F_62(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_52(x) + F_93(x))
Eq(F_93(x), F_82(x))
Eq(F_94(x), F_95(x))
Eq(F_95(x), F_4(x)*F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_4(x)*F_98(x))
Eq(F_98(x), F_25(x))
Eq(F_99(x), F_100(x)*F_4(x))
Eq(F_100(x), F_71(x) + F_75(x))
Eq(F_101(x), F_102(x)*F_4(x))
Eq(F_102(x), F_103(x) + F_106(x))
Eq(F_103(x), F_104(x) + F_49(x))
Eq(F_104(x), F_105(x) + F_18(x) + F_53(x))
Eq(F_105(x), F_4(x)*F_48(x))
Eq(F_106(x), F_107(x) + F_111(x))
Eq(F_107(x), F_108(x) + F_18(x) + F_47(x))
Eq(F_108(x), F_109(x)*F_4(x))
Eq(F_109(x), F_110(x) + F_15(x))
Eq(F_110(x), F_18(x) + F_19(x) + F_43(x))
Eq(F_111(x), F_112(x) + F_18(x) + F_88(x) + F_91(x))
Eq(F_112(x), F_113(x)*F_4(x))
Eq(F_113(x), F_114(x) + F_75(x))
Eq(F_114(x), F_72(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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "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], "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, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}], "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": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"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": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 0]]}], "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, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "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": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [0, 1], [0, 1], [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], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 1], [0, 1], [0, 1], [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], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "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], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "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, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "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]]}]]}, {"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, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], 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