0132_0321_1032_1302_3120
Counting sequence:
1, 1, 2, 6, 19, 55, 148, 377, 920, 2171, 4992, 11253, 24984, 54823, 119200, 257281, 552008, 1178483, 2505344, 5306733, 11204664, 23590623, 49542496, 103805881, 217051624, 452980715, 943713728, 1962928997, 4076857560, 8455710231, 17515406112, 36238778353, 74893483144, 154618812643, 318901310720, 657129984221, 1352914685048, 2783138793423, 5720896422624, 11751030504873, 24120536315944, 49478023230043, 101429947640896, 207807697626581, 425510999924504, 870813209171975, 1781208836968608, 3641582511163617, 7441494696755400, 15199648742340691, 31032616182312832, 63331869759858253, 129197014310149304, 263460578201129663, 537054255563884640, 1094374709450980761, 2229281815548342888, 4539628424389404363, 9241386435364199104, 18807032043899129413, 38262582434139668824, 77822201560962102263, 158238476507289675296, 321665099785310230481, 653706493112082155784, 1328165573307087632835, 2697836320780021836288, 5478682989891736738237, 11123386676446859528440, 22578814746220491077551, 45821712279094526109152, 92971590131496140034953, 188599511409606455607464, 382511685112441262189883, 775648694811339226224960, 1572548038795591856030901, 3187597375937010519109528, 6460197348565674652195303, 13090399890514656532218784, 26520810167795927519964353, 53721641109125083950847304, 108803323765316625723391283, 220326730624766167090029696, 446093627437798165466401581, 903067587252127993505329464, 1827895839257319312155547295, 3699313008020765274600700768, 7485668675053783849780436857, 15145422668132074300718760680, 30639015972313161803753104811, 61974373216724350012137179072, 125341428977644752833536092453, 253468223043681611285595441624, 512507176264147433808237177303, 1036155812881863290090566715680, 2094594546470863425129317918641, 4233754934356000540155004568968, 8556641551540548460102746350243, 17291546468738191679790966865664, 34939619668790572878752881793693, 70592292800209524795847659435384
Generating function in Maple syntax:
-(x^8+3*x^7-4*x^6+8*x^5-20*x^4+28*x^3-20*x^2+7*x-1)/(2*x-1)^2/(x-1)^4
Generating function in latex syntax:
-\frac{x^{8}+3 x^{7}-4 x^{6}+8 x^{5}-20 x^{4}+28 x^{3}-20 x^{2}+7 x -1}{\left(2 x -1\right)^{2} \left(x -1\right)^{4}}
Generating function in sympy syntax:
(-x**8 - 3*x**7 + 4*x**6 - 8*x**5 + 20*x**4 - 28*x**3 + 20*x**2 - 7*x + 1)/((x - 1)**4*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^2*(x-1)^4*F(x)+x^8+3*x^7-4*x^6+8*x^5-20*x^4+28*x^3-20*x^2+7*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{2} \left(x -1\right)^{4} F \! \left(x \right)+x^{8}+3 x^{7}-4 x^{6}+8 x^{5}-20 x^{4}+28 x^{3}-20 x^{2}+7 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,1/48*(27*n-27)*2^n-1/3*n^3+2*n^2-20/3*n+8)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ \frac{\left(27 n -27\right) 2^{n}}{48}-\frac{n^{3}}{3}+2 n^{2}-\frac{20 n}{3}+8 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 55
a(6) = 148
a(7) = 377
a(8) = 920
a(n+2) = -1/3*n^3+4*n^2-4*a(n)+4*a(n+1)-44/3*n+20, n >= 9
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) = 55
a \! \left(6\right) = 148
a \! \left(7\right) = 377
a \! \left(8\right) = 920
a \! \left(n +2\right) = -\frac{n^{3}}{3}+4 n^{2}-4 a \! \left(n \right)+4 a \! \left(n +1\right)-\frac{44 n}{3}+20, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/21749/
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[14,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[14,x]*F[7,x]
F[7,x] = F[29,x]+F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[20,x]
F[10,x] = F[11,x]+F[15,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[10,x]*F[14,x]
F[14,x] = x
F[15,x] = F[12,x]+F[16,x]
F[16,x] = F[14,x]*F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[14,x]*F[19,x]
F[19,x] = F[1,x]+F[17,x]
F[20,x] = F[1,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[14,x]*F[24,x]
F[24,x] = F[25,x]+F[28,x]
F[25,x] = F[1,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[19,x]^2*F[14,x]
F[28,x] = F[19,x]*F[22,x]
F[29,x] = F[19,x]*F[30,x]
F[30,x] = F[31,x]+F[67,x]
F[31,x] = F[14,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[14,x]*F[34,x]
F[34,x] = F[35,x]+F[49,x]
F[35,x] = F[14,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[14,x]*F[38,x]
F[38,x] = F[39,x]+F[42,x]
F[39,x] = F[14,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[14,x]*F[39,x]
F[42,x] = F[43,x]+F[45,x]
F[43,x] = F[44,x]
F[44,x] = x^2
F[45,x] = 2*F[46,x]+F[47,x]+F[48,x]
F[46,x] = 0
F[47,x] = F[14,x]*F[40,x]
F[48,x] = F[14,x]*F[42,x]
F[49,x] = F[50,x]+F[53,x]
F[50,x] = F[51,x]
F[51,x] = F[14,x]*F[52,x]
F[52,x] = F[14,x]+F[50,x]
F[53,x] = 2*F[46,x]+F[54,x]+F[59,x]
F[54,x] = F[14,x]*F[55,x]
F[55,x] = F[40,x]+F[56,x]
F[56,x] = 2*F[46,x]+F[54,x]+F[57,x]
F[57,x] = F[14,x]*F[58,x]
F[58,x] = F[50,x]+F[56,x]
F[59,x] = F[14,x]*F[60,x]
F[60,x] = F[58,x]+F[61,x]
F[61,x] = F[62,x]+F[64,x]
F[62,x] = F[63,x]
F[63,x] = F[14,x]*F[50,x]
F[64,x] = 3*F[46,x]+F[65,x]+F[66,x]
F[65,x] = F[14,x]*F[56,x]
F[66,x] = F[14,x]*F[61,x]
F[67,x] = F[68,x]
F[68,x] = F[16,x]+F[46,x]+F[69,x]
F[69,x] = F[14,x]*F[70,x]
F[70,x] = F[71,x]+F[82,x]
F[71,x] = F[14,x]+F[72,x]
F[72,x] = F[16,x]+F[46,x]+F[73,x]
F[73,x] = F[14,x]*F[74,x]
F[74,x] = F[75,x]+F[78,x]
F[75,x] = F[14,x]+F[76,x]
F[76,x] = F[16,x]+F[46,x]+F[77,x]
F[77,x] = F[14,x]*F[75,x]
F[78,x] = F[43,x]+F[79,x]
F[79,x] = 2*F[46,x]+F[80,x]+F[81,x]
F[80,x] = F[14,x]*F[76,x]
F[81,x] = F[14,x]*F[78,x]
F[82,x] = F[83,x]+F[87,x]
F[83,x] = F[46,x]+F[84,x]+F[85,x]
F[84,x] = x^2
F[85,x] = F[14,x]*F[86,x]
F[86,x] = F[14,x]+F[83,x]
F[87,x] = F[46,x]+F[88,x]+F[90,x]+F[95,x]
F[88,x] = F[14,x]*F[89,x]
F[89,x] = F[16,x]
F[90,x] = F[14,x]*F[91,x]
F[91,x] = F[76,x]+F[92,x]
F[92,x] = F[46,x]+F[88,x]+F[90,x]+F[93,x]
F[93,x] = F[14,x]*F[94,x]
F[94,x] = F[83,x]+F[92,x]
F[95,x] = F[14,x]*F[96,x]
F[96,x] = F[94,x]+F[97,x]
F[97,x] = F[100,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[14,x]*F[83,x]
F[100,x] = 3*F[46,x]+F[101,x]+F[102,x]
F[101,x] = F[14,x]*F[92,x]
F[102,x] = F[14,x]*F[97,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_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{14}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{29}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{20}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{10}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = F_{12}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \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_{28}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{19} \left(x \right)^{2} F_{14}\! \left(x \right)
F_{28}\! \left(x \right) = F_{19}\! \left(x \right) F_{22}\! \left(x \right)
F_{29}\! \left(x \right) = F_{19}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{67}\! \left(x \right)
F_{31}\! \left(x \right) = F_{14}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{14}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{49}\! \left(x \right)
F_{35}\! \left(x \right) = F_{14}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{14}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = F_{14}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{14}\! \left(x \right) F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{45}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = x^{2}
F_{45}\! \left(x \right) = 2 F_{46}\! \left(x \right)+F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{46}\! \left(x \right) = 0
F_{47}\! \left(x \right) = F_{14}\! \left(x \right) F_{40}\! \left(x \right)
F_{48}\! \left(x \right) = F_{14}\! \left(x \right) F_{42}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{53}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{14}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{14}\! \left(x \right)+F_{50}\! \left(x \right)
F_{53}\! \left(x \right) = 2 F_{46}\! \left(x \right)+F_{54}\! \left(x \right)+F_{59}\! \left(x \right)
F_{54}\! \left(x \right) = F_{14}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{40}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = 2 F_{46}\! \left(x \right)+F_{54}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{14}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{50}\! \left(x \right)+F_{56}\! \left(x \right)
F_{59}\! \left(x \right) = F_{14}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{58}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{64}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{14}\! \left(x \right) F_{50}\! \left(x \right)
F_{64}\! \left(x \right) = 3 F_{46}\! \left(x \right)+F_{65}\! \left(x \right)+F_{66}\! \left(x \right)
F_{65}\! \left(x \right) = F_{14}\! \left(x \right) F_{56}\! \left(x \right)
F_{66}\! \left(x \right) = F_{14}\! \left(x \right) F_{61}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{16}\! \left(x \right)+F_{46}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{14}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{82}\! \left(x \right)
F_{71}\! \left(x \right) = F_{14}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{16}\! \left(x \right)+F_{46}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{14}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{78}\! \left(x \right)
F_{75}\! \left(x \right) = F_{14}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{16}\! \left(x \right)+F_{46}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{14}\! \left(x \right) F_{75}\! \left(x \right)
F_{78}\! \left(x \right) = F_{43}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = 2 F_{46}\! \left(x \right)+F_{80}\! \left(x \right)+F_{81}\! \left(x \right)
F_{80}\! \left(x \right) = F_{14}\! \left(x \right) F_{76}\! \left(x \right)
F_{81}\! \left(x \right) = F_{14}\! \left(x \right) F_{78}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{87}\! \left(x \right)
F_{83}\! \left(x \right) = F_{46}\! \left(x \right)+F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = x^{2}
F_{85}\! \left(x \right) = F_{14}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{14}\! \left(x \right)+F_{83}\! \left(x \right)
F_{87}\! \left(x \right) = F_{46}\! \left(x \right)+F_{88}\! \left(x \right)+F_{90}\! \left(x \right)+F_{95}\! \left(x \right)
F_{88}\! \left(x \right) = F_{14}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{16}\! \left(x \right)
F_{90}\! \left(x \right) = F_{14}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{76}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{46}\! \left(x \right)+F_{88}\! \left(x \right)+F_{90}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{14}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{83}\! \left(x \right)+F_{92}\! \left(x \right)
F_{95}\! \left(x \right) = F_{14}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{94}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{100}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{14}\! \left(x \right) F_{83}\! \left(x \right)
F_{100}\! \left(x \right) = 3 F_{46}\! \left(x \right)+F_{101}\! \left(x \right)+F_{102}\! \left(x \right)
F_{101}\! \left(x \right) = F_{14}\! \left(x \right) F_{92}\! \left(x \right)
F_{102}\! \left(x \right) = F_{14}\! \left(x \right) F_{97}\! \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_14(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_14(x)*F_7(x))
Eq(F_7(x), F_29(x) + F_8(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_20(x))
Eq(F_10(x), F_11(x) + F_15(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_10(x)*F_14(x))
Eq(F_14(x), x)
Eq(F_15(x), F_12(x) + F_16(x))
Eq(F_16(x), F_14(x)*F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_14(x)*F_19(x))
Eq(F_19(x), F_1(x) + F_17(x))
Eq(F_20(x), F_1(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_14(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_28(x))
Eq(F_25(x), F_1(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_14(x)*F_19(x)**2)
Eq(F_28(x), F_19(x)*F_22(x))
Eq(F_29(x), F_19(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_67(x))
Eq(F_31(x), F_14(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_14(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_49(x))
Eq(F_35(x), F_14(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_14(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_42(x))
Eq(F_39(x), F_14(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_14(x)*F_39(x))
Eq(F_42(x), F_43(x) + F_45(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), x**2)
Eq(F_45(x), 2*F_46(x) + F_47(x) + F_48(x))
Eq(F_46(x), 0)
Eq(F_47(x), F_14(x)*F_40(x))
Eq(F_48(x), F_14(x)*F_42(x))
Eq(F_49(x), F_50(x) + F_53(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_14(x)*F_52(x))
Eq(F_52(x), F_14(x) + F_50(x))
Eq(F_53(x), 2*F_46(x) + F_54(x) + F_59(x))
Eq(F_54(x), F_14(x)*F_55(x))
Eq(F_55(x), F_40(x) + F_56(x))
Eq(F_56(x), 2*F_46(x) + F_54(x) + F_57(x))
Eq(F_57(x), F_14(x)*F_58(x))
Eq(F_58(x), F_50(x) + F_56(x))
Eq(F_59(x), F_14(x)*F_60(x))
Eq(F_60(x), F_58(x) + F_61(x))
Eq(F_61(x), F_62(x) + F_64(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_14(x)*F_50(x))
Eq(F_64(x), 3*F_46(x) + F_65(x) + F_66(x))
Eq(F_65(x), F_14(x)*F_56(x))
Eq(F_66(x), F_14(x)*F_61(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_16(x) + F_46(x) + F_69(x))
Eq(F_69(x), F_14(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_82(x))
Eq(F_71(x), F_14(x) + F_72(x))
Eq(F_72(x), F_16(x) + F_46(x) + F_73(x))
Eq(F_73(x), F_14(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_78(x))
Eq(F_75(x), F_14(x) + F_76(x))
Eq(F_76(x), F_16(x) + F_46(x) + F_77(x))
Eq(F_77(x), F_14(x)*F_75(x))
Eq(F_78(x), F_43(x) + F_79(x))
Eq(F_79(x), 2*F_46(x) + F_80(x) + F_81(x))
Eq(F_80(x), F_14(x)*F_76(x))
Eq(F_81(x), F_14(x)*F_78(x))
Eq(F_82(x), F_83(x) + F_87(x))
Eq(F_83(x), F_46(x) + F_84(x) + F_85(x))
Eq(F_84(x), x**2)
Eq(F_85(x), F_14(x)*F_86(x))
Eq(F_86(x), F_14(x) + F_83(x))
Eq(F_87(x), F_46(x) + F_88(x) + F_90(x) + F_95(x))
Eq(F_88(x), F_14(x)*F_89(x))
Eq(F_89(x), F_16(x))
Eq(F_90(x), F_14(x)*F_91(x))
Eq(F_91(x), F_76(x) + F_92(x))
Eq(F_92(x), F_46(x) + F_88(x) + F_90(x) + F_93(x))
Eq(F_93(x), F_14(x)*F_94(x))
Eq(F_94(x), F_83(x) + F_92(x))
Eq(F_95(x), F_14(x)*F_96(x))
Eq(F_96(x), F_94(x) + F_97(x))
Eq(F_97(x), F_100(x) + F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_14(x)*F_83(x))
Eq(F_100(x), F_101(x) + F_102(x) + 3*F_46(x))
Eq(F_101(x), F_14(x)*F_92(x))
Eq(F_102(x), F_14(x)*F_97(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": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "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, 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, 3, 0, 2], "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, 3, 2], "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": [1, 3, 0, 2], "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, 3, 2], "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": [1, 3, 0, 2], "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": false, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 0], [0, 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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 2], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 2], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"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, 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, 3, 0, 2], "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, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "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, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 3]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 3], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 3], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}], "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": 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