0132_0213_1203_1230_2301
Counting sequence:
1, 1, 2, 6, 19, 55, 143, 340, 757, 1611, 3329, 6756, 13571, 27119, 54075, 107772, 214857, 428603, 855533, 1708668, 3414023, 6823599, 13641367, 27275236, 54540989, 109070155, 218125753, 436233780, 872446187, 1744866831, 3489703379, 6979371116, 13958700561, 27917352699, 55834649445, 111669234572, 223338395567, 446676707343, 893353319663, 1786706531988, 3573412943173, 7146825750859, 14293651350257, 28587302531716, 57174604875859, 114349209543855, 228698418857963, 457396837462620, 914793674646617, 1829587348987451, 3659174697640029, 7318349394914076, 14636698789428951, 29273397578423279, 58546795156374215, 117093590312235972, 234187180623916877, 468374361247233483, 936748722493818793, 1873497444986938708, 3746994889973124923, 7493989779945440719, 14987979559890012547, 29975959119779093196, 59951918239557188129, 119903836479113308155, 239807672958225474773, 479615345916449730860, 959230691832898162047, 1918461383665794939471, 3836922767331588405279, 7673845534663175243636, 15347691069326348822741, 30695382138652695878859, 61390764277305389884385, 122781528554610777783972, 245563057109221553466787, 491126114218443104711023, 982252228436886207072923, 1964504456873772411664828, 3929008913747544820711273, 7858017827495089638661179, 15716035654990179274412237, 31432071309980358545759676, 62864142619960717088293799, 125728285239921434173195055, 251456570479842868342824183, 502913140959685736681902500, 1005826281919371473359872477, 2011652563838742946715618891, 4023305127677485893426911129, 8046610255354971786849287796, 16093220510709943573693825931, 32186441021419887147382679439, 64372882042839774294760155955, 128745764085679548589514870572, 257491528171359097179024053297, 514983056342718194358042163963, 1029966112685436388716078122053, 2059932225370872777432149766348, 4119864450741745554864292774223
Generating function in Maple syntax:
-(x^7+x^6+4*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{x^{7}+x^{6}+4 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:
(-x**7 - x**6 - 4*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)+x^7+x^6+4*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)+x^{7}+x^{6}+4 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),1,1+13/4*2^n-15/2*n+29/12*n^2-n^3+1/12*n^4)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 1+\frac{13 \,2^{n}}{4}-\frac{15 n}{2}+\frac{29 n^{2}}{12}-n^{3}+\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) = 55
a(6) = 143
a(7) = 340
a(n+1) = -1/12*n^4+4/3*n^3-59/12*n^2+2*a(n)+29/3*n-7, 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) = 55
a \! \left(6\right) = 143
a \! \left(7\right) = 340
a \! \left(n +1\right) = -\frac{n^{4}}{12}+\frac{4 n^{3}}{3}-\frac{59 n^{2}}{12}+2 a \! \left(n \right)+\frac{29 n}{3}-7, \quad n \geq 8
Specification 1
Strategy pack name: row_and_col_placements
Tree: http://permpal.com/tree/21622/
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[8,x]
F[3,x] = F[1,x]+F[4,x]+F[49,x]
F[4,x] = F[5,x]*F[8,x]
F[5,x] = F[3,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[8,x]*F[9,x]
F[8,x] = x
F[9,x] = F[10,x]+F[33,x]+F[7,x]
F[10,x] = F[11,x]*F[14,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[8,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[8,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[1,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[18,x]*F[8,x]
F[21,x] = F[22,x]+F[29,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[8,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[1,x]+F[8,x]
F[26,x] = F[22,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[12,x]*F[8,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[8,x]
F[31,x] = F[12,x]+F[32,x]
F[32,x] = F[30,x]
F[33,x] = F[34,x]
F[34,x] = F[11,x]*F[35,x]*F[8,x]
F[35,x] = F[36,x]+F[44,x]
F[36,x] = F[14,x]*F[37,x]
F[37,x] = F[11,x]+F[38,x]
F[38,x] = F[12,x]+F[39,x]
F[39,x] = F[40,x]+F[41,x]+F[43,x]
F[40,x] = 0
F[41,x] = F[42,x]*F[8,x]
F[42,x] = F[12,x]+F[39,x]
F[43,x] = F[38,x]*F[8,x]
F[44,x] = F[12,x]+F[45,x]
F[45,x] = F[40,x]+F[46,x]+F[48,x]
F[46,x] = F[47,x]*F[8,x]
F[47,x] = F[12,x]+F[45,x]
F[48,x] = F[44,x]*F[8,x]
F[49,x] = F[50,x]*F[8,x]
F[50,x] = F[51,x]+F[62,x]
F[51,x] = F[14,x]+F[52,x]
F[52,x] = F[19,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[55,x]*F[8,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[8,x]
F[57,x] = F[58,x]
F[58,x] = F[59,x]*F[8,x]
F[59,x] = F[60,x]+F[61,x]
F[60,x] = F[8,x]
F[61,x] = F[58,x]
F[62,x] = F[63,x]+F[91,x]
F[63,x] = F[12,x]+F[64,x]
F[64,x] = F[40,x]+F[65,x]+F[67,x]
F[65,x] = F[66,x]*F[8,x]
F[66,x] = F[15,x]+F[64,x]
F[67,x] = F[68,x]*F[8,x]
F[68,x] = F[69,x]+F[73,x]
F[69,x] = F[12,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[72,x]*F[8,x]
F[72,x] = F[19,x]+F[70,x]
F[73,x] = F[74,x]+F[87,x]
F[74,x] = F[40,x]+F[46,x]+F[75,x]
F[75,x] = F[76,x]*F[8,x]
F[76,x] = F[77,x]+F[81,x]
F[77,x] = F[12,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[8,x]*F[80,x]
F[80,x] = F[78,x]+F[8,x]
F[81,x] = F[74,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[8,x]*F[84,x]
F[84,x] = F[85,x]+F[86,x]
F[85,x] = F[28,x]
F[86,x] = F[83,x]
F[87,x] = F[88,x]
F[88,x] = F[8,x]*F[89,x]
F[89,x] = F[32,x]+F[90,x]
F[90,x] = F[88,x]
F[91,x] = F[92,x]+F[97,x]
F[92,x] = F[40,x]+F[93,x]+F[95,x]
F[93,x] = F[8,x]*F[94,x]
F[94,x] = F[19,x]+F[92,x]
F[95,x] = F[8,x]*F[96,x]
F[96,x] = F[12,x]+F[92,x]
F[97,x] = 2*F[40,x]+F[100,x]+F[98,x]
F[98,x] = F[8,x]*F[99,x]
F[99,x] = F[53,x]+F[97,x]
F[100,x] = F[101,x]*F[8,x]
F[101,x] = F[102,x]+F[103,x]
F[102,x] = F[85,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[8,x]
F[105,x] = F[106,x]+F[107,x]
F[106,x] = F[85,x]
F[107,x] = F[104,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_{8}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{49}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{8}\! \left(x \right)
F_{5}\! \left(x \right) = F_{3}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right) F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = x
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{33}\! \left(x \right)+F_{7}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \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_{11}\! \left(x \right) F_{8}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{8}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{18}\! \left(x \right) F_{8}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{29}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{8}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{8}\! \left(x \right)
F_{26}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{8}\! \left(x \right)
F_{31}\! \left(x \right) = F_{12}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{30}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{11}\! \left(x \right) F_{35}\! \left(x \right) F_{8}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{44}\! \left(x \right)
F_{36}\! \left(x \right) = F_{14}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{11}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = 0
F_{41}\! \left(x \right) = F_{42}\! \left(x \right) F_{8}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right)+F_{39}\! \left(x \right)
F_{43}\! \left(x \right) = F_{38}\! \left(x \right) F_{8}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{40}\! \left(x \right)+F_{46}\! \left(x \right)+F_{48}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right) F_{8}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right)+F_{45}\! \left(x \right)
F_{48}\! \left(x \right) = F_{44}\! \left(x \right) F_{8}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right) F_{8}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{62}\! \left(x \right)
F_{51}\! \left(x \right) = F_{14}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{19}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right) F_{8}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{8}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right) F_{8}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{61}\! \left(x \right)
F_{60}\! \left(x \right) = F_{8}\! \left(x \right)
F_{61}\! \left(x \right) = F_{58}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{91}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{40}\! \left(x \right)+F_{65}\! \left(x \right)+F_{67}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right) F_{8}\! \left(x \right)
F_{66}\! \left(x \right) = F_{15}\! \left(x \right)+F_{64}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right) F_{8}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{73}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right) F_{8}\! \left(x \right)
F_{72}\! \left(x \right) = F_{19}\! \left(x \right)+F_{70}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{87}\! \left(x \right)
F_{74}\! \left(x \right) = F_{40}\! \left(x \right)+F_{46}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right) F_{8}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{81}\! \left(x \right)
F_{77}\! \left(x \right) = F_{12}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{8}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{78}\! \left(x \right)+F_{8}\! \left(x \right)
F_{81}\! \left(x \right) = F_{74}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{8}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{86}\! \left(x \right)
F_{85}\! \left(x \right) = F_{28}\! \left(x \right)
F_{86}\! \left(x \right) = F_{83}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{8}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{32}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{88}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{97}\! \left(x \right)
F_{92}\! \left(x \right) = F_{40}\! \left(x \right)+F_{93}\! \left(x \right)+F_{95}\! \left(x \right)
F_{93}\! \left(x \right) = F_{8}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{19}\! \left(x \right)+F_{92}\! \left(x \right)
F_{95}\! \left(x \right) = F_{8}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right)+F_{92}\! \left(x \right)
F_{97}\! \left(x \right) = 2 F_{40}\! \left(x \right)+F_{100}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{8}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{53}\! \left(x \right)+F_{97}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{8}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{103}\! \left(x \right)
F_{102}\! \left(x \right) = F_{85}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{8}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{107}\! \left(x \right)
F_{106}\! \left(x \right) = F_{85}\! \left(x \right)
F_{107}\! \left(x \right) = F_{104}\! \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)*F_8(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_49(x))
Eq(F_4(x), F_5(x)*F_8(x))
Eq(F_5(x), F_3(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_8(x)*F_9(x))
Eq(F_8(x), x)
Eq(F_9(x), F_10(x) + F_33(x) + F_7(x))
Eq(F_10(x), F_11(x)*F_14(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_8(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_8(x))
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_1(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_18(x)*F_8(x))
Eq(F_21(x), F_22(x) + F_29(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_8(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_1(x) + F_8(x))
Eq(F_26(x), F_22(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_12(x)*F_8(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_8(x))
Eq(F_31(x), F_12(x) + F_32(x))
Eq(F_32(x), F_30(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_11(x)*F_35(x)*F_8(x))
Eq(F_35(x), F_36(x) + F_44(x))
Eq(F_36(x), F_14(x)*F_37(x))
Eq(F_37(x), F_11(x) + F_38(x))
Eq(F_38(x), F_12(x) + F_39(x))
Eq(F_39(x), F_40(x) + F_41(x) + F_43(x))
Eq(F_40(x), 0)
Eq(F_41(x), F_42(x)*F_8(x))
Eq(F_42(x), F_12(x) + F_39(x))
Eq(F_43(x), F_38(x)*F_8(x))
Eq(F_44(x), F_12(x) + F_45(x))
Eq(F_45(x), F_40(x) + F_46(x) + F_48(x))
Eq(F_46(x), F_47(x)*F_8(x))
Eq(F_47(x), F_12(x) + F_45(x))
Eq(F_48(x), F_44(x)*F_8(x))
Eq(F_49(x), F_50(x)*F_8(x))
Eq(F_50(x), F_51(x) + F_62(x))
Eq(F_51(x), F_14(x) + F_52(x))
Eq(F_52(x), F_19(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_55(x)*F_8(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_8(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_59(x)*F_8(x))
Eq(F_59(x), F_60(x) + F_61(x))
Eq(F_60(x), F_8(x))
Eq(F_61(x), F_58(x))
Eq(F_62(x), F_63(x) + F_91(x))
Eq(F_63(x), F_12(x) + F_64(x))
Eq(F_64(x), F_40(x) + F_65(x) + F_67(x))
Eq(F_65(x), F_66(x)*F_8(x))
Eq(F_66(x), F_15(x) + F_64(x))
Eq(F_67(x), F_68(x)*F_8(x))
Eq(F_68(x), F_69(x) + F_73(x))
Eq(F_69(x), F_12(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_72(x)*F_8(x))
Eq(F_72(x), F_19(x) + F_70(x))
Eq(F_73(x), F_74(x) + F_87(x))
Eq(F_74(x), F_40(x) + F_46(x) + F_75(x))
Eq(F_75(x), F_76(x)*F_8(x))
Eq(F_76(x), F_77(x) + F_81(x))
Eq(F_77(x), F_12(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_8(x)*F_80(x))
Eq(F_80(x), F_78(x) + F_8(x))
Eq(F_81(x), F_74(x) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_8(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_86(x))
Eq(F_85(x), F_28(x))
Eq(F_86(x), F_83(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_8(x)*F_89(x))
Eq(F_89(x), F_32(x) + F_90(x))
Eq(F_90(x), F_88(x))
Eq(F_91(x), F_92(x) + F_97(x))
Eq(F_92(x), F_40(x) + F_93(x) + F_95(x))
Eq(F_93(x), F_8(x)*F_94(x))
Eq(F_94(x), F_19(x) + F_92(x))
Eq(F_95(x), F_8(x)*F_96(x))
Eq(F_96(x), F_12(x) + F_92(x))
Eq(F_97(x), F_100(x) + 2*F_40(x) + F_98(x))
Eq(F_98(x), F_8(x)*F_99(x))
Eq(F_99(x), F_53(x) + F_97(x))
Eq(F_100(x), F_101(x)*F_8(x))
Eq(F_101(x), F_102(x) + F_103(x))
Eq(F_102(x), F_85(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_8(x))
Eq(F_105(x), F_106(x) + F_107(x))
Eq(F_106(x), F_85(x))
Eq(F_107(x), F_104(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "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": "row_and_col_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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 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, 3, 0, 1], "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], "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, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 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, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 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, 0, 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, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [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, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "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, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 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, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "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}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": 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"pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 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, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [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, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 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, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [3, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 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