0132_1230_3021_3120
Counting sequence:
1, 1, 2, 6, 20, 63, 182, 490, 1255, 3106, 7505, 17819, 41736, 96673, 221808, 504704, 1139933, 2557588, 5703859, 12651337, 27922022, 61346331, 134223482, 292559766, 635445635, 1375742038, 2969579557, 6392133895, 13723779860, 29393702501, 62813920020, 133949319484, 285078485241, 605590424168, 1284195261863, 2718714344149, 5746666293778, 12128987702143, 25563645411134, 53807350357362, 113112258788927, 237494511690186, 498078767482937, 1043436534870451, 2183630092885600, 4565172278660713, 9534964836221432, 19896762416396600, 41482374692910165, 86412817850364796, 179862510118319835, 374080244048690849, 777433885675080446, 1614540466412592163, 3350678122763940418, 6949054225032990094, 14402511608331185723, 29831843931702531198, 61753358090504634509, 127758114229246653087, 264163139743044266732, 545908332431342528941, 1127557231505496862492, 2327748517801224600436, 4803070988192125095665, 9905901567582029851088, 20420545689596474313807, 42077023232131487954605, 86662803658287474256170, 178416908680918784041991, 367163994043114916226950, 755283489353963882279914, 1553068277053754570623351, 3192319742419880165484658, 6559367044705937202909473, 13472911575627097795822539, 27663622856650381663043768, 56781734590024614050760753, 116510225865359886713657984, 238989522965067004976150512, 490068304126280301698015437, 1004617356099756844182410596, 2058800670803713484526278147, 4217942184635441190551593721, 8638983906966140082452167830, 17689002592601254084302693163, 36209746149097373040801404682, 74102317039098309892791883910, 151608969186231415541554341875, 310103979840987758862232946086, 634134785123936045817078821365, 1296432706141614492888110394679, 2649810654090356478421578069956, 5414749731834253322408772145653, 11062232191054158136498576981028, 22594881597036760777458818381484, 46140501144244693606040161255913, 94202285229460297398723760266808, 192286750422119547339531170925559, 392417088933151264100823189621637, 800679810369155395720355165855042
Generating function in Maple syntax:
-(3*x^8+14*x^7-66*x^6+127*x^5-145*x^4+102*x^3-43*x^2+10*x-1)/(2*x-1)^3/(x-1)^5
Generating function in latex syntax:
-\frac{3 x^{8}+14 x^{7}-66 x^{6}+127 x^{5}-145 x^{4}+102 x^{3}-43 x^{2}+10 x -1}{\left(2 x -1\right)^{3} \left(x -1\right)^{5}}
Generating function in sympy syntax:
(-3*x**8 - 14*x**7 + 66*x**6 - 127*x**5 + 145*x**4 - 102*x**3 + 43*x**2 - 10*x + 1)/((x - 1)**5*(2*x - 1)**3)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^3*(x-1)^5*F(x)+3*x^8+14*x^7-66*x^6+127*x^5-145*x^4+102*x^3-43*x^2+10*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{3} \left(x -1\right)^{5} F \! \left(x \right)+3 x^{8}+14 x^{7}-66 x^{6}+127 x^{5}-145 x^{4}+102 x^{3}-43 x^{2}+10 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/48*(3*n^2+3*n+18)*2^n+1/24*n^4-5/12*n^3+23/24*n^2-19/12*n+1)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(3 n^{2}+3 n +18\right) 2^{n}}{48}+\frac{n^{4}}{24}-\frac{5 n^{3}}{12}+\frac{23 n^{2}}{24}-\frac{19 n}{12}+1 & \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) = 63
a(6) = 182
a(7) = 490
a(8) = 1255
a(n+3) = 8*a(n)-12*a(n+1)+6*a(n+2)-1/24*(n-1)*(n-6)*(n^2-15*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) = 20
a \! \left(5\right) = 63
a \! \left(6\right) = 182
a \! \left(7\right) = 490
a \! \left(8\right) = 1255
a \! \left(n +3\right) = 8 a \! \left(n \right)-12 a \! \left(n +1\right)+6 a \! \left(n +2\right)-\frac{\left(n -1\right) \left(n -6\right) \left(n^{2}-15 n +20\right)}{24}, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15649/
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[38,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[14,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]*F[21,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[12,x]
F[23,x] = F[19,x]
F[24,x] = F[25,x]+F[26,x]+F[37,x]
F[25,x] = 0
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[10,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[10,x]*F[12,x]
F[31,x] = F[24,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[29,x]
F[36,x] = F[32,x]
F[37,x] = F[12,x]*F[13,x]
F[38,x] = F[39,x]+F[51,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[41,x]
F[41,x] = F[42,x]+F[45,x]
F[42,x] = F[1,x]+F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[12,x]*F[42,x]
F[45,x] = F[39,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[43,x]
F[50,x] = F[46,x]
F[51,x] = F[25,x]+F[52,x]+F[88,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[54,x]+F[73,x]
F[54,x] = F[55,x]+F[6,x]
F[55,x] = F[25,x]+F[56,x]+F[61,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[10,x]+F[58,x]
F[58,x] = F[25,x]+F[56,x]+F[59,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = F[43,x]+F[58,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[60,x]+F[63,x]
F[63,x] = F[64,x]+F[68,x]
F[64,x] = F[65,x]
F[65,x] = F[12,x]*F[66,x]
F[66,x] = F[12,x]+F[67,x]
F[67,x] = F[65,x]
F[68,x] = 2*F[25,x]+F[69,x]+F[72,x]
F[69,x] = F[12,x]*F[70,x]
F[70,x] = F[29,x]+F[71,x]
F[71,x] = F[69,x]
F[72,x] = F[12,x]*F[63,x]
F[73,x] = F[51,x]+F[74,x]
F[74,x] = 2*F[25,x]+F[75,x]+F[79,x]
F[75,x] = F[12,x]*F[76,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = F[55,x]
F[78,x] = F[74,x]
F[79,x] = F[12,x]*F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[46,x]+F[82,x]
F[82,x] = 2*F[25,x]+F[83,x]+F[87,x]
F[83,x] = F[12,x]*F[84,x]
F[84,x] = F[85,x]+F[86,x]
F[85,x] = F[58,x]
F[86,x] = F[82,x]
F[87,x] = F[12,x]*F[81,x]
F[88,x] = F[12,x]*F[89,x]
F[89,x] = F[90,x]+F[96,x]
F[90,x] = F[39,x]+F[91,x]
F[91,x] = F[25,x]+F[92,x]+F[95,x]
F[92,x] = F[12,x]*F[93,x]
F[93,x] = F[57,x]+F[94,x]
F[94,x] = F[82,x]+F[91,x]
F[95,x] = F[12,x]*F[90,x]
F[96,x] = F[97,x]+F[98,x]
F[97,x] = F[47,x]
F[98,x] = 2*F[25,x]+F[83,x]+F[99,x]
F[99,x] = F[12,x]*F[96,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_{38}\! \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_{14}\! \left(x \right)+F_{19}\! \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_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{37}\! \left(x \right)
F_{25}\! \left(x \right) = 0
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{10}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{31}\! \left(x \right) = F_{24}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{29}\! \left(x \right)
F_{36}\! \left(x \right) = F_{32}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{51}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{45}\! \left(x \right)
F_{42}\! \left(x \right) = F_{1}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{39}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{43}\! \left(x \right)
F_{50}\! \left(x \right) = F_{46}\! \left(x \right)
F_{51}\! \left(x \right) = F_{25}\! \left(x \right)+F_{52}\! \left(x \right)+F_{88}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{73}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{6}\! \left(x \right)
F_{55}\! \left(x \right) = F_{25}\! \left(x \right)+F_{56}\! \left(x \right)+F_{61}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{10}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{25}\! \left(x \right)+F_{56}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{43}\! \left(x \right)+F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{60}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{68}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{65}\! \left(x \right)
F_{68}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{69}\! \left(x \right)+F_{72}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{29}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{69}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right) F_{63}\! \left(x \right)
F_{73}\! \left(x \right) = F_{51}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{75}\! \left(x \right)+F_{79}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{55}\! \left(x \right)
F_{78}\! \left(x \right) = F_{74}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{46}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{83}\! \left(x \right)+F_{87}\! \left(x \right)
F_{83}\! \left(x \right) = F_{12}\! \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_{58}\! \left(x \right)
F_{86}\! \left(x \right) = F_{82}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{81}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{96}\! \left(x \right)
F_{90}\! \left(x \right) = F_{39}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{25}\! \left(x \right)+F_{92}\! \left(x \right)+F_{95}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{57}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{82}\! \left(x \right)+F_{91}\! \left(x \right)
F_{95}\! \left(x \right) = F_{12}\! \left(x \right) F_{90}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)+F_{98}\! \left(x \right)
F_{97}\! \left(x \right) = F_{47}\! \left(x \right)
F_{98}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{83}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{12}\! \left(x \right) F_{96}\! \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_38(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_14(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_12(x))
Eq(F_23(x), F_19(x))
Eq(F_24(x), F_25(x) + F_26(x) + F_37(x))
Eq(F_25(x), 0)
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_10(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_10(x)*F_12(x))
Eq(F_31(x), F_24(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_29(x))
Eq(F_36(x), F_32(x))
Eq(F_37(x), F_12(x)*F_13(x))
Eq(F_38(x), F_39(x) + F_51(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_45(x))
Eq(F_42(x), F_1(x) + F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_12(x)*F_42(x))
Eq(F_45(x), F_39(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_43(x))
Eq(F_50(x), F_46(x))
Eq(F_51(x), F_25(x) + F_52(x) + F_88(x))
Eq(F_52(x), F_12(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_73(x))
Eq(F_54(x), F_55(x) + F_6(x))
Eq(F_55(x), F_25(x) + F_56(x) + F_61(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_10(x) + F_58(x))
Eq(F_58(x), F_25(x) + F_56(x) + F_59(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_43(x) + F_58(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_60(x) + F_63(x))
Eq(F_63(x), F_64(x) + F_68(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_12(x)*F_66(x))
Eq(F_66(x), F_12(x) + F_67(x))
Eq(F_67(x), F_65(x))
Eq(F_68(x), 2*F_25(x) + F_69(x) + F_72(x))
Eq(F_69(x), F_12(x)*F_70(x))
Eq(F_70(x), F_29(x) + F_71(x))
Eq(F_71(x), F_69(x))
Eq(F_72(x), F_12(x)*F_63(x))
Eq(F_73(x), F_51(x) + F_74(x))
Eq(F_74(x), 2*F_25(x) + F_75(x) + F_79(x))
Eq(F_75(x), F_12(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_55(x))
Eq(F_78(x), F_74(x))
Eq(F_79(x), F_12(x)*F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_46(x) + F_82(x))
Eq(F_82(x), 2*F_25(x) + F_83(x) + F_87(x))
Eq(F_83(x), F_12(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_86(x))
Eq(F_85(x), F_58(x))
Eq(F_86(x), F_82(x))
Eq(F_87(x), F_12(x)*F_81(x))
Eq(F_88(x), F_12(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_96(x))
Eq(F_90(x), F_39(x) + F_91(x))
Eq(F_91(x), F_25(x) + F_92(x) + F_95(x))
Eq(F_92(x), F_12(x)*F_93(x))
Eq(F_93(x), F_57(x) + F_94(x))
Eq(F_94(x), F_82(x) + F_91(x))
Eq(F_95(x), F_12(x)*F_90(x))
Eq(F_96(x), F_97(x) + F_98(x))
Eq(F_97(x), F_47(x))
Eq(F_98(x), 2*F_25(x) + F_83(x) + F_99(x))
Eq(F_99(x), F_12(x)*F_96(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:
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{"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "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": [3, 1, 2, 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, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": 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"pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "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": [3, 1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[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, 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": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": 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