0132_0213_0231_2031_2310
Counting sequence:
1, 1, 2, 6, 19, 55, 142, 334, 736, 1557, 3223, 6618, 13597, 28075, 58332, 121878, 255694, 537737, 1131997, 2382706, 5010947, 10524255, 22068586, 46197790, 96543628, 201417949, 419541331, 872548938, 1812099385, 3758286771, 7784853352, 16106392102, 33286306266, 68719837329, 141734338681, 292058258402, 601295975743, 1236951215911, 2542621363286, 5222681055150, 10720239303736, 21990233609509, 45079977926095, 92358978066874, 189116001471637, 387028094646843, 791648373860020, 1618481118156342, 3307330978647334, 6755399443599385, 13792273861632981, 28147497674165586, 57420895252386235, 117093590315382383, 238690780254748930, 486388759760516926, 990791918026432292, 2017612633067355885, 4107282860167748875, 8358680908406013994, 17005592192957919025, 34587645138212925763, 70328211781025811904, 142962266571257842758, 290536219160934970546, 590295810358715944737, 1199038364791131956209, 2434970217729672772546, 4943727411754172702583, 10035028776098009913399, 20365205457375359840110, 41320706725109411557070, 83822005070936219623504, 170005193383307245981237, 344732753249484120163079, 698910239464707512535450, 1416709944860893586435341, 2871198821584744313747659, 5817955506895402928666764, 11787026741242634480433238, 23876284937388926229234814, 48357032784585167018863017, 97922991388784963183736013, 198263834416799184686363442, 401363372112056886039114355, 812398150781030805441429631, 1644139114675895677641599898, 3326963855579459488835027550, 6731298963614255244810163132, 13617340432139183023939202813, 27544165874099711116557132739, 55707301767842112370515116554, 112652543574969605015877868073, 227780967228509970581499591891, 460513694614161462262538255128, 930930909542605966724208911974, 1881668859713778017846739914890, 3802951800684688204490184461233, 7685131763883640746573841934953, 15528719852795810168334697086882, 31374352355648677687043491389103
Generating function in Maple syntax:
-(3*x^8+2*x^7-34*x^6+76*x^5-96*x^4+75*x^3-35*x^2+9*x-1)/(2*x-1)^2/(x-1)^6
Generating function in latex syntax:
-\frac{3 x^{8}+2 x^{7}-34 x^{6}+76 x^{5}-96 x^{4}+75 x^{3}-35 x^{2}+9 x -1}{\left(2 x -1\right)^{2} \left(x -1\right)^{6}}
Generating function in sympy syntax:
(-3*x**8 - 2*x**7 + 34*x**6 - 76*x**5 + 96*x**4 - 75*x**3 + 35*x**2 - 9*x + 1)/((x - 1)**6*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^2*(x-1)^6*F(x)+3*x^8+2*x^7-34*x^6+76*x^5-96*x^4+75*x^3-35*x^2+9*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{2} \left(x -1\right)^{6} F \! \left(x \right)+3 x^{8}+2 x^{7}-34 x^{6}+76 x^{5}-96 x^{4}+75 x^{3}-35 x^{2}+9 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,2-41/20*n+35/24*n^2-11/24*n^3+1/120*n^5+1/24*n^4+1/4*2^n*n-1/4*2^n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 2-\frac{41 n}{20}+\frac{35 n^{2}}{24}-\frac{11 n^{3}}{24}+\frac{n^{5}}{120}+\frac{n^{4}}{24}+\frac{2^{n} n}{4}-\frac{2^{n}}{4} & \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) = 142
a(7) = 334
a(8) = 736
a(n+2) = 1/120*n^5-1/24*n^4-19/24*n^3+109/24*n^2+4*a(n+1)-4*a(n)-403/60*n+5, 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) = 142
a \! \left(7\right) = 334
a \! \left(8\right) = 736
a \! \left(n +2\right) = \frac{n^{5}}{120}-\frac{n^{4}}{24}-\frac{19 n^{3}}{24}+\frac{109 n^{2}}{24}+4 a \! \left(n +1\right)-4 a \! \left(n \right)-\frac{403 n}{60}+5, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18195/
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[19,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[17,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[1,x]+F[14,x]
F[17,x] = F[18,x]
F[18,x] = F[12,x]*F[13,x]
F[19,x] = F[20,x]+F[41,x]
F[20,x] = F[21,x]
F[21,x] = F[12,x]*F[22,x]
F[22,x] = F[23,x]+F[5,x]
F[23,x] = F[14,x]+F[24,x]
F[24,x] = F[25,x]+F[26,x]+F[28,x]
F[25,x] = 0
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[24,x]+F[6,x]
F[28,x] = F[12,x]*F[29,x]
F[29,x] = F[30,x]+F[35,x]
F[30,x] = F[14,x]+F[31,x]
F[31,x] = F[25,x]+F[32,x]+F[34,x]
F[32,x] = F[12,x]*F[33,x]
F[33,x] = F[10,x]+F[31,x]
F[34,x] = F[12,x]*F[30,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[37,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[14,x]+F[36,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[35,x]
F[41,x] = F[25,x]+F[42,x]+F[81,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[44,x]+F[59,x]
F[44,x] = F[45,x]+F[6,x]
F[45,x] = F[25,x]+F[46,x]+F[54,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[48,x]+F[51,x]
F[48,x] = F[10,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[12,x]*F[48,x]
F[51,x] = F[17,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[12,x]*F[51,x]
F[54,x] = F[12,x]*F[55,x]
F[55,x] = F[13,x]+F[56,x]
F[56,x] = F[36,x]+F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[12,x]*F[56,x]
F[59,x] = F[24,x]+F[60,x]
F[60,x] = F[25,x]+F[61,x]+F[63,x]+F[73,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[45,x]+F[60,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[65,x]+F[70,x]
F[65,x] = F[31,x]+F[66,x]
F[66,x] = 2*F[25,x]+F[67,x]+F[69,x]
F[67,x] = F[12,x]*F[68,x]
F[68,x] = F[49,x]+F[66,x]
F[69,x] = F[12,x]*F[65,x]
F[70,x] = F[39,x]+F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[12,x]*F[70,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[35,x]+F[75,x]
F[75,x] = F[76,x]+F[79,x]
F[76,x] = F[77,x]
F[77,x] = F[12,x]*F[78,x]
F[78,x] = F[36,x]+F[76,x]
F[79,x] = F[80,x]
F[80,x] = F[12,x]*F[75,x]
F[81,x] = F[12,x]*F[82,x]
F[82,x] = F[83,x]+F[94,x]
F[83,x] = F[20,x]+F[84,x]
F[84,x] = F[25,x]+F[85,x]+F[93,x]
F[85,x] = F[12,x]*F[86,x]
F[86,x] = F[87,x]+F[89,x]
F[87,x] = F[10,x]+F[88,x]
F[88,x] = F[18,x]+F[25,x]+F[46,x]
F[89,x] = F[31,x]+F[90,x]
F[90,x] = F[25,x]+F[40,x]+F[63,x]+F[91,x]
F[91,x] = F[12,x]*F[92,x]
F[92,x] = F[88,x]+F[90,x]
F[93,x] = F[12,x]*F[83,x]
F[94,x] = F[95,x]+F[96,x]
F[95,x] = F[37,x]
F[96,x] = F[97,x]
F[97,x] = F[12,x]*F[94,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_{19}\! \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_{17}\! \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_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{41}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{5}\! \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_{26}\! \left(x \right)+F_{28}\! \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_{24}\! \left(x \right)+F_{6}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{35}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{25}\! \left(x \right)+F_{32}\! \left(x \right)+F_{34}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{10}\! \left(x \right)+F_{31}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{30}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{14}\! \left(x \right)+F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{41}\! \left(x \right) = F_{25}\! \left(x \right)+F_{42}\! \left(x \right)+F_{81}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{59}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{6}\! \left(x \right)
F_{45}\! \left(x \right) = F_{25}\! \left(x \right)+F_{46}\! \left(x \right)+F_{54}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{51}\! \left(x \right)
F_{48}\! \left(x \right) = F_{10}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = F_{17}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{51}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{13}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{36}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{59}\! \left(x \right) = F_{24}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{25}\! \left(x \right)+F_{61}\! \left(x \right)+F_{63}\! \left(x \right)+F_{73}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{45}\! \left(x \right)+F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{70}\! \left(x \right)
F_{65}\! \left(x \right) = F_{31}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{67}\! \left(x \right)+F_{69}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{49}\! \left(x \right)+F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{70}\! \left(x \right) = F_{39}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right) F_{70}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{35}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{79}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{36}\! \left(x \right)+F_{76}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \left(x \right)
F_{81}\! \left(x \right) = F_{12}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{94}\! \left(x \right)
F_{83}\! \left(x \right) = F_{20}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{25}\! \left(x \right)+F_{85}\! \left(x \right)+F_{93}\! \left(x \right)
F_{85}\! \left(x \right) = F_{12}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{89}\! \left(x \right)
F_{87}\! \left(x \right) = F_{10}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{18}\! \left(x \right)+F_{25}\! \left(x \right)+F_{46}\! \left(x \right)
F_{89}\! \left(x \right) = F_{31}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{25}\! \left(x \right)+F_{40}\! \left(x \right)+F_{63}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{88}\! \left(x \right)+F_{90}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{83}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)+F_{96}\! \left(x \right)
F_{95}\! \left(x \right) = F_{37}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{12}\! \left(x \right) F_{94}\! \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_19(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_17(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_1(x) + F_14(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_12(x)*F_13(x))
Eq(F_19(x), F_20(x) + F_41(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_12(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_5(x))
Eq(F_23(x), F_14(x) + F_24(x))
Eq(F_24(x), F_25(x) + F_26(x) + F_28(x))
Eq(F_25(x), 0)
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_24(x) + F_6(x))
Eq(F_28(x), F_12(x)*F_29(x))
Eq(F_29(x), F_30(x) + F_35(x))
Eq(F_30(x), F_14(x) + F_31(x))
Eq(F_31(x), F_25(x) + F_32(x) + F_34(x))
Eq(F_32(x), F_12(x)*F_33(x))
Eq(F_33(x), F_10(x) + F_31(x))
Eq(F_34(x), F_12(x)*F_30(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_14(x) + F_36(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_35(x))
Eq(F_41(x), F_25(x) + F_42(x) + F_81(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_59(x))
Eq(F_44(x), F_45(x) + F_6(x))
Eq(F_45(x), F_25(x) + F_46(x) + F_54(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_51(x))
Eq(F_48(x), F_10(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_12(x)*F_48(x))
Eq(F_51(x), F_17(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_12(x)*F_51(x))
Eq(F_54(x), F_12(x)*F_55(x))
Eq(F_55(x), F_13(x) + F_56(x))
Eq(F_56(x), F_36(x) + F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_12(x)*F_56(x))
Eq(F_59(x), F_24(x) + F_60(x))
Eq(F_60(x), F_25(x) + F_61(x) + F_63(x) + F_73(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_45(x) + F_60(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_70(x))
Eq(F_65(x), F_31(x) + F_66(x))
Eq(F_66(x), 2*F_25(x) + F_67(x) + F_69(x))
Eq(F_67(x), F_12(x)*F_68(x))
Eq(F_68(x), F_49(x) + F_66(x))
Eq(F_69(x), F_12(x)*F_65(x))
Eq(F_70(x), F_39(x) + F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_12(x)*F_70(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_35(x) + F_75(x))
Eq(F_75(x), F_76(x) + F_79(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_12(x)*F_78(x))
Eq(F_78(x), F_36(x) + F_76(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_12(x)*F_75(x))
Eq(F_81(x), F_12(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_94(x))
Eq(F_83(x), F_20(x) + F_84(x))
Eq(F_84(x), F_25(x) + F_85(x) + F_93(x))
Eq(F_85(x), F_12(x)*F_86(x))
Eq(F_86(x), F_87(x) + F_89(x))
Eq(F_87(x), F_10(x) + F_88(x))
Eq(F_88(x), F_18(x) + F_25(x) + F_46(x))
Eq(F_89(x), F_31(x) + F_90(x))
Eq(F_90(x), F_25(x) + F_40(x) + F_63(x) + F_91(x))
Eq(F_91(x), F_12(x)*F_92(x))
Eq(F_92(x), F_88(x) + F_90(x))
Eq(F_93(x), F_12(x)*F_83(x))
Eq(F_94(x), F_95(x) + F_96(x))
Eq(F_95(x), F_37(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_12(x)*F_94(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": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 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": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [1, 0]]}, {"patt": [1, 0], 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