0132_0321_1230_2031_2301
Counting sequence:
1, 1, 2, 6, 19, 52, 129, 299, 661, 1414, 2957, 6089, 12409, 25116, 50609, 101687, 203949, 408594, 818021, 1637029, 3275217, 6551784, 13105129, 26212051, 52426149, 104854622, 209711869, 419426689, 838856681, 1677717044, 3355438177, 6710880879, 13421766749, 26843538986, 53687083989, 107374174557, 214748356289, 429496720384, 858993449241, 1717986907659, 3435973825237, 6871947661174, 13743895333869, 27487790680121, 54975581373529, 109951162761292, 219902325537809, 439804651091879, 879609302201101, 1759218604420674, 3518437208860997, 7036874417742869, 14073748835507889, 28147497671039256, 56294995342103369, 112589990684233027, 225179981368493829, 450359962737016974, 900719925474064861, 1801439850948162289, 3602879701896358857, 7205759403792753764, 14411518807585545409, 28823037615171130591, 57646075230342302909, 115292150460684649562, 230584300921369344949, 461168601842738737869, 922337203685477525921, 1844674407370955104304, 3689348814741910263417, 7378697629483820584059, 14757395258967641227829, 29514790517935282517926, 59029581035870565100749, 118059162071741130269097, 236118324143482260608569, 472236648286964521290364, 944473296573929042656881, 1888946593147858085392919, 3777893186295716170868077, 7555786372591432341821554, 15111572745182864683731749, 30223145490365729367555461, 60446290980731458735206289, 120892581961462917470511432, 241785163922925834941125289, 483570327845851669882356659, 967140655691703339764823141, 1934281311383406679529759934, 3868562622766813359059637437, 7737125245533626718119396449, 15474250491067253436238918569, 30948500982134506872477966996, 61897001964269013744956068129, 123794003928538027489912274767, 247588007857076054979824692509, 495176015714152109959649532554, 990352031428304219919299217301, 1980704062856608439838598591549, 3961408125713216879677197344897
Generating function in Maple syntax:
(x^7-3*x^6+3*x^5-4*x^4+8*x^3-10*x^2+5*x-1)/(2*x-1)/(x-1)^4
Generating function in latex syntax:
\frac{x^{7}-3 x^{6}+3 x^{5}-4 x^{4}+8 x^{3}-10 x^{2}+5 x -1}{\left(2 x -1\right) \left(x -1\right)^{4}}
Generating function in sympy syntax:
(x**7 - 3*x**6 + 3*x**5 - 4*x**4 + 8*x**3 - 10*x**2 + 5*x - 1)/((x - 1)**4*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
-(2*x-1)*(x-1)^4*F(x)+x^7-3*x^6+3*x^5-4*x^4+8*x^3-10*x^2+5*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right) \left(x -1\right)^{4} F \! \left(x \right)+x^{7}-3 x^{6}+3 x^{5}-4 x^{4}+8 x^{3}-10 x^{2}+5 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,-3-7/3*n-1/2*n^2-1/6*n^3+25/8*2^n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ -3-\frac{7 n}{3}-\frac{n^{2}}{2}-\frac{n^{3}}{6}+\frac{25 \,2^{n}}{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) = 52
a(6) = 129
a(7) = 299
a(n+1) = 2*a(n)+1/6*n*(n^2+5), 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) = 52
a \! \left(6\right) = 129
a \! \left(7\right) = 299
a \! \left(n +1\right) = 2 a \! \left(n \right)+\frac{n \left(n^{2}+5\right)}{6}, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/19493/
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[26,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[12,x]
F[17,x] = F[18,x]+F[19,x]+F[23,x]
F[18,x] = 0
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[10,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[10,x]*F[12,x]
F[23,x] = F[12,x]*F[24,x]
F[24,x] = F[12,x]+F[25,x]
F[25,x] = F[18,x]+F[22,x]+F[23,x]
F[26,x] = F[27,x]+F[56,x]
F[27,x] = F[28,x]
F[28,x] = F[12,x]*F[29,x]
F[29,x] = F[30,x]+F[33,x]
F[30,x] = F[1,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[12,x]*F[16,x]
F[33,x] = F[27,x]+F[34,x]
F[34,x] = F[18,x]+F[35,x]+F[54,x]
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[37,x]+F[41,x]
F[37,x] = F[31,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[12,x]*F[40,x]
F[40,x] = F[12,x]
F[41,x] = F[34,x]+F[42,x]
F[42,x] = 2*F[18,x]+F[43,x]+F[47,x]
F[43,x] = F[12,x]*F[44,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[38,x]
F[46,x] = F[42,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[12,x]*F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[1,x]+F[51,x]
F[54,x] = F[12,x]*F[55,x]
F[55,x] = F[49,x]+F[51,x]
F[56,x] = F[18,x]+F[57,x]+F[95,x]
F[57,x] = F[12,x]*F[58,x]
F[58,x] = F[59,x]+F[65,x]
F[59,x] = F[6,x]+F[60,x]
F[60,x] = F[18,x]+F[61,x]+F[63,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[10,x]+F[25,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[24,x]
F[65,x] = F[56,x]+F[66,x]
F[66,x] = F[18,x]+F[67,x]+F[91,x]+F[93,x]
F[67,x] = F[12,x]*F[68,x]
F[68,x] = F[69,x]+F[73,x]
F[69,x] = F[60,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[12,x]*F[72,x]
F[72,x] = F[25,x]
F[73,x] = F[66,x]+F[74,x]
F[74,x] = 2*F[18,x]+F[75,x]+F[79,x]+F[90,x]
F[75,x] = F[12,x]*F[76,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = F[70,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] = 2*F[18,x]+F[82,x]+F[88,x]
F[82,x] = F[12,x]*F[83,x]
F[83,x] = F[18,x]+F[84,x]+F[86,x]
F[84,x] = F[12,x]*F[85,x]
F[85,x] = F[10,x]+F[83,x]
F[86,x] = F[12,x]*F[87,x]
F[87,x] = F[51,x]+F[83,x]
F[88,x] = F[12,x]*F[89,x]
F[89,x] = F[49,x]+F[81,x]
F[90,x] = 0
F[91,x] = F[12,x]*F[92,x]
F[92,x] = F[81,x]+F[83,x]
F[93,x] = F[12,x]*F[94,x]
F[94,x] = F[89,x]
F[95,x] = F[12,x]*F[96,x]
F[96,x] = F[87,x]+F[97,x]
F[97,x] = F[100,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[12,x]*F[55,x]
F[100,x] = 2*F[18,x]+F[101,x]+F[88,x]
F[101,x] = F[102,x]*F[12,x]
F[102,x] = F[103,x]+F[83,x]
F[103,x] = F[82,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_{26}\! \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_{12}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{23}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{10}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{18}\! \left(x \right)+F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{56}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \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_{33}\! \left(x \right)
F_{30}\! \left(x \right) = F_{1}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{33}\! \left(x \right) = F_{27}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{18}\! \left(x \right)+F_{35}\! \left(x \right)+F_{54}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{41}\! \left(x \right)
F_{37}\! \left(x \right) = F_{31}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right)
F_{41}\! \left(x \right) = F_{34}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{43}\! \left(x \right)+F_{47}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{46}\! \left(x \right)
F_{45}\! \left(x \right) = F_{38}\! \left(x \right)
F_{46}\! \left(x \right) = F_{42}\! \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_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{1}\! \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_{49}\! \left(x \right)+F_{51}\! \left(x \right)
F_{56}\! \left(x \right) = F_{18}\! \left(x \right)+F_{57}\! \left(x \right)+F_{95}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{65}\! \left(x \right)
F_{59}\! \left(x \right) = F_{6}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{18}\! \left(x \right)+F_{61}\! \left(x \right)+F_{63}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{10}\! \left(x \right)+F_{25}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{24}\! \left(x \right)
F_{65}\! \left(x \right) = F_{56}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{18}\! \left(x \right)+F_{67}\! \left(x \right)+F_{91}\! \left(x \right)+F_{93}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{73}\! \left(x \right)
F_{69}\! \left(x \right) = F_{60}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{12}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{25}\! \left(x \right)
F_{73}\! \left(x \right) = F_{66}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{75}\! \left(x \right)+F_{79}\! \left(x \right)+F_{90}\! \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_{70}\! \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) = 2 F_{18}\! \left(x \right)+F_{82}\! \left(x \right)+F_{88}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{18}\! \left(x \right)+F_{84}\! \left(x \right)+F_{86}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{10}\! \left(x \right)+F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{12}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{51}\! \left(x \right)+F_{83}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{49}\! \left(x \right)+F_{81}\! \left(x \right)
F_{90}\! \left(x \right) = 0
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{81}\! \left(x \right)+F_{83}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{89}\! \left(x \right)
F_{95}\! \left(x \right) = F_{12}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{87}\! \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_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{100}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{101}\! \left(x \right)+F_{88}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{12}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{83}\! \left(x \right)
F_{103}\! \left(x \right) = F_{82}\! \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_26(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_12(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_23(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_12(x)*F_20(x))
Eq(F_20(x), F_10(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_10(x)*F_12(x))
Eq(F_23(x), F_12(x)*F_24(x))
Eq(F_24(x), F_12(x) + F_25(x))
Eq(F_25(x), F_18(x) + F_22(x) + F_23(x))
Eq(F_26(x), F_27(x) + F_56(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_12(x)*F_29(x))
Eq(F_29(x), F_30(x) + F_33(x))
Eq(F_30(x), F_1(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_12(x)*F_16(x))
Eq(F_33(x), F_27(x) + F_34(x))
Eq(F_34(x), F_18(x) + F_35(x) + F_54(x))
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_41(x))
Eq(F_37(x), F_31(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_12(x)*F_40(x))
Eq(F_40(x), F_12(x))
Eq(F_41(x), F_34(x) + F_42(x))
Eq(F_42(x), 2*F_18(x) + F_43(x) + F_47(x))
Eq(F_43(x), F_12(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_38(x))
Eq(F_46(x), F_42(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_12(x)*F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_12(x)*F_53(x))
Eq(F_53(x), F_1(x) + F_51(x))
Eq(F_54(x), F_12(x)*F_55(x))
Eq(F_55(x), F_49(x) + F_51(x))
Eq(F_56(x), F_18(x) + F_57(x) + F_95(x))
Eq(F_57(x), F_12(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_65(x))
Eq(F_59(x), F_6(x) + F_60(x))
Eq(F_60(x), F_18(x) + F_61(x) + F_63(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_10(x) + F_25(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_24(x))
Eq(F_65(x), F_56(x) + F_66(x))
Eq(F_66(x), F_18(x) + F_67(x) + F_91(x) + F_93(x))
Eq(F_67(x), F_12(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_73(x))
Eq(F_69(x), F_60(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_12(x)*F_72(x))
Eq(F_72(x), F_25(x))
Eq(F_73(x), F_66(x) + F_74(x))
Eq(F_74(x), 2*F_18(x) + F_75(x) + F_79(x) + F_90(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_70(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), 2*F_18(x) + F_82(x) + F_88(x))
Eq(F_82(x), F_12(x)*F_83(x))
Eq(F_83(x), F_18(x) + F_84(x) + F_86(x))
Eq(F_84(x), F_12(x)*F_85(x))
Eq(F_85(x), F_10(x) + F_83(x))
Eq(F_86(x), F_12(x)*F_87(x))
Eq(F_87(x), F_51(x) + F_83(x))
Eq(F_88(x), F_12(x)*F_89(x))
Eq(F_89(x), F_49(x) + F_81(x))
Eq(F_90(x), 0)
Eq(F_91(x), F_12(x)*F_92(x))
Eq(F_92(x), F_81(x) + F_83(x))
Eq(F_93(x), F_12(x)*F_94(x))
Eq(F_94(x), F_89(x))
Eq(F_95(x), F_12(x)*F_96(x))
Eq(F_96(x), F_87(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_12(x)*F_55(x))
Eq(F_100(x), F_101(x) + 2*F_18(x) + F_88(x))
Eq(F_101(x), F_102(x)*F_12(x))
Eq(F_102(x), F_103(x) + F_83(x))
Eq(F_103(x), F_82(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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1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": 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[2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 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}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[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": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 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"ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 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