0123_0132_0231_2130_3012
Counting sequence:
1, 1, 2, 6, 19, 53, 129, 289, 617, 1281, 2617, 5297, 10665, 21409, 42905, 85905, 171913, 343937, 687993, 1376113, 2752361, 5504865, 11009881, 22019921, 44040009, 88080193, 176160569, 352321329, 704642857, 1409285921, 2818572057, 5637144337, 11274288905, 22548578049, 45097156345, 90194312945, 180388626153, 360777252577, 721554505433, 1443109011153, 2886218022601, 5772436045505, 11544872091321, 23089744182961, 46179488366249, 92358976732833, 184717953466009, 369435906932369, 738871813865097, 1477743627730561, 2955487255461497, 5910974510923377, 11821949021847145, 23643898043694689, 47287796087389785, 94575592174779985, 189151184349560393, 378302368699121217, 756604737398242873, 1513209474796486193, 3026418949592972841, 6052837899185946145, 12105675798371892761, 24211351596743786001, 48422703193487572489, 96845406386975145473, 193690812773950291449, 387381625547900583409, 774763251095801167337, 1549526502191602335201, 3099053004383204670937, 6198106008766409342417, 12396212017532818685385, 24792424035065637371329, 49584848070131274743225, 99169696140262549487025, 198339392280525098974633, 396678784561050197949857, 793357569122100395900313, 1586715138244200791801233, 3173430276488401583603081, 6346860552976803167206785, 12693721105953606334414201, 25387442211907212668829041, 50774884423814425337658729, 101549768847628850675318113, 203099537695257701350636889, 406199075390515402701274449, 812398150781030805402549577, 1624796301562061610805099841, 3249592603124123221610200377, 6499185206248246443220401457, 12998370412496492886440803625, 25996740824992985772881607969, 51993481649985971545763216665, 103986963299971943091526434065, 207973926599943886183052868873, 415947853199887772366105738497, 831895706399775544732211477753, 1663791412799551089464422956273, 3327582825599102178928845913321
Generating function in Maple syntax:
-(3*x^5+3*x^4+x^3+3*x^2-3*x+1)/(2*x-1)/(x-1)^2
Generating function in latex syntax:
-\frac{3 x^{5}+3 x^{4}+x^{3}+3 x^{2}-3 x +1}{\left(2 x -1\right) \left(x -1\right)^{2}}
Generating function in sympy syntax:
(-3*x**5 - 3*x**4 - x**3 - 3*x**2 + 3*x - 1)/((x - 1)**2*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(x-1)^2*F(x)+3*x^5+3*x^4+x^3+3*x^2-3*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(x -1\right)^{2} F \! \left(x \right)+3 x^{5}+3 x^{4}+x^{3}+3 x^{2}-3 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,9-8*n+21/8*2^n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ 9-8 n +\frac{21 \,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) = 53
a(n+1) = 2*a(n)+8*n-17, n >= 6
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) = 53
a \! \left(n +1\right) = 2 a \! \left(n \right)+8 n -17, \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16178/
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[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[17,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = F[1,x]+F[4,x]
F[11,x] = F[12,x]+F[7,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[4,x]
F[14,x] = F[15,x]+F[16,x]
F[15,x] = F[4,x]
F[16,x] = F[12,x]
F[17,x] = F[18,x]+F[49,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[24,x]
F[21,x] = F[1,x]+F[22,x]
F[22,x] = F[23,x]
F[23,x] = F[21,x]*F[4,x]
F[24,x] = F[18,x]+F[25,x]
F[25,x] = F[26,x]+F[27,x]+F[48,x]
F[26,x] = 0
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[33,x]
F[29,x] = F[22,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[22,x]+F[30,x]
F[33,x] = F[34,x]+F[39,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[22,x]
F[38,x] = F[34,x]
F[39,x] = F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[30,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[47,x]
F[46,x] = F[30,x]
F[47,x] = F[44,x]
F[48,x] = F[24,x]*F[4,x]
F[49,x] = F[140,x]+F[26,x]+F[50,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]+F[66,x]
F[52,x] = F[53,x]+F[7,x]
F[53,x] = F[26,x]+F[54,x]+F[57,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[4,x]+F[56,x]
F[56,x] = F[54,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[59,x]+F[60,x]
F[59,x] = F[22,x]+F[56,x]
F[60,x] = F[53,x]+F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[56,x]
F[65,x] = F[61,x]
F[66,x] = F[120,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[70,x]+F[72,x]
F[70,x] = F[7,x]+F[71,x]
F[71,x] = F[54,x]
F[72,x] = F[67,x]+F[73,x]
F[73,x] = 2*F[26,x]+F[74,x]+F[96,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x]+F[81,x]
F[76,x] = F[71,x]+F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[56,x]+F[80,x]
F[80,x] = F[78,x]
F[81,x] = F[82,x]+F[87,x]
F[82,x] = F[83,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[85,x]+F[86,x]
F[85,x] = F[71,x]
F[86,x] = F[82,x]
F[87,x] = F[88,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[77,x]
F[91,x] = F[92,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[94,x]+F[95,x]
F[94,x] = F[77,x]
F[95,x] = F[92,x]
F[96,x] = F[4,x]*F[97,x]
F[97,x] = F[101,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[4,x]
F[100,x] = F[55,x]+F[97,x]
F[101,x] = 2*F[26,x]+F[102,x]+F[96,x]
F[102,x] = F[103,x]*F[4,x]
F[103,x] = F[104,x]+F[105,x]
F[104,x] = F[56,x]+F[80,x]
F[105,x] = F[106,x]+F[111,x]
F[106,x] = F[107,x]
F[107,x] = F[108,x]*F[4,x]
F[108,x] = F[109,x]+F[110,x]
F[109,x] = F[56,x]
F[110,x] = F[106,x]
F[111,x] = F[112,x]
F[112,x] = F[113,x]*F[4,x]
F[113,x] = F[114,x]+F[115,x]
F[114,x] = F[80,x]
F[115,x] = F[116,x]
F[116,x] = F[117,x]*F[4,x]
F[117,x] = F[118,x]+F[119,x]
F[118,x] = F[80,x]
F[119,x] = F[116,x]
F[120,x] = 2*F[26,x]+F[121,x]+F[96,x]
F[121,x] = F[122,x]*F[4,x]
F[122,x] = F[123,x]+F[125,x]
F[123,x] = F[124,x]+F[53,x]
F[124,x] = F[78,x]
F[125,x] = F[126,x]+F[131,x]
F[126,x] = F[127,x]
F[127,x] = F[128,x]*F[4,x]
F[128,x] = F[129,x]+F[130,x]
F[129,x] = F[53,x]
F[130,x] = F[126,x]
F[131,x] = F[132,x]
F[132,x] = F[133,x]*F[4,x]
F[133,x] = F[134,x]+F[135,x]
F[134,x] = F[124,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]*F[4,x]
F[137,x] = F[138,x]+F[139,x]
F[138,x] = F[124,x]
F[139,x] = F[136,x]
F[140,x] = F[141,x]*F[4,x]
F[141,x] = F[142,x]+F[171,x]
F[142,x] = F[143,x]+F[18,x]
F[143,x] = F[144,x]+F[170,x]+F[26,x]
F[144,x] = F[145,x]*F[4,x]
F[145,x] = F[146,x]+F[149,x]
F[146,x] = F[147,x]+F[4,x]
F[147,x] = F[148,x]+F[26,x]+F[54,x]
F[148,x] = F[22,x]*F[4,x]
F[149,x] = F[150,x]+F[98,x]
F[150,x] = 2*F[26,x]+F[151,x]+F[96,x]
F[151,x] = F[152,x]*F[4,x]
F[152,x] = F[153,x]+F[155,x]
F[153,x] = F[147,x]+F[154,x]
F[154,x] = F[78,x]
F[155,x] = F[156,x]+F[161,x]
F[156,x] = F[157,x]
F[157,x] = F[158,x]*F[4,x]
F[158,x] = F[159,x]+F[160,x]
F[159,x] = F[147,x]
F[160,x] = F[156,x]
F[161,x] = F[162,x]
F[162,x] = F[163,x]*F[4,x]
F[163,x] = F[164,x]+F[165,x]
F[164,x] = F[154,x]
F[165,x] = F[166,x]
F[166,x] = F[167,x]*F[4,x]
F[167,x] = F[168,x]+F[169,x]
F[168,x] = F[154,x]
F[169,x] = F[166,x]
F[170,x] = F[18,x]*F[4,x]
F[171,x] = F[172,x]+F[202,x]
F[172,x] = F[173,x]+F[26,x]+F[27,x]
F[173,x] = F[174,x]*F[4,x]
F[174,x] = F[175,x]+F[196,x]
F[175,x] = F[176,x]+F[18,x]
F[176,x] = F[170,x]+F[177,x]+F[26,x]
F[177,x] = F[178,x]*F[4,x]
F[178,x] = F[179,x]+F[181,x]
F[179,x] = F[180,x]+F[4,x]
F[180,x] = F[148,x]
F[181,x] = F[182,x]+F[187,x]
F[182,x] = F[183,x]
F[183,x] = F[184,x]*F[4,x]
F[184,x] = F[185,x]+F[186,x]
F[185,x] = F[4,x]
F[186,x] = F[182,x]
F[187,x] = F[188,x]
F[188,x] = F[189,x]*F[4,x]
F[189,x] = F[190,x]+F[191,x]
F[190,x] = F[180,x]
F[191,x] = F[192,x]
F[192,x] = F[193,x]*F[4,x]
F[193,x] = F[194,x]+F[195,x]
F[194,x] = F[180,x]
F[195,x] = F[192,x]
F[196,x] = F[172,x]+F[197,x]
F[197,x] = F[198,x]
F[198,x] = F[199,x]*F[4,x]
F[199,x] = F[200,x]+F[201,x]
F[200,x] = F[182,x]
F[201,x] = F[198,x]
F[202,x] = 2*F[26,x]+F[203,x]+F[217,x]
F[203,x] = F[204,x]*F[4,x]
F[204,x] = F[205,x]+F[207,x]
F[205,x] = F[206,x]+F[56,x]
F[206,x] = F[78,x]
F[207,x] = F[106,x]+F[208,x]
F[208,x] = F[209,x]
F[209,x] = F[210,x]*F[4,x]
F[210,x] = F[211,x]+F[212,x]
F[211,x] = F[206,x]
F[212,x] = F[213,x]
F[213,x] = F[214,x]*F[4,x]
F[214,x] = F[215,x]+F[216,x]
F[215,x] = F[206,x]
F[216,x] = F[213,x]
F[217,x] = F[218,x]*F[4,x]
F[218,x] = F[219,x]+F[220,x]
F[219,x] = F[98,x]
F[220,x] = F[221,x]
F[221,x] = 2*F[26,x]+F[102,x]+F[217,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{17}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{7}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)
F_{15}\! \left(x \right) = F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{12}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{49}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{24}\! \left(x \right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{18}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)+F_{48}\! \left(x \right)
F_{26}\! \left(x \right) = 0
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{33}\! \left(x \right)
F_{29}\! \left(x \right) = F_{22}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{22}\! \left(x \right)+F_{30}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{39}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{22}\! \left(x \right)
F_{38}\! \left(x \right) = F_{34}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{30}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{47}\! \left(x \right)
F_{46}\! \left(x \right) = F_{30}\! \left(x \right)
F_{47}\! \left(x \right) = F_{44}\! \left(x \right)
F_{48}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{49}\! \left(x \right) = F_{140}\! \left(x \right)+F_{26}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{66}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{7}\! \left(x \right)
F_{53}\! \left(x \right) = F_{26}\! \left(x \right)+F_{54}\! \left(x \right)+F_{57}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{54}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{60}\! \left(x \right)
F_{59}\! \left(x \right) = F_{22}\! \left(x \right)+F_{56}\! \left(x \right)
F_{60}\! \left(x \right) = F_{53}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{56}\! \left(x \right)
F_{65}\! \left(x \right) = F_{61}\! \left(x \right)
F_{66}\! \left(x \right) = F_{120}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{72}\! \left(x \right)
F_{70}\! \left(x \right) = F_{7}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{54}\! \left(x \right)
F_{72}\! \left(x \right) = F_{67}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{74}\! \left(x \right)+F_{96}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{81}\! \left(x \right)
F_{76}\! \left(x \right) = F_{71}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{56}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{78}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{87}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \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_{71}\! \left(x \right)
F_{86}\! \left(x \right) = F_{82}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = F_{77}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{95}\! \left(x \right)
F_{94}\! \left(x \right) = F_{77}\! \left(x \right)
F_{95}\! \left(x \right) = F_{92}\! \left(x \right)
F_{96}\! \left(x \right) = F_{4}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{101}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{4}\! \left(x \right)
F_{100}\! \left(x \right) = F_{55}\! \left(x \right)+F_{97}\! \left(x \right)
F_{101}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{102}\! \left(x \right)+F_{96}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{4}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{105}\! \left(x \right)
F_{104}\! \left(x \right) = F_{56}\! \left(x \right)+F_{80}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{111}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{4}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{56}\! \left(x \right)
F_{110}\! \left(x \right) = F_{106}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{115}\! \left(x \right)
F_{114}\! \left(x \right) = F_{80}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{4}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{119}\! \left(x \right)
F_{118}\! \left(x \right) = F_{80}\! \left(x \right)
F_{119}\! \left(x \right) = F_{116}\! \left(x \right)
F_{120}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{121}\! \left(x \right)+F_{96}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{4}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{125}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{53}\! \left(x \right)
F_{124}\! \left(x \right) = F_{78}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{131}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right) F_{4}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{130}\! \left(x \right)
F_{129}\! \left(x \right) = F_{53}\! \left(x \right)
F_{130}\! \left(x \right) = F_{126}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{4}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{135}\! \left(x \right)
F_{134}\! \left(x \right) = F_{124}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{4}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{139}\! \left(x \right)
F_{138}\! \left(x \right) = F_{124}\! \left(x \right)
F_{139}\! \left(x \right) = F_{136}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{4}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{171}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{18}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{170}\! \left(x \right)+F_{26}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right) F_{4}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{149}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{4}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{26}\! \left(x \right)+F_{54}\! \left(x \right)
F_{148}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{98}\! \left(x \right)
F_{150}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{151}\! \left(x \right)+F_{96}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{4}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{155}\! \left(x \right)
F_{153}\! \left(x \right) = F_{147}\! \left(x \right)+F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{78}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{161}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right) F_{4}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{160}\! \left(x \right)
F_{159}\! \left(x \right) = F_{147}\! \left(x \right)
F_{160}\! \left(x \right) = F_{156}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right) F_{4}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)+F_{165}\! \left(x \right)
F_{164}\! \left(x \right) = F_{154}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right) F_{4}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)+F_{169}\! \left(x \right)
F_{168}\! \left(x \right) = F_{154}\! \left(x \right)
F_{169}\! \left(x \right) = F_{166}\! \left(x \right)
F_{170}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{202}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)+F_{26}\! \left(x \right)+F_{27}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right) F_{4}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)+F_{196}\! \left(x \right)
F_{175}\! \left(x \right) = F_{176}\! \left(x \right)+F_{18}\! \left(x \right)
F_{176}\! \left(x \right) = F_{170}\! \left(x \right)+F_{177}\! \left(x \right)+F_{26}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right) F_{4}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)+F_{181}\! \left(x \right)
F_{179}\! \left(x \right) = F_{180}\! \left(x \right)+F_{4}\! \left(x \right)
F_{180}\! \left(x \right) = F_{148}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right)+F_{187}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right) F_{4}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{186}\! \left(x \right)
F_{185}\! \left(x \right) = F_{4}\! \left(x \right)
F_{186}\! \left(x \right) = F_{182}\! \left(x \right)
F_{187}\! \left(x \right) = F_{188}\! \left(x \right)
F_{188}\! \left(x \right) = F_{189}\! \left(x \right) F_{4}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)+F_{191}\! \left(x \right)
F_{190}\! \left(x \right) = F_{180}\! \left(x \right)
F_{191}\! \left(x \right) = F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right) F_{4}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)+F_{195}\! \left(x \right)
F_{194}\! \left(x \right) = F_{180}\! \left(x \right)
F_{195}\! \left(x \right) = F_{192}\! \left(x \right)
F_{196}\! \left(x \right) = F_{172}\! \left(x \right)+F_{197}\! \left(x \right)
F_{197}\! \left(x \right) = F_{198}\! \left(x \right)
F_{198}\! \left(x \right) = F_{199}\! \left(x \right) F_{4}\! \left(x \right)
F_{199}\! \left(x \right) = F_{200}\! \left(x \right)+F_{201}\! \left(x \right)
F_{200}\! \left(x \right) = F_{182}\! \left(x \right)
F_{201}\! \left(x \right) = F_{198}\! \left(x \right)
F_{202}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{203}\! \left(x \right)+F_{217}\! \left(x \right)
F_{203}\! \left(x \right) = F_{204}\! \left(x \right) F_{4}\! \left(x \right)
F_{204}\! \left(x \right) = F_{205}\! \left(x \right)+F_{207}\! \left(x \right)
F_{205}\! \left(x \right) = F_{206}\! \left(x \right)+F_{56}\! \left(x \right)
F_{206}\! \left(x \right) = F_{78}\! \left(x \right)
F_{207}\! \left(x \right) = F_{106}\! \left(x \right)+F_{208}\! \left(x \right)
F_{208}\! \left(x \right) = F_{209}\! \left(x \right)
F_{209}\! \left(x \right) = F_{210}\! \left(x \right) F_{4}\! \left(x \right)
F_{210}\! \left(x \right) = F_{211}\! \left(x \right)+F_{212}\! \left(x \right)
F_{211}\! \left(x \right) = F_{206}\! \left(x \right)
F_{212}\! \left(x \right) = F_{213}\! \left(x \right)
F_{213}\! \left(x \right) = F_{214}\! \left(x \right) F_{4}\! \left(x \right)
F_{214}\! \left(x \right) = F_{215}\! \left(x \right)+F_{216}\! \left(x \right)
F_{215}\! \left(x \right) = F_{206}\! \left(x \right)
F_{216}\! \left(x \right) = F_{213}\! \left(x \right)
F_{217}\! \left(x \right) = F_{218}\! \left(x \right) F_{4}\! \left(x \right)
F_{218}\! \left(x \right) = F_{219}\! \left(x \right)+F_{220}\! \left(x \right)
F_{219}\! \left(x \right) = F_{98}\! \left(x \right)
F_{220}\! \left(x \right) = F_{221}\! \left(x \right)
F_{221}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{102}\! \left(x \right)+F_{217}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_17(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), F_1(x) + F_4(x))
Eq(F_11(x), F_12(x) + F_7(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_4(x))
Eq(F_14(x), F_15(x) + F_16(x))
Eq(F_15(x), F_4(x))
Eq(F_16(x), F_12(x))
Eq(F_17(x), F_18(x) + F_49(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_24(x))
Eq(F_21(x), F_1(x) + F_22(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_21(x)*F_4(x))
Eq(F_24(x), F_18(x) + F_25(x))
Eq(F_25(x), F_26(x) + F_27(x) + F_48(x))
Eq(F_26(x), 0)
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_33(x))
Eq(F_29(x), F_22(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_22(x) + F_30(x))
Eq(F_33(x), F_34(x) + F_39(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_22(x))
Eq(F_38(x), F_34(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_30(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_47(x))
Eq(F_46(x), F_30(x))
Eq(F_47(x), F_44(x))
Eq(F_48(x), F_24(x)*F_4(x))
Eq(F_49(x), F_140(x) + F_26(x) + F_50(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_66(x))
Eq(F_52(x), F_53(x) + F_7(x))
Eq(F_53(x), F_26(x) + F_54(x) + F_57(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_4(x) + F_56(x))
Eq(F_56(x), F_54(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_60(x))
Eq(F_59(x), F_22(x) + F_56(x))
Eq(F_60(x), F_53(x) + F_61(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_56(x))
Eq(F_65(x), F_61(x))
Eq(F_66(x), F_120(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_72(x))
Eq(F_70(x), F_7(x) + F_71(x))
Eq(F_71(x), F_54(x))
Eq(F_72(x), F_67(x) + F_73(x))
Eq(F_73(x), 2*F_26(x) + F_74(x) + F_96(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_81(x))
Eq(F_76(x), F_71(x) + F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_56(x) + F_80(x))
Eq(F_80(x), F_78(x))
Eq(F_81(x), F_82(x) + F_87(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_86(x))
Eq(F_85(x), F_71(x))
Eq(F_86(x), F_82(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_77(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_95(x))
Eq(F_94(x), F_77(x))
Eq(F_95(x), F_92(x))
Eq(F_96(x), F_4(x)*F_97(x))
Eq(F_97(x), F_101(x) + F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_4(x))
Eq(F_100(x), F_55(x) + F_97(x))
Eq(F_101(x), F_102(x) + 2*F_26(x) + F_96(x))
Eq(F_102(x), F_103(x)*F_4(x))
Eq(F_103(x), F_104(x) + F_105(x))
Eq(F_104(x), F_56(x) + F_80(x))
Eq(F_105(x), F_106(x) + F_111(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x)*F_4(x))
Eq(F_108(x), F_109(x) + F_110(x))
Eq(F_109(x), F_56(x))
Eq(F_110(x), F_106(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_113(x)*F_4(x))
Eq(F_113(x), F_114(x) + F_115(x))
Eq(F_114(x), F_80(x))
Eq(F_115(x), F_116(x))
Eq(F_116(x), F_117(x)*F_4(x))
Eq(F_117(x), F_118(x) + F_119(x))
Eq(F_118(x), F_80(x))
Eq(F_119(x), F_116(x))
Eq(F_120(x), F_121(x) + 2*F_26(x) + F_96(x))
Eq(F_121(x), F_122(x)*F_4(x))
Eq(F_122(x), F_123(x) + F_125(x))
Eq(F_123(x), F_124(x) + F_53(x))
Eq(F_124(x), F_78(x))
Eq(F_125(x), F_126(x) + F_131(x))
Eq(F_126(x), F_127(x))
Eq(F_127(x), F_128(x)*F_4(x))
Eq(F_128(x), F_129(x) + F_130(x))
Eq(F_129(x), F_53(x))
Eq(F_130(x), F_126(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_133(x)*F_4(x))
Eq(F_133(x), F_134(x) + F_135(x))
Eq(F_134(x), F_124(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x)*F_4(x))
Eq(F_137(x), F_138(x) + F_139(x))
Eq(F_138(x), F_124(x))
Eq(F_139(x), F_136(x))
Eq(F_140(x), F_141(x)*F_4(x))
Eq(F_141(x), F_142(x) + F_171(x))
Eq(F_142(x), F_143(x) + F_18(x))
Eq(F_143(x), F_144(x) + F_170(x) + F_26(x))
Eq(F_144(x), F_145(x)*F_4(x))
Eq(F_145(x), F_146(x) + F_149(x))
Eq(F_146(x), F_147(x) + F_4(x))
Eq(F_147(x), F_148(x) + F_26(x) + F_54(x))
Eq(F_148(x), F_22(x)*F_4(x))
Eq(F_149(x), F_150(x) + F_98(x))
Eq(F_150(x), F_151(x) + 2*F_26(x) + F_96(x))
Eq(F_151(x), F_152(x)*F_4(x))
Eq(F_152(x), F_153(x) + F_155(x))
Eq(F_153(x), F_147(x) + F_154(x))
Eq(F_154(x), F_78(x))
Eq(F_155(x), F_156(x) + F_161(x))
Eq(F_156(x), F_157(x))
Eq(F_157(x), F_158(x)*F_4(x))
Eq(F_158(x), F_159(x) + F_160(x))
Eq(F_159(x), F_147(x))
Eq(F_160(x), F_156(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_163(x)*F_4(x))
Eq(F_163(x), F_164(x) + F_165(x))
Eq(F_164(x), F_154(x))
Eq(F_165(x), F_166(x))
Eq(F_166(x), F_167(x)*F_4(x))
Eq(F_167(x), F_168(x) + F_169(x))
Eq(F_168(x), F_154(x))
Eq(F_169(x), F_166(x))
Eq(F_170(x), F_18(x)*F_4(x))
Eq(F_171(x), F_172(x) + F_202(x))
Eq(F_172(x), F_173(x) + F_26(x) + F_27(x))
Eq(F_173(x), F_174(x)*F_4(x))
Eq(F_174(x), F_175(x) + F_196(x))
Eq(F_175(x), F_176(x) + F_18(x))
Eq(F_176(x), F_170(x) + F_177(x) + F_26(x))
Eq(F_177(x), F_178(x)*F_4(x))
Eq(F_178(x), F_179(x) + F_181(x))
Eq(F_179(x), F_180(x) + F_4(x))
Eq(F_180(x), F_148(x))
Eq(F_181(x), F_182(x) + F_187(x))
Eq(F_182(x), F_183(x))
Eq(F_183(x), F_184(x)*F_4(x))
Eq(F_184(x), F_185(x) + F_186(x))
Eq(F_185(x), F_4(x))
Eq(F_186(x), F_182(x))
Eq(F_187(x), F_188(x))
Eq(F_188(x), F_189(x)*F_4(x))
Eq(F_189(x), F_190(x) + F_191(x))
Eq(F_190(x), F_180(x))
Eq(F_191(x), F_192(x))
Eq(F_192(x), F_193(x)*F_4(x))
Eq(F_193(x), F_194(x) + F_195(x))
Eq(F_194(x), F_180(x))
Eq(F_195(x), F_192(x))
Eq(F_196(x), F_172(x) + F_197(x))
Eq(F_197(x), F_198(x))
Eq(F_198(x), F_199(x)*F_4(x))
Eq(F_199(x), F_200(x) + F_201(x))
Eq(F_200(x), F_182(x))
Eq(F_201(x), F_198(x))
Eq(F_202(x), F_203(x) + F_217(x) + 2*F_26(x))
Eq(F_203(x), F_204(x)*F_4(x))
Eq(F_204(x), F_205(x) + F_207(x))
Eq(F_205(x), F_206(x) + F_56(x))
Eq(F_206(x), F_78(x))
Eq(F_207(x), F_106(x) + F_208(x))
Eq(F_208(x), F_209(x))
Eq(F_209(x), F_210(x)*F_4(x))
Eq(F_210(x), F_211(x) + F_212(x))
Eq(F_211(x), F_206(x))
Eq(F_212(x), F_213(x))
Eq(F_213(x), F_214(x)*F_4(x))
Eq(F_214(x), F_215(x) + F_216(x))
Eq(F_215(x), F_206(x))
Eq(F_216(x), F_213(x))
Eq(F_217(x), F_218(x)*F_4(x))
Eq(F_218(x), F_219(x) + F_220(x))
Eq(F_219(x), F_98(x))
Eq(F_220(x), F_221(x))
Eq(F_221(x), F_102(x) + F_217(x) + 2*F_26(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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