0123_0231_1320_2130_3021

Counting sequence:
1, 1, 2, 6, 19, 50, 102, 192, 354, 649, 1189, 2182, 4013, 7394, 13641, 25185, 46514, 85910, 158650, 292904, 540600, 997435, 1839725, 3392254, 6253183, 11523980, 21232629, 39112521, 72035848, 132651304, 244237642, 449634104, 827671458, 1523402149, 2803716393, 5159659062, 9494656893, 17470782358, 32145729389, 59144551625, 108815079458, 200192761698, 368293812382, 677530476792, 1246387296296, 2292810656863, 4217697749633, 7758464096886, 14271510220335, 26251778181240, 48288396333305, 88822434687785, 163380002993928, 300518977763548, 552766952989598, 1016739615044336, 1870144764643666, 3439844232825825, 6327040731513213, 11637534748135494, 21405236850632093, 39371134487596746, 72416045381843649, 133195878172873777, 244988658790601026, 450609644546413070, 828808844459276050, 1524430872946779880, 2803887750052354088, 5157189580708792259, 9485608705058201221, 17446848650420012718, 32089910052137954511, 59022793138167790340, 108560240687228336461, 199674058454588291049, 367258895703541215704, 675496112845968860304, 1242433788428266191778, 2285196436402555119656, 4203138698525736858674, 7730788923630283719549, 14219156419681247945185, 26153136403233666331382, 48103166469064268062925, 88475596375894650226110, 162732121054627122585989, 299311242789936046739673, 550519540917242363394770, 1012563844348940082441178, 1862396148340037586152790, 3425481993477273675300408, 6300445966321224080797304, 11588330548164561722479527, 21314268928144058595723961, 39203062302836869896391654, 72105689059533514829148191, 132623064431109493433223536, 243931887214462952885292337, 448660756266684085986169289, 825215894894817731869736248

Generating function in Maple syntax:
-(2*x^13+3*x^12-6*x^11-12*x^10+3*x^9+20*x^8+14*x^7-17*x^6-6*x^5+x^3+5*x^2-4*x+1)/(x^2+x-1)/(x^3+x^2+x-1)/(x-1)^3

Generating function in latex syntax:
-\frac{2 x^{13}+3 x^{12}-6 x^{11}-12 x^{10}+3 x^{9}+20 x^{8}+14 x^{7}-17 x^{6}-6 x^{5}+x^{3}+5 x^{2}-4 x +1}{\left(x^{2}+x -1\right) \left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{3}}

Generating function in sympy syntax:
(-2*x**13 - 3*x**12 + 6*x**11 + 12*x**10 - 3*x**9 - 20*x**8 - 14*x**7 + 17*x**6 + 6*x**5 - x**3 - 5*x**2 + 4*x - 1)/((x - 1)**3*(x**2 + x - 1)*(x**3 + x**2 + x - 1))

Implicit equation for the generating function in Maple syntax:
(x^2+x-1)*(x^3+x^2+x-1)*(x-1)^3*F(x)+2*x^13+3*x^12-6*x^11-12*x^10+3*x^9+20*x^8+14*x^7-17*x^6-6*x^5+x^3+5*x^2-4*x+1 = 0

Implicit equation for the generating function in latex syntax:
\left(x^{2}+x -1\right) \left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{3} F \! \left(x \right)+2 x^{13}+3 x^{12}-6 x^{11}-12 x^{10}+3 x^{9}+20 x^{8}+14 x^{7}-17 x^{6}-6 x^{5}+x^{3}+5 x^{2}-4 x +1 = 0

Explicit closed form in Maple syntax:
-3/2-4*n+n^2-47/11*Sum(_alpha^(3-n),_alpha = RootOf(_Z^5+2*_Z^4+_Z^3-_Z^2-2*_Z+1))-247/22*Sum(_alpha^(2-n),_alpha = RootOf(_Z^5+2*_Z^4+_Z^3-_Z^2-2*_Z+1))-233/22*Sum(_alpha^(1-n),_alpha = RootOf(_Z^5+2*_Z^4+_Z^3-_Z^2-2*_Z+1))-43/22*Sum(_alpha^(-n),_alpha = RootOf(_Z^5+2*_Z^4+_Z^3-_Z^2-2*_Z+1))+87/11*Sum(_alpha^(-n-1),_alpha = RootOf(_Z^5+2*_Z^4+_Z^3-_Z^2-2*_Z+1))-piecewise(n = 0,-2,Or(n = 1,n = 2),-1,n = 3,3,n = 4,5,n = 5,2,0)

Explicit closed form in latex syntax:
-\frac{3}{2}-4 n +n^{2}-\frac{47 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{5}+2 \textit{\_Z}^{4}+\textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{3-n}\right)}{11}-\frac{247 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{5}+2 \textit{\_Z}^{4}+\textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{2-n}\right)}{22}-\frac{233 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{5}+2 \textit{\_Z}^{4}+\textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{1-n}\right)}{22}-\frac{43 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{5}+2 \textit{\_Z}^{4}+\textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n}\right)}{22}+\frac{87 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{5}+2 \textit{\_Z}^{4}+\textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n -1}\right)}{11}-\left(\left\{\begin{array}{cc}-2 & n =0 \\ -1 & n =1\text{ or } n =2 \\ 3 & n =3 \\ 5 & n =4 \\ 2 & n =5 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 50
a(6) = 102
a(7) = 192
a(8) = 354
a(9) = 649
a(10) = 1189
a(11) = 2182
a(12) = 4013
a(13) = 7394
a(n+5) = 2*n^2+a(n+3)+2*a(n+4)-a(n)-2*a(n+1)-a(n+2)-12*n-5, n >= 14

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) = 50
a \! \left(6\right) = 102
a \! \left(7\right) = 192
a \! \left(8\right) = 354
a \! \left(9\right) = 649
a \! \left(10\right) = 1189
a \! \left(11\right) = 2182
a \! \left(12\right) = 4013
a \! \left(13\right) = 7394
a \! \left(n +5\right) = 2 n^{2}+a \! \left(n +3\right)+2 a \! \left(n +4\right)-a \! \left(n \right)-2 a \! \left(n +1\right)-a \! \left(n +2\right)-12 n -5, \quad n \geq 14

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/17536/
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[29,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[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[24,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[4,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[4,x]
F[23,x] = F[19,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[11,x]
F[28,x] = F[24,x]
F[29,x] = F[30,x]+F[68,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[33,x]+F[36,x]
F[33,x] = F[1,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[17,x]*F[4,x]
F[36,x] = F[30,x]+F[37,x]
F[37,x] = F[38,x]+F[39,x]+F[64,x]
F[38,x] = 0
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[41,x]+F[44,x]
F[41,x] = F[34,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[22,x]*F[4,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[39,x]
F[46,x] = 2*F[38,x]+F[47,x]+F[51,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[42,x]
F[50,x] = F[47,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[56,x]+F[58,x]
F[56,x] = F[4,x]+F[57,x]
F[57,x] = F[43,x]
F[58,x] = F[53,x]+F[59,x]
F[59,x] = 2*F[38,x]+F[51,x]+F[60,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[62,x]+F[63,x]
F[62,x] = F[57,x]
F[63,x] = F[60,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[30,x]+F[66,x]
F[66,x] = F[38,x]+F[54,x]+F[67,x]
F[67,x] = F[30,x]*F[4,x]
F[68,x] = F[138,x]+F[38,x]+F[69,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[71,x]+F[84,x]
F[71,x] = F[7,x]+F[72,x]
F[72,x] = F[38,x]+F[73,x]+F[78,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[11,x]+F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[4,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[80,x]+F[83,x]
F[80,x] = F[34,x]+F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[27,x]*F[4,x]
F[83,x] = F[43,x]
F[84,x] = F[108,x]+F[85,x]
F[85,x] = F[86,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[88,x]+F[90,x]
F[88,x] = F[7,x]+F[89,x]
F[89,x] = F[82,x]
F[90,x] = F[85,x]+F[91,x]
F[91,x] = 2*F[38,x]+F[92,x]+F[96,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[94,x]+F[95,x]
F[94,x] = F[89,x]
F[95,x] = F[92,x]
F[96,x] = F[4,x]*F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[4,x]
F[100,x] = F[101,x]+F[102,x]
F[101,x] = F[11,x]+F[81,x]
F[102,x] = F[103,x]+F[98,x]
F[103,x] = 2*F[38,x]+F[104,x]+F[96,x]
F[104,x] = F[105,x]*F[4,x]
F[105,x] = F[106,x]+F[107,x]
F[106,x] = F[81,x]
F[107,x] = F[104,x]
F[108,x] = 2*F[38,x]+F[109,x]+F[135,x]
F[109,x] = F[110,x]*F[4,x]
F[110,x] = F[111,x]+F[115,x]
F[111,x] = F[112,x]+F[72,x]
F[112,x] = F[113,x]
F[113,x] = F[114,x]*F[4,x]
F[114,x] = F[75,x]
F[115,x] = F[116,x]+F[117,x]
F[116,x] = F[109,x]
F[117,x] = 3*F[38,x]+F[118,x]+F[122,x]
F[118,x] = F[119,x]*F[4,x]
F[119,x] = F[120,x]+F[121,x]
F[120,x] = F[112,x]
F[121,x] = F[118,x]
F[122,x] = F[123,x]*F[4,x]
F[123,x] = F[124,x]
F[124,x] = F[125,x]
F[125,x] = F[126,x]*F[4,x]
F[126,x] = F[127,x]+F[129,x]
F[127,x] = F[128,x]+F[75,x]
F[128,x] = F[113,x]
F[129,x] = F[124,x]+F[130,x]
F[130,x] = 3*F[38,x]+F[122,x]+F[131,x]
F[131,x] = F[132,x]*F[4,x]
F[132,x] = F[133,x]+F[134,x]
F[133,x] = F[128,x]
F[134,x] = F[131,x]
F[135,x] = F[136,x]*F[4,x]
F[136,x] = F[137,x]+F[98,x]
F[137,x] = F[125,x]
F[138,x] = F[139,x]*F[4,x]
F[139,x] = F[140,x]+F[165,x]
F[140,x] = F[141,x]+F[30,x]
F[141,x] = F[142,x]+F[162,x]+F[38,x]
F[142,x] = F[143,x]*F[4,x]
F[143,x] = F[144,x]+F[149,x]
F[144,x] = F[11,x]+F[145,x]
F[145,x] = F[146,x]+F[38,x]+F[73,x]
F[146,x] = F[147,x]*F[4,x]
F[147,x] = F[148,x]+F[34,x]
F[148,x] = F[43,x]
F[149,x] = F[150,x]+F[98,x]
F[150,x] = 2*F[38,x]+F[135,x]+F[151,x]
F[151,x] = F[152,x]*F[4,x]
F[152,x] = F[153,x]+F[155,x]
F[153,x] = F[145,x]+F[154,x]
F[154,x] = F[113,x]
F[155,x] = F[156,x]+F[157,x]
F[156,x] = F[151,x]
F[157,x] = 3*F[38,x]+F[122,x]+F[158,x]
F[158,x] = F[159,x]*F[4,x]
F[159,x] = F[160,x]+F[161,x]
F[160,x] = F[154,x]
F[161,x] = F[158,x]
F[162,x] = F[163,x]*F[4,x]
F[163,x] = F[164,x]+F[30,x]
F[164,x] = F[54,x]
F[165,x] = F[166,x]+F[167,x]
F[166,x] = F[39,x]
F[167,x] = F[168,x]
F[168,x] = F[169,x]*F[4,x]
F[169,x] = F[170,x]+F[171,x]
F[170,x] = F[81,x]
F[171,x] = F[104,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{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_{29}\! \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_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
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_{16}\! \left(x \right) F_{4}\! \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_{4}\! \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_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{11}\! \left(x \right)
F_{28}\! \left(x \right) = F_{24}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{68}\! \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_{33}\! \left(x \right)+F_{36}\! \left(x \right)
F_{33}\! \left(x \right) = F_{1}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)+F_{64}\! \left(x \right)
F_{38}\! \left(x \right) = 0
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{41}\! \left(x \right) = F_{34}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{46}\! \left(x \right)
F_{45}\! \left(x \right) = F_{39}\! \left(x \right)
F_{46}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{47}\! \left(x \right)+F_{51}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \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_{42}\! \left(x \right)
F_{50}\! \left(x \right) = F_{47}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{58}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{43}\! \left(x \right)
F_{58}\! \left(x \right) = F_{53}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{51}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{63}\! \left(x \right)
F_{62}\! \left(x \right) = F_{57}\! \left(x \right)
F_{63}\! \left(x \right) = F_{60}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{30}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{38}\! \left(x \right)+F_{54}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{68}\! \left(x \right) = F_{138}\! \left(x \right)+F_{38}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{84}\! \left(x \right)
F_{71}\! \left(x \right) = F_{7}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{38}\! \left(x \right)+F_{73}\! \left(x \right)+F_{78}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{11}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{83}\! \left(x \right)
F_{80}\! \left(x \right) = F_{34}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{83}\! \left(x \right) = F_{43}\! \left(x \right)
F_{84}\! \left(x \right) = F_{108}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{90}\! \left(x \right)
F_{88}\! \left(x \right) = F_{7}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{82}\! \left(x \right)
F_{90}\! \left(x \right) = F_{85}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{92}\! \left(x \right)+F_{96}\! \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_{89}\! \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_{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_{101}\! \left(x \right)+F_{102}\! \left(x \right)
F_{101}\! \left(x \right) = F_{11}\! \left(x \right)+F_{81}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{98}\! \left(x \right)
F_{103}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{104}\! \left(x \right)+F_{96}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{4}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{107}\! \left(x \right)
F_{106}\! \left(x \right) = F_{81}\! \left(x \right)
F_{107}\! \left(x \right) = F_{104}\! \left(x \right)
F_{108}\! \left(x \right) = 2 F_{38}\! \left(x \right)+F_{109}\! \left(x \right)+F_{135}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{4}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{115}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{72}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{4}\! \left(x \right)
F_{114}\! \left(x \right) = F_{75}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{117}\! \left(x \right)
F_{116}\! \left(x \right) = F_{109}\! \left(x \right)
F_{117}\! \left(x \right) = 3 F_{38}\! \left(x \right)+F_{118}\! \left(x \right)+F_{122}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{4}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{121}\! \left(x \right)
F_{120}\! \left(x \right) = F_{112}\! \left(x \right)
F_{121}\! \left(x \right) = F_{118}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{4}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{4}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{129}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{75}\! \left(x \right)
F_{128}\! \left(x \right) = F_{113}\! \left(x \right)
F_{129}\! \left(x \right) = F_{124}\! \left(x \right)+F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = 3 F_{38}\! \left(x \right)+F_{122}\! \left(x \right)+F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right) F_{4}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{134}\! \left(x \right)
F_{133}\! \left(x \right) = F_{128}\! \left(x \right)
F_{134}\! \left(x \right) = F_{131}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{4}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{98}\! \left(x \right)
F_{137}\! \left(x \right) = F_{125}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{4}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{165}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{30}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{162}\! \left(x \right)+F_{38}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right) F_{4}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{149}\! \left(x \right)
F_{144}\! \left(x \right) = F_{11}\! \left(x \right)+F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right)+F_{38}\! \left(x \right)+F_{73}\! \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_{34}\! \left(x \right)
F_{148}\! \left(x \right) = F_{43}\! \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_{38}\! \left(x \right)+F_{135}\! \left(x \right)+F_{151}\! \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_{145}\! \left(x \right)+F_{154}\! \left(x \right)
F_{154}\! \left(x \right) = F_{113}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)+F_{157}\! \left(x \right)
F_{156}\! \left(x \right) = F_{151}\! \left(x \right)
F_{157}\! \left(x \right) = 3 F_{38}\! \left(x \right)+F_{122}\! \left(x \right)+F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right) F_{4}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{161}\! \left(x \right)
F_{160}\! \left(x \right) = F_{154}\! \left(x \right)
F_{161}\! \left(x \right) = F_{158}\! \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_{30}\! \left(x \right)
F_{164}\! \left(x \right) = F_{54}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)+F_{167}\! \left(x \right)
F_{166}\! \left(x \right) = F_{39}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right) F_{4}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)+F_{171}\! \left(x \right)
F_{170}\! \left(x \right) = F_{81}\! \left(x \right)
F_{171}\! \left(x \right) = F_{104}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_29(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_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_24(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_4(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_4(x))
Eq(F_23(x), F_19(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_11(x))
Eq(F_28(x), F_24(x))
Eq(F_29(x), F_30(x) + F_68(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_36(x))
Eq(F_33(x), F_1(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_17(x)*F_4(x))
Eq(F_36(x), F_30(x) + F_37(x))
Eq(F_37(x), F_38(x) + F_39(x) + F_64(x))
Eq(F_38(x), 0)
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_44(x))
Eq(F_41(x), F_34(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_22(x)*F_4(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_39(x))
Eq(F_46(x), 2*F_38(x) + F_47(x) + F_51(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_42(x))
Eq(F_50(x), F_47(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_58(x))
Eq(F_56(x), F_4(x) + F_57(x))
Eq(F_57(x), F_43(x))
Eq(F_58(x), F_53(x) + F_59(x))
Eq(F_59(x), 2*F_38(x) + F_51(x) + F_60(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_63(x))
Eq(F_62(x), F_57(x))
Eq(F_63(x), F_60(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_30(x) + F_66(x))
Eq(F_66(x), F_38(x) + F_54(x) + F_67(x))
Eq(F_67(x), F_30(x)*F_4(x))
Eq(F_68(x), F_138(x) + F_38(x) + F_69(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_84(x))
Eq(F_71(x), F_7(x) + F_72(x))
Eq(F_72(x), F_38(x) + F_73(x) + F_78(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_11(x) + F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_4(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_83(x))
Eq(F_80(x), F_34(x) + F_81(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_27(x)*F_4(x))
Eq(F_83(x), F_43(x))
Eq(F_84(x), F_108(x) + F_85(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_90(x))
Eq(F_88(x), F_7(x) + F_89(x))
Eq(F_89(x), F_82(x))
Eq(F_90(x), F_85(x) + F_91(x))
Eq(F_91(x), 2*F_38(x) + F_92(x) + F_96(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_89(x))
Eq(F_95(x), F_92(x))
Eq(F_96(x), F_4(x)*F_97(x))
Eq(F_97(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_101(x) + F_102(x))
Eq(F_101(x), F_11(x) + F_81(x))
Eq(F_102(x), F_103(x) + F_98(x))
Eq(F_103(x), F_104(x) + 2*F_38(x) + F_96(x))
Eq(F_104(x), F_105(x)*F_4(x))
Eq(F_105(x), F_106(x) + F_107(x))
Eq(F_106(x), F_81(x))
Eq(F_107(x), F_104(x))
Eq(F_108(x), F_109(x) + F_135(x) + 2*F_38(x))
Eq(F_109(x), F_110(x)*F_4(x))
Eq(F_110(x), F_111(x) + F_115(x))
Eq(F_111(x), F_112(x) + F_72(x))
Eq(F_112(x), F_113(x))
Eq(F_113(x), F_114(x)*F_4(x))
Eq(F_114(x), F_75(x))
Eq(F_115(x), F_116(x) + F_117(x))
Eq(F_116(x), F_109(x))
Eq(F_117(x), F_118(x) + F_122(x) + 3*F_38(x))
Eq(F_118(x), F_119(x)*F_4(x))
Eq(F_119(x), F_120(x) + F_121(x))
Eq(F_120(x), F_112(x))
Eq(F_121(x), F_118(x))
Eq(F_122(x), F_123(x)*F_4(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_126(x)*F_4(x))
Eq(F_126(x), F_127(x) + F_129(x))
Eq(F_127(x), F_128(x) + F_75(x))
Eq(F_128(x), F_113(x))
Eq(F_129(x), F_124(x) + F_130(x))
Eq(F_130(x), F_122(x) + F_131(x) + 3*F_38(x))
Eq(F_131(x), F_132(x)*F_4(x))
Eq(F_132(x), F_133(x) + F_134(x))
Eq(F_133(x), F_128(x))
Eq(F_134(x), F_131(x))
Eq(F_135(x), F_136(x)*F_4(x))
Eq(F_136(x), F_137(x) + F_98(x))
Eq(F_137(x), F_125(x))
Eq(F_138(x), F_139(x)*F_4(x))
Eq(F_139(x), F_140(x) + F_165(x))
Eq(F_140(x), F_141(x) + F_30(x))
Eq(F_141(x), F_142(x) + F_162(x) + F_38(x))
Eq(F_142(x), F_143(x)*F_4(x))
Eq(F_143(x), F_144(x) + F_149(x))
Eq(F_144(x), F_11(x) + F_145(x))
Eq(F_145(x), F_146(x) + F_38(x) + F_73(x))
Eq(F_146(x), F_147(x)*F_4(x))
Eq(F_147(x), F_148(x) + F_34(x))
Eq(F_148(x), F_43(x))
Eq(F_149(x), F_150(x) + F_98(x))
Eq(F_150(x), F_135(x) + F_151(x) + 2*F_38(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_145(x) + F_154(x))
Eq(F_154(x), F_113(x))
Eq(F_155(x), F_156(x) + F_157(x))
Eq(F_156(x), F_151(x))
Eq(F_157(x), F_122(x) + F_158(x) + 3*F_38(x))
Eq(F_158(x), F_159(x)*F_4(x))
Eq(F_159(x), F_160(x) + F_161(x))
Eq(F_160(x), F_154(x))
Eq(F_161(x), F_158(x))
Eq(F_162(x), F_163(x)*F_4(x))
Eq(F_163(x), F_164(x) + F_30(x))
Eq(F_164(x), F_54(x))
Eq(F_165(x), F_166(x) + F_167(x))
Eq(F_166(x), F_39(x))
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_169(x)*F_4(x))
Eq(F_169(x), F_170(x) + F_171(x))
Eq(F_170(x), F_81(x))
Eq(F_171(x), F_104(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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