0132_0231_2031_2103
Counting sequence:
1, 1, 2, 6, 20, 63, 186, 533, 1524, 4391, 12727, 36952, 107221, 310822, 900626, 2609544, 7561994, 21915285, 63513945, 184071644, 533455836, 1545991313, 4480386232, 12984482524, 37630018321, 109054698187, 316048887611, 915933740445, 2654445443291, 7692784162896, 22294272411831, 64610494989431, 187246123560603, 542653491722114, 1572651040809256, 4557662173025650, 13208451171212197, 38279094806229814, 110935724457573749, 321500156267468148, 931731874305846581, 2700229746798935883, 7825470917540355834, 22678809147186612905, 65724911606916059952, 190475786348471960936, 552013297516513005472, 1599776467531729048528, 4636273723079630334817, 13436273424171179424661, 38939341012240231496696, 112849168113830270583300, 327045461297902352647079, 947802589449938682941454, 2746803899992735392564528, 7960446351379929680503361, 23069978207532503581198281, 66858549257575794301306079, 193761154371970274298088513, 561534543606694631041030189, 1627369761940237757752215838, 4716241186281050493053190229, 13668025206916999570570409357, 39610975282676264247359305401, 114795615247383998654678153366, 332686412944464747953936537814, 964150495812401181455725428900, 2794181374429843634661153483023, 8097749871125698538727670394010, 23467894237429965117536304560681, 68011740138206793836125356284536, 197103189141248283883482492385495, 571220014231428407507316809107783, 1655438991526034395414024881902932, 4797587945779567241900901151005677, 13903774295102092544413293471385590, 40294194047907058572553429809173174, 116775635126811924756834885207748572, 338424660958781829442525421578546182, 980780374439340733707168323513786825, 2842376025908262501763933224084794877, 8237421632010565579496763662400484628, 23872673610041780250844718248914006880, 69184821507368273916656306074279799173, 200502868057183253271329240968121492668, 581072541971864954707112320311599158324, 1683992365322916964421312514677993021033, 4880337791977754741602046965399020522795, 14143589635122307387956430901835594663431, 40989197119831450289012649053033648977317, 118789806822182308653738277128194690737119, 344261883529896664640402640864070916836064, 997697088850058737885171736805633039538035, 2891401949276323892355810543201047459508467, 8379502481975627635557666947327822460727675, 24284434705804140766925518474480435380969478, 70378136440556749334680943902514006731634512, 203961185378624539444267606418600055496517434, 591095008265674288732779679889243537864654981, 1713038233956128678779325066799810202138117326, 4964514925621886292397580303432712091295049161
Generating function in Maple syntax:
-(x-1)^4/(x^5-2*x^4+9*x^3-9*x^2+5*x-1)
Generating function in latex syntax:
-\frac{\left(x -1\right)^{4}}{x^{5}-2 x^{4}+9 x^{3}-9 x^{2}+5 x -1}
Generating function in sympy syntax:
-(x - 1)**4/(x**5 - 2*x**4 + 9*x**3 - 9*x**2 + 5*x - 1)
Implicit equation for the generating function in Maple syntax:
(x^5-2*x^4+9*x^3-9*x^2+5*x-1)*F(x)+(x-1)^4 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{5}-2 x^{4}+9 x^{3}-9 x^{2}+5 x -1\right) F \! \left(x \right)+\left(x -1\right)^{4} = 0
Explicit closed form in Maple syntax:
2482/193617*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)^(-n+3)+2482/193617*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^(-n+3)+2482/193617*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)^(-n+3)+2482/193617*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)^(-n+3)+2482/193617*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 5)^(-n+3)-1873/64539*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)^(-n+2)-1873/64539*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^(-n+2)-1873/64539*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)^(-n+2)-1873/64539*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)^(-n+2)-1873/64539*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 5)^(-n+2)+5314/64539*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)^(-n+1)+5314/64539*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^(-n+1)+5314/64539*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)^(-n+1)+5314/64539*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)^(-n+1)+5314/64539*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 5)^(-n+1)+14834/193617*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)^(-n-1)+14834/193617*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^(-n-1)+14834/193617*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)^(-n-1)+14834/193617*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)^(-n-1)+14834/193617*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 5)^(-n-1)+37/639*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 1)^(-n)+37/639*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 2)^(-n)+37/639*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 3)^(-n)+37/639*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 4)^(-n)+37/639*RootOf(_Z^5-2*_Z^4+9*_Z^3-9*_Z^2+5*_Z-1,index = 5)^(-n)
Explicit closed form in latex syntax:
\frac{2482 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{193617}+\frac{2482 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{193617}+\frac{2482 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{193617}+\frac{2482 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{193617}+\frac{2482 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{193617}-\frac{1873 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{64539}-\frac{1873 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{64539}-\frac{1873 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{64539}-\frac{1873 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{64539}-\frac{1873 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{64539}+\frac{5314 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{64539}+\frac{5314 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{64539}+\frac{5314 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{64539}+\frac{5314 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{64539}+\frac{5314 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +1}}{64539}+\frac{14834 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{193617}+\frac{14834 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{193617}+\frac{14834 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{193617}+\frac{14834 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{193617}+\frac{14834 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{193617}+\frac{37 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{639}+\frac{37 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{639}+\frac{37 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{639}+\frac{37 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{639}+\frac{37 \mathit{RootOf}\! \left(\textit{\_Z}^{5}-2 \textit{\_Z}^{4}+9 \textit{\_Z}^{3}-9 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{639}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(n+5) = a(n)-2*a(n+1)+9*a(n+2)-9*a(n+3)+5*a(n+4), n >= 5
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 20
a \! \left(n +5\right) = a \! \left(n \right)-2 a \! \left(n +1\right)+9 a \! \left(n +2\right)-9 a \! \left(n +3\right)+5 a \! \left(n +4\right), \quad n \geq 5
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15378/
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[20,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[7,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]
F[17,x] = F[11,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[17,x]*F[4,x]
F[20,x] = F[2,x]+F[21,x]
F[21,x] = F[22,x]+F[23,x]+F[47,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[27,x]
F[25,x] = F[26,x]+F[7,x]
F[26,x] = F[15,x]
F[27,x] = F[28,x]+F[41,x]
F[28,x] = F[29,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[31,x]+F[34,x]
F[31,x] = F[2,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[31,x]*F[4,x]
F[34,x] = F[28,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]
F[38,x] = F[32,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[38,x]*F[4,x]
F[41,x] = F[42,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[32,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[4,x]*F[44,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[49,x]+F[57,x]
F[49,x] = F[2,x]+F[50,x]
F[50,x] = F[22,x]+F[51,x]+F[56,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = F[11,x]+F[14,x]
F[54,x] = F[32,x]+F[55,x]
F[55,x] = F[42,x]
F[56,x] = F[4,x]*F[49,x]
F[57,x] = F[21,x]+F[58,x]
F[58,x] = 2*F[22,x]+F[42,x]+F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[68,x]
F[61,x] = F[14,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[18,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[4,x]*F[65,x]
F[68,x] = F[35,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[39,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[4,x]*F[72,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_{20}\! \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_{7}\! \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_{17}\! \left(x \right) = F_{11}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{47}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{27}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{7}\! \left(x \right)
F_{26}\! \left(x \right) = F_{15}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{41}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{34}\! \left(x \right)
F_{31}\! \left(x \right) = F_{2}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{28}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{32}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{32}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \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_{57}\! \left(x \right)
F_{49}\! \left(x \right) = F_{2}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{22}\! \left(x \right)+F_{51}\! \left(x \right)+F_{56}\! \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_{54}\! \left(x \right)
F_{53}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{54}\! \left(x \right) = F_{32}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{42}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{57}\! \left(x \right) = F_{21}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{42}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{68}\! \left(x \right)
F_{61}\! \left(x \right) = F_{14}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{18}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{68}\! \left(x \right) = F_{35}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{39}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \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_20(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_7(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))
Eq(F_17(x), F_11(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_17(x)*F_4(x))
Eq(F_20(x), F_2(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_47(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_27(x))
Eq(F_25(x), F_26(x) + F_7(x))
Eq(F_26(x), F_15(x))
Eq(F_27(x), F_28(x) + F_41(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_31(x) + F_34(x))
Eq(F_31(x), F_2(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_31(x)*F_4(x))
Eq(F_34(x), F_28(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_32(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_38(x)*F_4(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_32(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_4(x)*F_44(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_57(x))
Eq(F_49(x), F_2(x) + F_50(x))
Eq(F_50(x), F_22(x) + F_51(x) + F_56(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), F_11(x) + F_14(x))
Eq(F_54(x), F_32(x) + F_55(x))
Eq(F_55(x), F_42(x))
Eq(F_56(x), F_4(x)*F_49(x))
Eq(F_57(x), F_21(x) + F_58(x))
Eq(F_58(x), 2*F_22(x) + F_42(x) + F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_68(x))
Eq(F_61(x), F_14(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_18(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_4(x)*F_65(x))
Eq(F_68(x), F_35(x) + F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_39(x) + F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_4(x)*F_72(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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 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, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 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, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 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, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 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": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 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, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 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, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 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, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 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, 1, 0, 3], "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, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 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