0123_0231_0312_1320_2103
Counting sequence:
1, 1, 2, 6, 19, 50, 111, 245, 546, 1209, 2655, 5829, 12812, 28151, 61822, 135766, 298182, 654884, 1438242, 3158637, 6936986, 15234968, 33458865, 73481985, 161380408, 354422040, 778378008, 1709465711, 3754311035, 8245179317, 18107977865, 39768554420, 87339289762, 191813648925, 421259160466, 925165030067, 2031837912116, 4462301499679, 9800060602279, 21522792176884, 47268134544963, 103809790337585, 227985992542859, 500700489103328, 1099633258133157, 2415003237879948, 5303805242185950, 11648162456185082, 25581574437633754, 56181990349963764, 123386308664405507, 270979740500378002, 595122915633797408, 1307002818950511497, 2870426131928245221, 6304000312311891074, 13844780569542929542, 30405764518196642984, 66776826927098601861, 146654579653245022399, 322081277637677589955, 707351585269252674597, 1553478267512912757944, 3411732973944354281536, 7492812824562050180965, 16455638366977665592162, 36139703527236415284655, 79369644732684156841326, 174310796441506408134763, 382819576154158442502877, 840744411009720075766446, 1846434217772180220347509, 4055119815147420562365351, 8905812379843022669889173, 19558853439718122342751784, 42954952514182246874180659, 94337224376800856464154378, 207182440725095836595871502, 455011942829258576506531750, 999292543290220988996005796, 2194635993214256054960924370, 4819836968715082563221762577, 10585276317722652162290165318, 23247274845566168378928325800, 51055425623651974821540795205, 112127400004022951269675663769, 246253041240690301899165369132, 540818393346438360110997766056, 1187739786311696657393065174168, 2608501887775236449932961465027, 5728764984505903684515193942499, 12581454666184538831466444423189, 27631261178522443748137754584329, 60683491263356195955826536461792, 133272458615540664870375723185050, 292691601219001268501392296027593, 642806280563006195359300800312430, 1411724533981679825217061906679855, 3100414884092666748146101005064440, 6809099241472903434456317123637011, 14954073636436949687615836639026071
Generating function in Maple syntax:
(x^8+3*x^7+6*x^6+11*x^5+5*x^4+x^3-x+1)/(x-1)/(x^5+3*x^4+2*x^3+x^2+x-1)
Generating function in latex syntax:
\frac{x^{8}+3 x^{7}+6 x^{6}+11 x^{5}+5 x^{4}+x^{3}-x +1}{\left(x -1\right) \left(x^{5}+3 x^{4}+2 x^{3}+x^{2}+x -1\right)}
Generating function in sympy syntax:
(x**8 + 3*x**7 + 6*x**6 + 11*x**5 + 5*x**4 + x**3 - x + 1)/((x - 1)*(x**5 + 3*x**4 + 2*x**3 + x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
-(x-1)*(x^5+3*x^4+2*x^3+x^2+x-1)*F(x)+x^8+3*x^7+6*x^6+11*x^5+5*x^4+x^3-x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x -1\right) \left(x^{5}+3 x^{4}+2 x^{3}+x^{2}+x -1\right) F \! \left(x \right)+x^{8}+3 x^{7}+6 x^{6}+11 x^{5}+5 x^{4}+x^{3}-x +1 = 0
Explicit closed form in Maple syntax:
1/371*((121*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+54)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^2+(121*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^2+417*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+162)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)+54*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^2+162*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+407)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)^(1-n)+1/371*(((-121*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-54)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)-54*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-205)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)+(-54*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-205)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)-205*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-208)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 4)^(1-n)+1/371*(-121*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^3-363*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^2-242*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)+299)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^(1-n)+1/371*((121*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+54)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)+54*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+205)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)^(2-n)+1/371*(-121*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^2-363*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)+43)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^(2-n)+1/371*(-121*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)-54)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^(-n+3)+60/53*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^(1-n)+285/371*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^(2-n)+309/371*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^(-n+3)+121/371*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^(-n+4)+1/371*(((-121*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-54)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)-54*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-205)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^2+((-121*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-54)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^2+(-121*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)^2-471*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-367)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)-54*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)^2-367*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-615)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)+(-54*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-205)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^2+(-54*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)^2-367*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-615)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)-205*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)^2-615*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)-384)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 4)^(-n)+1/371*((((121*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 4)+54)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)+54*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 4)+205)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+(54*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 4)+205)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)+205*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 4)+208)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)+((54*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 4)+205)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)+205*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 4)+208)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+(205*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 4)+208)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)+208*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 4)+240)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 5)^(-n)+1/371*((121*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+54)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^3+(121*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^2+417*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+162)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^2+(121*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^3+417*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^2+404*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+108)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)+54*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^3+162*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^2+108*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)+26)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 3)^(-n)+1/371*(-121*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^4-363*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^3-242*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^2-121*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)-28)*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 2)^(-n)+piecewise(n = 0,5,Or(n = 1,n = 2),1,0)+93/371*RootOf(_Z^5+3*_Z^4+2*_Z^3+_Z^2+_Z-1,index = 1)^(-n)-27/7
Explicit closed form in latex syntax:
\frac{\left(\left(121 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+54\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(121 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{2}+417 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+162\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)+54 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{2}+162 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+407\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{1-n}}{371}+\frac{\left(\left(\left(-121 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-54\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)-54 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-205\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)+\left(-54 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-205\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)-205 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-208\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)^{1-n}}{371}+\frac{\left(-121 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{3}-363 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{2}-242 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)+299\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{1-n}}{371}+\frac{\left(\left(121 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+54\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)+54 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+205\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{2-n}}{371}+\frac{\left(-121 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{2}-363 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)+43\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{2-n}}{371}+\frac{\left(-121 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)-54\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{371}+\frac{60 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{1-n}}{53}+\frac{285 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{2-n}}{371}+\frac{309 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{371}+\frac{121 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}}{371}+\frac{\left(\left(\left(-121 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-54\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)-54 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-205\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-121 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-54\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-121 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{2}-471 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-367\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)-54 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{2}-367 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-615\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)+\left(-54 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-205\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-54 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{2}-367 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-615\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)-205 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{2}-615 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)-384\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{371}+\frac{\left(\left(\left(\left(121 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)+54\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)+54 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)+205\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+\left(54 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)+205\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)+205 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)+208\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)+\left(\left(54 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)+205\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)+205 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)+208\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+\left(205 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)+208\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)+208 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)+240\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{371}+\frac{\left(\left(121 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+54\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(121 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{2}+417 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+162\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(121 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{3}+417 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{2}+404 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+108\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)+54 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{3}+162 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{2}+108 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)+26\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{371}+\frac{\left(-121 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{4}-363 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{3}-242 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{2}-121 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)-28\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{371}+\left(\left\{\begin{array}{cc}5 & n =0 \\ 1 & n =1\text{ or } n =2 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)+\frac{93 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+3 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{371}-\frac{27}{7}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 50
a(6) = 111
a(7) = 245
a(8) = 546
a(n+5) = a(n)+3*a(n+1)+2*a(n+2)+a(n+3)+a(4+n)+27, n >= 9
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 19
a \! \left(5\right) = 50
a \! \left(6\right) = 111
a \! \left(7\right) = 245
a \! \left(8\right) = 546
a \! \left(n +5\right) = a \! \left(n \right)+3 a \! \left(n +1\right)+2 a \! \left(n +2\right)+a \! \left(n +3\right)+a \! \left(4+n \right)+27, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/17046/
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[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[11,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[11,x]
F[17,x] = F[18,x]+F[2,x]
F[18,x] = F[19,x]+F[20,x]+F[56,x]
F[19,x] = 0
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[32,x]
F[22,x] = F[23,x]+F[7,x]
F[23,x] = F[19,x]+F[24,x]+F[30,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[26,x]
F[26,x] = F[11,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[11,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[13,x]
F[32,x] = F[33,x]+F[40,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[36,x]
F[36,x] = F[2,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[2,x]
F[40,x] = 2*F[19,x]+F[41,x]+F[54,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[37,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[11,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[16,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[47,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[68,x]
F[58,x] = F[2,x]+F[59,x]
F[59,x] = F[19,x]+F[60,x]+F[66,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[62,x]+F[64,x]
F[62,x] = F[11,x]+F[63,x]
F[63,x] = F[19,x]+F[24,x]+F[28,x]
F[64,x] = F[37,x]+F[65,x]
F[65,x] = 2*F[19,x]+F[41,x]+F[45,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[2,x]+F[47,x]
F[68,x] = F[47,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[14,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_{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_{11}\! \left(x \right)+F_{14}\! \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_{11}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{2}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{56}\! \left(x \right)
F_{19}\! \left(x \right) = 0
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_{32}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{7}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)+F_{30}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{13}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{40}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{2}\! \left(x \right)
F_{40}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{41}\! \left(x \right)+F_{54}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{37}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{11}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{16}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{47}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{68}\! \left(x \right)
F_{58}\! \left(x \right) = F_{2}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{19}\! \left(x \right)+F_{60}\! \left(x \right)+F_{66}\! \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_{64}\! \left(x \right)
F_{62}\! \left(x \right) = F_{11}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)+F_{28}\! \left(x \right)
F_{64}\! \left(x \right) = F_{37}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{41}\! \left(x \right)+F_{45}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{2}\! \left(x \right)+F_{47}\! \left(x \right)
F_{68}\! \left(x \right) = F_{47}\! \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_{14}\! \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_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_11(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_11(x))
Eq(F_17(x), F_18(x) + F_2(x))
Eq(F_18(x), F_19(x) + F_20(x) + F_56(x))
Eq(F_19(x), 0)
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_32(x))
Eq(F_22(x), F_23(x) + F_7(x))
Eq(F_23(x), F_19(x) + F_24(x) + F_30(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_11(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_11(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_13(x))
Eq(F_32(x), F_33(x) + F_40(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_2(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_2(x))
Eq(F_40(x), 2*F_19(x) + F_41(x) + F_54(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_37(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_11(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_16(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_47(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_68(x))
Eq(F_58(x), F_2(x) + F_59(x))
Eq(F_59(x), F_19(x) + F_60(x) + F_66(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_64(x))
Eq(F_62(x), F_11(x) + F_63(x))
Eq(F_63(x), F_19(x) + F_24(x) + F_28(x))
Eq(F_64(x), F_37(x) + F_65(x))
Eq(F_65(x), 2*F_19(x) + F_41(x) + F_45(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_2(x) + F_47(x))
Eq(F_68(x), F_47(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_14(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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