Av(1234, 1342, 1432, 2143, 3142)
Generating Function
\(\displaystyle -\frac{x^{3}+2 x -1}{x^{5}-x^{4}-2 x^{3}+x^{2}-3 x +1}\)
Counting Sequence
1, 1, 2, 6, 19, 55, 159, 464, 1356, 3958, 11550, 33709, 98385, 287148, 838069, ...
Implicit Equation for the Generating Function
\(\displaystyle \left(x^{5}-x^{4}-2 x^{3}+x^{2}-3 x +1\right) F \! \left(x \right)+x^{3}+2 x -1 = 0\)
Recurrence
\(\displaystyle a \! \left(0\right) = 1\)
\(\displaystyle a \! \left(1\right) = 1\)
\(\displaystyle a \! \left(2\right) = 2\)
\(\displaystyle a \! \left(3\right) = 6\)
\(\displaystyle a \! \left(4\right) = 19\)
\(\displaystyle a \! \left(n +5\right) = -a \! \left(n \right)+a \! \left(n +1\right)+2 a \! \left(n +2\right)-a \! \left(n +3\right)+3 a \! \left(n +4\right), \quad n \geq 5\)
\(\displaystyle a \! \left(1\right) = 1\)
\(\displaystyle a \! \left(2\right) = 2\)
\(\displaystyle a \! \left(3\right) = 6\)
\(\displaystyle a \! \left(4\right) = 19\)
\(\displaystyle a \! \left(n +5\right) = -a \! \left(n \right)+a \! \left(n +1\right)+2 a \! \left(n +2\right)-a \! \left(n +3\right)+3 a \! \left(n +4\right), \quad n \geq 5\)
Explicit Closed Form
\(\displaystyle \frac{781153 \left(\left(\left(\left(\mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)-\frac{278}{131}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)-\frac{278 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{131}+\frac{83}{131}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)+\left(-\frac{278 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{131}+\frac{83}{131}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)+\frac{83 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{131}+\frac{187}{131}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)+\left(\left(-\frac{278 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{131}+\frac{83}{131}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)+\frac{83 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{131}+\frac{187}{131}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)+\left(\frac{83 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{131}+\frac{187}{131}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)+\frac{187 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{131}-\frac{1684}{131}\right) \left(\left(\left(\left(-\frac{6237 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}-1\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{2}+\left(\frac{4738 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}+\frac{5691}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)-\frac{6103 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}-\frac{8299}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{6237 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}-1\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{3}+\left(\frac{5012 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}+\frac{23448}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{2}+\left(-\frac{5150 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}+\frac{18117}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)-\frac{2196 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}-\frac{67309}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{4738 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}+\frac{5691}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{3}+\left(-\frac{5150 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}+\frac{18117}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{2}+\left(\frac{9588 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}-\frac{52937}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)+\frac{20807}{5963}+\frac{54778 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)+\left(-\frac{6103 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}-\frac{8299}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{3}+\left(-\frac{2196 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}-\frac{67309}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{2}+\left(\frac{20807}{5963}+\frac{54778 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)-\frac{54801 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}-\frac{101760}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{-n +1}+\left(\left(\left(\frac{6237 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{2}}{5963}-\frac{4738 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}+\frac{6103}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{2}+\left(-\frac{4738 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{2}}{5963}+\frac{2548 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{1359}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)-\frac{1359 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}+\frac{6103 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{2}}{5963}+\frac{4511}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{4738 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{2}}{5963}+\frac{2548 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{1359}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{2}+\left(-\frac{29144 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}+\frac{2548 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{2}}{5963}+\frac{2101}{89}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)-\frac{77650}{5963}-\frac{1359 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{2}}{5963}+\frac{2101 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{89}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)+\left(-\frac{1359 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}+\frac{6103 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{2}}{5963}+\frac{4511}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{2}+\left(-\frac{77650}{5963}-\frac{1359 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{2}}{5963}+\frac{2101 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{89}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)-\frac{77650 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}+\frac{4511 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{2}}{5963}-\frac{83422}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)^{-n +1}+\left(\left(\left(1+\frac{6237 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)+\mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)-\frac{11794}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{4}+\left(\left(-\frac{17757}{5963}-\frac{274 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)-\frac{17757 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{28612}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{132}{5963}-\frac{18437 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)-\frac{132 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}+\frac{63994}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{57861}{5963}+\frac{26951 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)+\frac{57861 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}+\frac{9413}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)+\left(\frac{34273 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{71399}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)-\frac{71399 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{252976}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{-n +1}+\left(\left(\left(-\frac{6237 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}-1\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{2}+\left(\frac{4738 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}+\frac{5691}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)-\frac{6103 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}-\frac{8299}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{4738 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}+\frac{5691}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{2}+\left(\frac{33466}{5963}-\frac{2548 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)+\frac{1359 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}-\frac{80119}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)+\left(-\frac{6103 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}-\frac{8299}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{2}+\left(\frac{1359 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}-\frac{80119}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)-\frac{4511 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}+\frac{18338}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{-n +2}+\left(\left(\left(1+\frac{6237 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)+\mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)-\frac{11794}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{17757}{5963}-\frac{274 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)-\frac{17757 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{28612}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{15349}{5963}+\frac{2602 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)+\frac{15349 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}+\frac{27596}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)+\left(\frac{3555 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{12810}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)-\frac{12810 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{57270}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{-n +2}+\left(\left(\left(1+\frac{6237 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)+\mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)-\frac{11794}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{5691}{5963}-\frac{4738 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)-\frac{5691 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{32107}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)+\left(\frac{6103 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}+\frac{8299}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)+\frac{8299 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}+\frac{75608}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{-n +3}+\left(\left(\left(\frac{28310}{5963}+\frac{32640 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)+\frac{28310 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{59605}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)+\left(\frac{28310 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{59605}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)-\frac{59605 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{212570}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{-n +1}+\left(\left(\left(\frac{15481}{5963}+\frac{21039 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)+\frac{15481 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{36398}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)+\left(\frac{15481 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{36398}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)-\frac{36398 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{138082}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{-n +2}+\left(\left(\left(\frac{12066}{5963}-\frac{4464 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)+\frac{12066 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{3495}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)+\left(\frac{12066 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{3495}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)-\frac{3495 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}+\frac{35202}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{-n +3}+\left(\left(\left(-1-\frac{6237 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)-\mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)+\frac{11794}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)+\left(-\mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)+\frac{11794}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)+\frac{11794 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}+\frac{454}{67}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{-n +4}+\left(\left(\left(-\mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)+\frac{11794}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{2}+\left(\frac{5691 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}+\frac{32107}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)-\frac{8299 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}-\frac{75608}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{3}-\left(\left(\mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)-\frac{11794}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{2}+\left(-\frac{5691 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}-\frac{32107}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)+\frac{8299 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}+\frac{75608}{5963}\right) \left(\mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)-1\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{2}+\left(\left(\frac{5691 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}+\frac{32107}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{3}+\left(-\frac{13990 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}-\frac{107715}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{2}+\left(\frac{69321 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}-\frac{54227}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)+\frac{140752}{5963}-\frac{61355 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)+\left(-\frac{8299 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}-\frac{75608}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{3}+\left(\frac{8299 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}+\frac{75608}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{2}+\left(\frac{140752}{5963}-\frac{61355 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)-\frac{26371 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)}{5963}-\frac{449164}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{-n}+\left(\left(\left(\mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{2}-\frac{5691 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}+\frac{8299}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{2}+\left(-\frac{5691 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{2}}{5963}-\frac{33466 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}+\frac{80119}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)+\frac{80119 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}+\frac{8299 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{2}}{5963}-\frac{18338}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{5691 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{2}}{5963}-\frac{33466 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}+\frac{80119}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{2}+\left(\frac{263025 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{33466 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{2}}{5963}-\frac{159812}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)-\frac{8033}{5963}+\frac{80119 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{2}}{5963}-\frac{159812 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)+\left(\frac{80119 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}+\frac{8299 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{2}}{5963}-\frac{18338}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{2}+\left(-\frac{8033}{5963}+\frac{80119 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{2}}{5963}-\frac{159812 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)-\frac{8033 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{18338 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)^{2}}{5963}-\frac{390161}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)^{-n}+\left(\left(\left(\mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)-\frac{11794}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)-\frac{11794 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{454}{67}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{4}+\left(\left(-\mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)+\frac{11794}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)+\frac{11794 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}+\frac{454}{67}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{3}+\left(\left(\frac{23588}{5963}-2 \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)+\frac{23588 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}+\frac{908}{67}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{65621}{5963}+\frac{72404 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)-\frac{65621 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{80289}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)+\left(-\frac{77953 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{10464}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)-\frac{342556}{5963}-\frac{10464 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)^{-n}+\left(\left(\left(-\frac{53827}{5963}+\frac{66441 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)-\frac{53827 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{39883}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =2\right)+\left(-\frac{53827 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}-\frac{39883}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =4\right)-\frac{475568}{5963}-\frac{39883 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =3\right)}{5963}\right) \mathit{RootOf} \left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =1\right)^{-n}-\frac{472413 \mathit{RootOf}\left(Z^{5}-Z^{4}-2 Z^{3}+Z^{2}-3 Z +1, \mathit{index} =5\right)^{-n}}{5963}\right)}{3782610891}\)
This specification was found using the strategy pack "Point Placements" and has 67 rules.
Found on January 18, 2022.Finding the specification took 1 seconds.
Copy 67 equations to clipboard:
\(\begin{align*}
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_{14}\! \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_{13}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{13}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{19}\! \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_{60}\! \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_{31}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\
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_{30}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{4}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{36}\! \left(x \right)+F_{53}\! \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_{40}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= 2 F_{22}\! \left(x \right)+F_{42}\! \left(x \right)+F_{49}\! \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_{45}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= 2 F_{22}\! \left(x \right)+F_{42}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{4}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{4}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{46}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{2}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{54}\! \left(x \right) &= 2 F_{22}\! \left(x \right)+F_{49}\! \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_{57}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= 2 F_{22}\! \left(x \right)+F_{47}\! \left(x \right)+F_{55}\! \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_{65}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{36}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{34}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= 2 F_{22}\! \left(x \right)+F_{42}\! \left(x \right)+F_{47}\! \left(x \right)\\
\end{align*}\)