Av(1243, 1324, 1342, 1432, 2314)
Generating Function
\(\displaystyle \frac{\left(2 x -1\right)^{3}}{x^{5}-6 x^{4}+17 x^{3}-17 x^{2}+7 x -1}\)
Counting Sequence
1, 1, 2, 6, 19, 60, 188, 585, 1811, 5587, 17199, 52879, 162468, 499005, 1532415, ...
Implicit Equation for the Generating Function
\(\displaystyle \left(x^{5}-6 x^{4}+17 x^{3}-17 x^{2}+7 x -1\right) F \! \left(x \right)-\left(2 x -1\right)^{3} = 0\)
Recurrence
\(\displaystyle a \! \left(0\right) = 1\)
\(\displaystyle a \! \left(1\right) = 1\)
\(\displaystyle a \! \left(2\right) = 2\)
\(\displaystyle a \! \left(3\right) = 6\)
\(\displaystyle a \! \left(4\right) = 19\)
\(\displaystyle a \! \left(n +5\right) = a \! \left(n \right)-6 a \! \left(n +1\right)+17 a \! \left(n +2\right)-17 a \! \left(n +3\right)+7 a \! \left(n +4\right), \quad n \geq 5\)
\(\displaystyle a \! \left(1\right) = 1\)
\(\displaystyle a \! \left(2\right) = 2\)
\(\displaystyle a \! \left(3\right) = 6\)
\(\displaystyle a \! \left(4\right) = 19\)
\(\displaystyle a \! \left(n +5\right) = a \! \left(n \right)-6 a \! \left(n +1\right)+17 a \! \left(n +2\right)-17 a \! \left(n +3\right)+7 a \! \left(n +4\right), \quad n \geq 5\)
Explicit Closed Form
\(\displaystyle -\frac{1457325 \left(\left(\left(\left(-1+\frac{688 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{2}+\left(\frac{106}{127}-\frac{599 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)+\frac{388 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{1143}-\frac{77}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{3}+\left(\left(-1+\frac{688 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{3}+\left(\frac{8378}{1143}-\frac{5108 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{2}+\left(-\frac{712}{127}+\frac{12124 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)-\frac{853 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{381}+\frac{1508}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{106}{127}-\frac{599 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{3}+\left(-\frac{712}{127}+\frac{12124 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{2}+\left(\frac{5446}{1905}-\frac{3521 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{635}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)+\frac{2138 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{5715}-\frac{727}{1905}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)+\left(\frac{388 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{1143}-\frac{77}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{3}+\left(-\frac{853 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{381}+\frac{1508}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{2}+\left(\frac{2138 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{5715}-\frac{727}{1905}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)+\frac{493 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{1905}+\frac{142}{5715}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{-n +1}+\left(\left(\left(-\frac{388}{1143}-\frac{688 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{2}}{381}+\frac{599 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{2}+\left(-\frac{2296}{1905}+\frac{7534 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{5715}+\frac{599 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{2}}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)+\frac{4216}{5715}-\frac{2296 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1905}-\frac{388 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{2}}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{2296}{1905}+\frac{7534 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{5715}+\frac{599 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{2}}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{2}+\left(\frac{17096}{1905}+\frac{7534 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{2}}{5715}-\frac{10588 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{635}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)+\frac{17096 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1905}-\frac{2851}{635}-\frac{2296 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{2}}{1905}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)+\left(\frac{4216}{5715}-\frac{2296 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1905}-\frac{388 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{2}}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{2}+\left(\frac{17096 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1905}-\frac{2851}{635}-\frac{2296 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{2}}{1905}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)-\frac{2851 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{635}+\frac{11194}{5715}+\frac{4216 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{2}}{5715}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)^{-n +1}+\left(\left(\left(-\frac{688 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{381}+1\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)-\frac{566}{1143}+\mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{4}+\left(\left(\frac{1503 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{127}-\frac{7424}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)+\frac{402}{127}-\frac{7424 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{3}+\left(\left(-\frac{13982 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{381}+\frac{7609}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)-\frac{10954}{1143}+\frac{7609 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{54157 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1905}-\frac{85882}{5715}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)+\frac{13328}{1905}-\frac{85882 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{5715}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)+\left(\frac{2346}{635}-\frac{37772 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{5715}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)+\frac{2346 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{635}-\frac{10228}{5715}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{-n +1}+\left(\left(\left(-1+\frac{688 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{2}+\left(\frac{106}{127}-\frac{599 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)+\frac{388 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{1143}-\frac{77}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{106}{127}-\frac{599 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{2}+\left(-\frac{7534 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{5715}+\frac{1541}{1905}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)-\frac{1202}{1905}+\frac{2296 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{1905}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)+\left(\frac{388 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{1143}-\frac{77}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{2}+\left(-\frac{1202}{1905}+\frac{2296 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{1905}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)-\frac{4216 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{5715}+\frac{614}{1905}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{-n +2}+\left(\left(\left(-\frac{688 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{381}+1\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)-\frac{566}{1143}+\mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{3}+\left(\left(\frac{1503 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{127}-\frac{7424}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)+\frac{402}{127}-\frac{7424 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{22718 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1905}+\frac{12221}{1905}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)-\frac{17806}{5715}+\frac{12221 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1905}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)+\left(-\frac{11146}{5715}+\frac{2187 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{635}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)-\frac{11146 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{5715}+\frac{1834}{1905}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{-n +2}+\left(\left(\left(-\frac{688 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{381}+1\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)-\frac{566}{1143}+\mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{599 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{381}-\frac{106}{127}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)+\frac{151}{381}-\frac{106 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{127}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)+\left(\frac{77}{381}-\frac{388 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)+\frac{77 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{381}-\frac{122}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{-n +3}+\left(\left(\left(-\frac{12236 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{635}+\frac{59383}{5715}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)-\frac{26996}{5715}+\frac{59383 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{5715}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)+\left(-\frac{26996}{5715}+\frac{59383 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{5715}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)-\frac{26996 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{5715}+\frac{8642}{5715}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{-n +1}+\left(\left(\left(\frac{47192 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1905}-\frac{8608}{635}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)+\frac{36964}{5715}-\frac{8608 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{635}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)+\left(\frac{36964}{5715}-\frac{8608 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{635}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)+\frac{36964 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{5715}-\frac{4456}{1905}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{-n +2}+\left(\left(\left(-\frac{3910 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{381}+\frac{6470}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)-\frac{1055}{381}+\frac{6470 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)+\left(-\frac{1055}{381}+\frac{6470 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)-\frac{1055 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{381}+\frac{1210}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{-n +3}+\left(\left(\left(\frac{688 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{381}-1\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)+\frac{566}{1143}-\mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)+\left(\frac{566}{1143}-\mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)+\frac{566 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1143}-\frac{74}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{-n +4}+\left(\left(\left(\frac{566}{1143}-\mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{2}+\left(-\frac{151}{381}+\frac{106 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{127}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)-\frac{77 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{381}+\frac{122}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{3}-\left(\mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)-6\right) \left(\left(-\frac{566}{1143}+\mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{2}+\left(\frac{151}{381}-\frac{106 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{127}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)+\frac{77 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{381}-\frac{122}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{151}{381}+\frac{106 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{127}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{3}+\left(\frac{2840}{1143}-\frac{1985 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{2}+\left(-\frac{2786}{1905}+\frac{5953 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{1905}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)-\frac{4253 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{5715}+\frac{2386}{5715}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)+\left(-\frac{77 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{381}+\frac{122}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{3}+\left(\frac{154 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{127}-\frac{244}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{2}+\left(-\frac{4253 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{5715}+\frac{2386}{5715}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)+\frac{149 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)}{635}-\frac{299}{1905}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{-n}+\left(\left(\left(\frac{77}{381}+\mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{2}-\frac{106 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{127}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{2}+\left(\frac{1202}{1905}-\frac{1541 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1905}-\frac{106 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{2}}{127}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)-\frac{614}{1905}+\frac{1202 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1905}+\frac{77 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{2}}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{1202}{1905}-\frac{1541 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1905}-\frac{106 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{2}}{127}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{2}+\left(-\frac{27731}{5715}-\frac{1541 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{2}}{1905}+\frac{17603 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1905}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)-\frac{27731 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{5715}+\frac{1377}{635}+\frac{1202 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{2}}{1905}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)+\left(-\frac{614}{1905}+\frac{1202 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1905}+\frac{77 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{2}}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{2}+\left(-\frac{27731 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{5715}+\frac{1377}{635}+\frac{1202 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{2}}{1905}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)+\frac{1377 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{635}-\frac{2596}{5715}-\frac{614 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)^{2}}{1905}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)^{-n}+\left(\left(\left(-\frac{566}{1143}+\mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)-\frac{566 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1143}+\frac{74}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{4}+\left(\left(-6 \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)+\frac{1132}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)-\frac{148}{127}+\frac{1132 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{381}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{3}+\left(\left(17 \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)-\frac{9622}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)+\frac{1258}{381}-\frac{9622 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1143}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{23387 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1905}+\frac{11269}{1905}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)-\frac{4253}{1905}+\frac{11269 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1905}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)+\left(-\frac{7984}{5715}+\frac{15382 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{5715}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)-\frac{7984 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{5715}+\frac{3328}{5715}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)^{-n}+\left(\left(\left(\frac{8998 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{1905}-\frac{14303}{5715}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)+\frac{679}{635}-\frac{14303 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{5715}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)+\left(\frac{679}{635}-\frac{14303 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{5715}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)+\frac{679 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{635}-\frac{1612}{5715}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)^{-n}-\frac{1777 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =5\right)^{-n}}{5715}\right) \left(\left(\left(\left(\mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)+\frac{20}{51}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)+\frac{20 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{51}-\frac{9}{17}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)+\left(\frac{20 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{51}-\frac{9}{17}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)-\frac{9 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{17}-\frac{262}{255}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =1\right)+\left(\left(\frac{20 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{51}-\frac{9}{17}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)-\frac{9 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{17}-\frac{262}{255}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =2\right)+\left(-\frac{9 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{17}-\frac{262}{255}\right) \mathit{RootOf} \left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =4\right)-\frac{262 \mathit{RootOf}\left(Z^{5}-6 Z^{4}+17 Z^{3}-17 Z^{2}+7 Z -1, \mathit{index} =3\right)}{255}+\frac{651}{85}\right)}{3157729}\)
This specification was found using the strategy pack "Point Placements" and has 69 rules.
Found on January 18, 2022.Finding the specification took 1 seconds.
Copy 69 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_{12}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{12}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{12}\! \left(x \right) &= x\\
F_{13}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{12}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{18}\! \left(x \right) &= 0\\
F_{19}\! \left(x \right) &= F_{12}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{12}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{13}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= 2 F_{18}\! \left(x \right)+F_{27}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{12}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{22}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{26}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{12}\! \left(x \right) F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{35}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{12}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= x^{2}\\
F_{40}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= 2 F_{18}\! \left(x \right)+F_{42}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{12}\! \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_{38}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{12}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{12}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{48}\! \left(x \right) &= 2 F_{18}\! \left(x \right)+F_{49}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{12}\! \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_{14}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{12}\! \left(x \right) F_{33}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{12}\! \left(x \right) F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{58}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{12}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{15}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= 2 F_{18}\! \left(x \right)+F_{53}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{12}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{63}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{12}\! \left(x \right) F_{56}\! \left(x \right)\\
\end{align*}\)