Av(1324, 1342, 1432, 2314, 3214)
Generating Function
\(\displaystyle \frac{\left(x -1\right)^{3}}{x^{5}+x^{4}+4 x^{3}-5 x^{2}+4 x -1}\)
Counting Sequence
1, 1, 2, 6, 19, 56, 156, 428, 1181, 3283, 9151, 25497, 70974, 197479, 549468, ...
Implicit Equation for the Generating Function
\(\displaystyle \left(x^{5}+x^{4}+4 x^{3}-5 x^{2}+4 x -1\right) F \! \left(x \right)-\left(x -1\right)^{3} = 0\)
Recurrence
\(\displaystyle a \! \left(0\right) = 1\)
\(\displaystyle a \! \left(1\right) = 1\)
\(\displaystyle a \! \left(2\right) = 2\)
\(\displaystyle a \! \left(3\right) = 6\)
\(\displaystyle a \! \left(4\right) = 19\)
\(\displaystyle a \! \left(n +5\right) = a \! \left(n \right)+a \! \left(n +1\right)+4 a \! \left(n +2\right)-5 a \! \left(n +3\right)+4 a \! \left(n +4\right), \quad n \geq 5\)
\(\displaystyle a \! \left(1\right) = 1\)
\(\displaystyle a \! \left(2\right) = 2\)
\(\displaystyle a \! \left(3\right) = 6\)
\(\displaystyle a \! \left(4\right) = 19\)
\(\displaystyle a \! \left(n +5\right) = a \! \left(n \right)+a \! \left(n +1\right)+4 a \! \left(n +2\right)-5 a \! \left(n +3\right)+4 a \! \left(n +4\right), \quad n \geq 5\)
Explicit Closed Form
\(\displaystyle -\frac{1486664225 \left(\left(\left(\left(\mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)-\frac{1822}{16075}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)-\frac{1822 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{16075}-\frac{542}{16075}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)+\left(-\frac{1822 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{16075}-\frac{542}{16075}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)-\frac{542 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{16075}-\frac{179}{3215}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)+\left(\left(-\frac{1822 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{16075}-\frac{542}{16075}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)-\frac{542 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{16075}-\frac{179}{3215}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)+\left(-\frac{542 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{16075}-\frac{179}{3215}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)-\frac{179 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{3215}+\frac{35933}{16075}\right) \left(\left(\left(\left(\frac{295255 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}-1\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{2}+\left(-\frac{77295 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}-\frac{203013}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)+\frac{19892}{92483}+\frac{18716 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{3}+\left(\left(\frac{295255 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}-1\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{3}+\left(\frac{125477 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}-\frac{517225}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{2}+\left(-\frac{261592 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}-\frac{6600840}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)+\frac{739824}{92483}+\frac{38608 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{77295 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}-\frac{203013}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{3}+\left(-\frac{261592 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}-\frac{6600840}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{2}+\left(\frac{2233298 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}-\frac{5275258}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)+\frac{457547}{92483}+\frac{422529 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)+\left(\frac{19892}{92483}+\frac{18716 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{3}+\left(\frac{739824}{92483}+\frac{38608 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{2}+\left(\frac{457547}{92483}+\frac{422529 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)-\frac{619611}{92483}-\frac{262385 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{-n +1}+\left(\left(\left(-\frac{18716}{92483}+\frac{77295 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}-\frac{295255 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{2}}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{2}+\left(-\frac{33531}{92483}+\frac{132084 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}+\frac{77295 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{2}}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)-\frac{33531 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}-\frac{18716 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{2}}{92483}-\frac{781}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{33531}{92483}+\frac{132084 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}+\frac{77295 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{2}}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{2}+\left(\frac{8682508 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}-\frac{332496}{92483}+\frac{132084 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{2}}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)-\frac{33531 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{2}}{92483}-\frac{467789}{92483}-\frac{332496 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)+\left(-\frac{33531 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}-\frac{18716 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{2}}{92483}-\frac{781}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{2}+\left(-\frac{33531 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{2}}{92483}-\frac{467789}{92483}-\frac{332496 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)-\frac{824234}{92483}-\frac{467789 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}-\frac{781 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{2}}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)^{-n +1}+\left(\left(\left(1-\frac{295255 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)+\mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)+\frac{221729}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{4}+\left(\left(\frac{314212}{92483}-\frac{202772 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)+\frac{314212 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}+\frac{6659340}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{3}+\left(\left(\frac{591661}{92483}-\frac{1088537 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)+\frac{591661 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}+\frac{7324527}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{1214689}{92483}+\frac{2706883 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)+\frac{1214689 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}+\frac{1104717}{4021}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)+\left(\frac{14251 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{4021}-\frac{341953}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)-\frac{3499339}{92483}-\frac{341953 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{-n +1}+\left(\left(\left(\frac{295255 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}-1\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{2}+\left(-\frac{77295 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}-\frac{203013}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)+\frac{19892}{92483}+\frac{18716 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{77295 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}-\frac{203013}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{2}+\left(-\frac{6384188}{92483}-\frac{132084 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)+\frac{33531 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}+\frac{720713}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)+\left(\frac{19892}{92483}+\frac{18716 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{2}+\left(\frac{33531 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}+\frac{720713}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)+\frac{204623}{92483}+\frac{781 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{-n +2}+\left(\left(\left(1-\frac{295255 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)+\mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)+\frac{221729}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{3}+\left(\left(\frac{314212}{92483}-\frac{202772 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)+\frac{314212 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}+\frac{6659340}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{216652}{92483}+\frac{129508 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)+\frac{216652 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}+\frac{6418500}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)+\left(-\frac{5077 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}-\frac{19111}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)-\frac{515309}{92483}-\frac{19111 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{-n +2}+\left(\left(\left(1-\frac{295255 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)+\mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)+\frac{221729}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{203013}{92483}+\frac{77295 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)+\frac{203013 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}+\frac{6417719}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)+\left(-\frac{18716 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}-\frac{19892}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)-\frac{719932}{92483}-\frac{19892 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{-n +3}+\left(\left(\left(\frac{34356}{4021}+\frac{860676 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)+\frac{34356 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{4021}+\frac{766692}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)+\left(\frac{34356 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{4021}+\frac{766692}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)+\frac{28688716}{92483}+\frac{766692 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{-n +1}+\left(\left(\left(-\frac{375009}{92483}+\frac{1218045 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)-\frac{375009 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}-\frac{906027}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)+\left(-\frac{375009 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}-\frac{906027}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)-\frac{26265753}{92483}-\frac{906027 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{-n +2}+\left(\left(\left(-\frac{111199}{92483}+\frac{280067 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)-\frac{111199 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}-\frac{241621}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)+\left(-\frac{111199 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}-\frac{241621}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)-\frac{7157543}{92483}-\frac{241621 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{-n +3}+\left(\left(\left(-1+\frac{295255 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)-\mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)-\frac{221729}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)+\left(-\mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)-\frac{221729}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)-\frac{6437611}{92483}-\frac{221729 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{-n +4}+\left(\left(\left(-\mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)-\frac{221729}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{2}+\left(-\frac{203013 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}-\frac{6417719}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)+\frac{719932}{92483}+\frac{19892 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{3}-\left(\left(\mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)+\frac{221729}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{2}+\left(\frac{203013 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}+\frac{6417719}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)-\frac{719932}{92483}-\frac{19892 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}\right) \left(\mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)+1\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{203013 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}-\frac{6417719}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{3}+\left(-\frac{183121 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}-\frac{5697787}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{2}+\left(\frac{778650 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}-\frac{26511714}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)+\frac{2578552}{92483}-\frac{297880 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)+\left(\frac{719932}{92483}+\frac{19892 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{3}+\left(\frac{719932}{92483}+\frac{19892 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{2}+\left(\frac{2578552}{92483}-\frac{297880 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)-\frac{13784896}{92483}-\frac{490688 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{-n}+\left(\left(\left(-\frac{19892}{92483}+\frac{203013 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}+\mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{2}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{2}+\left(-\frac{720713}{92483}+\frac{6384188 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}+\frac{203013 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{2}}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)-\frac{720713 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}-\frac{19892 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{2}}{92483}-\frac{204623}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{720713}{92483}+\frac{6384188 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}+\frac{203013 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{2}}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{2}+\left(\frac{5721412 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}-\frac{1223216}{92483}+\frac{6384188 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{2}}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)-\frac{720713 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{2}}{92483}-\frac{695311}{92483}-\frac{1223216 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)+\left(-\frac{720713 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}-\frac{19892 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{2}}{92483}-\frac{204623}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{2}+\left(-\frac{720713 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{2}}{92483}-\frac{695311}{92483}-\frac{1223216 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)-\frac{14714062}{92483}-\frac{695311 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}-\frac{204623 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)^{2}}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)^{-n}+\left(\left(\left(\mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)+\frac{221729}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)+\frac{6437611}{92483}+\frac{221729 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{4}+\left(\left(\mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)+\frac{221729}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)+\frac{6437611}{92483}+\frac{221729 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{3}+\left(\left(\frac{886916}{92483}+4 \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)+\frac{886916 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}+\frac{25750444}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{1560770}{92483}+\frac{1570810 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)-\frac{1560770 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}-\frac{33468630}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)+\left(-\frac{377448 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}-\frac{301176}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)-\frac{10086952}{92483}-\frac{301176 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)^{-n}+\left(\left(\left(-\frac{452125}{92483}+\frac{2033225 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)-\frac{452125 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}-\frac{1280575}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =2\right)+\left(-\frac{452125 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}-\frac{1280575}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =4\right)-\frac{36059125}{92483}-\frac{1280575 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf} \left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =1\right)^{-n}-\frac{14260544 \mathit{RootOf}\left(Z^{5}+Z^{4}+4 Z^{3}-5 Z^{2}+4 Z -1, \mathit{index} =5\right)^{-n}}{92483}\right)}{3177548674624}\)
This specification was found using the strategy pack "Point Placements" and has 78 rules.
Found on January 18, 2022.Finding the specification took 1 seconds.
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\(\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_{14}\! \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_{6}\! \left(x \right)\\
F_{10}\! \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_{11}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{17}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{16}\! \left(x \right) &= 0\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{21}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{19}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{25}\! \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_{11}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{38}\! \left(x \right) &= 2 F_{16}\! \left(x \right)+F_{39}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{4}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= 2 F_{16}\! \left(x \right)+F_{43}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{4}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{4}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{4}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{4}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{36}\! \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_{63}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{59}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{4}\! \left(x \right) F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{57}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{4}\! \left(x \right) F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= 2 F_{16}\! \left(x \right)+F_{65}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{4}\! \left(x \right) F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= 2 F_{16}\! \left(x \right)+F_{69}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{4}\! \left(x \right) F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{4}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{4}\! \left(x \right) F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{4}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{53}\! \left(x \right)\\
\end{align*}\)