Av(13425, 13452, 13542, 14325, 14352, 14532, 15342, 15432, 31425, 31452, 31542, 34125, 34152, 34215, 41325, 41352, 41532, 43125, 43152, 43215)
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Generating Function
\(\displaystyle -\frac{\left(x +1\right) \left(2 x -1\right)^{3} \left(x -1\right)^{4}}{24 x^{11}+32 x^{10}+22 x^{9}-116 x^{8}+120 x^{7}-94 x^{6}+18 x^{5}+69 x^{4}-80 x^{3}+40 x^{2}-10 x +1}\)
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Counting Sequence
1, 1, 2, 6, 24, 100, 400, 1480, 5212, 18006, 62294, 217456, 765176, 2702762, 9550282, ...
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Implicit Equation for the Generating Function
\(\displaystyle \left(24 x^{11}+32 x^{10}+22 x^{9}-116 x^{8}+120 x^{7}-94 x^{6}+18 x^{5}+69 x^{4}-80 x^{3}+40 x^{2}-10 x +1\right) F \! \left(x \right)+\left(x +1\right) \left(2 x -1\right)^{3} \left(x -1\right)^{4} = 0\)
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Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 100\)
\(\displaystyle a(6) = 400\)
\(\displaystyle a(7) = 1480\)
\(\displaystyle a(8) = 5212\)
\(\displaystyle a(9) = 18006\)
\(\displaystyle a(10) = 62294\)
\(\displaystyle a{\left(n + 11 \right)} = - 24 a{\left(n \right)} - 32 a{\left(n + 1 \right)} - 22 a{\left(n + 2 \right)} + 116 a{\left(n + 3 \right)} - 120 a{\left(n + 4 \right)} + 94 a{\left(n + 5 \right)} - 18 a{\left(n + 6 \right)} - 69 a{\left(n + 7 \right)} + 80 a{\left(n + 8 \right)} - 40 a{\left(n + 9 \right)} + 10 a{\left(n + 10 \right)}, \quad n \geq 11\)
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Explicit Closed Form
\(\displaystyle -\frac{95514659029303767287416955 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =1\right)^{-n}}{25847555963427144292137851}-\frac{95514659029303767287416955 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =2\right)^{-n}}{25847555963427144292137851}-\frac{95514659029303767287416955 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =3\right)^{-n}}{25847555963427144292137851}-\frac{95514659029303767287416955 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =4\right)^{-n}}{25847555963427144292137851}-\frac{95514659029303767287416955 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =5\right)^{-n}}{25847555963427144292137851}-\frac{95514659029303767287416955 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =6\right)^{-n}}{25847555963427144292137851}-\frac{95514659029303767287416955 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =7\right)^{-n}}{25847555963427144292137851}-\frac{95514659029303767287416955 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =8\right)^{-n}}{25847555963427144292137851}-\frac{95514659029303767287416955 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =9\right)^{-n}}{25847555963427144292137851}-\frac{95514659029303767287416955 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =10\right)^{-n}}{25847555963427144292137851}-\frac{95514659029303767287416955 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =11\right)^{-n}}{25847555963427144292137851}+\frac{13109836256345901206261018 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =1\right)^{-n -1}}{25847555963427144292137851}+\frac{13109836256345901206261018 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =2\right)^{-n -1}}{25847555963427144292137851}+\frac{13109836256345901206261018 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =3\right)^{-n -1}}{25847555963427144292137851}+\frac{13109836256345901206261018 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =4\right)^{-n -1}}{25847555963427144292137851}+\frac{13109836256345901206261018 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =5\right)^{-n -1}}{25847555963427144292137851}+\frac{13109836256345901206261018 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =6\right)^{-n -1}}{25847555963427144292137851}+\frac{13109836256345901206261018 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =7\right)^{-n -1}}{25847555963427144292137851}+\frac{13109836256345901206261018 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =8\right)^{-n -1}}{25847555963427144292137851}+\frac{13109836256345901206261018 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =9\right)^{-n -1}}{25847555963427144292137851}+\frac{13109836256345901206261018 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =10\right)^{-n -1}}{25847555963427144292137851}+\frac{13109836256345901206261018 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =11\right)^{-n -1}}{25847555963427144292137851}+\frac{289364992326264988768386705 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =1\right)^{-n +1}}{25847555963427144292137851}+\frac{289364992326264988768386705 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =2\right)^{-n +1}}{25847555963427144292137851}+\frac{289364992326264988768386705 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =3\right)^{-n +1}}{25847555963427144292137851}+\frac{289364992326264988768386705 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =4\right)^{-n +1}}{25847555963427144292137851}+\frac{289364992326264988768386705 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =5\right)^{-n +1}}{25847555963427144292137851}+\frac{289364992326264988768386705 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =6\right)^{-n +1}}{25847555963427144292137851}+\frac{289364992326264988768386705 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =7\right)^{-n +1}}{25847555963427144292137851}+\frac{289364992326264988768386705 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =8\right)^{-n +1}}{25847555963427144292137851}+\frac{289364992326264988768386705 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =9\right)^{-n +1}}{25847555963427144292137851}+\frac{289364992326264988768386705 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =10\right)^{-n +1}}{25847555963427144292137851}+\frac{289364992326264988768386705 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =11\right)^{-n +1}}{25847555963427144292137851}-\frac{369712618839302355365655132 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =1\right)^{-n +2}}{25847555963427144292137851}-\frac{369712618839302355365655132 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =2\right)^{-n +2}}{25847555963427144292137851}-\frac{369712618839302355365655132 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =3\right)^{-n +2}}{25847555963427144292137851}-\frac{369712618839302355365655132 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =4\right)^{-n +2}}{25847555963427144292137851}-\frac{369712618839302355365655132 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =5\right)^{-n +2}}{25847555963427144292137851}-\frac{369712618839302355365655132 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =6\right)^{-n +2}}{25847555963427144292137851}-\frac{369712618839302355365655132 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =7\right)^{-n +2}}{25847555963427144292137851}-\frac{369712618839302355365655132 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =8\right)^{-n +2}}{25847555963427144292137851}-\frac{369712618839302355365655132 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =9\right)^{-n +2}}{25847555963427144292137851}-\frac{369712618839302355365655132 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =10\right)^{-n +2}}{25847555963427144292137851}-\frac{369712618839302355365655132 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =11\right)^{-n +2}}{25847555963427144292137851}+\frac{33610396806596622668103854 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =1\right)^{-n +3}}{25847555963427144292137851}+\frac{33610396806596622668103854 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =2\right)^{-n +3}}{25847555963427144292137851}+\frac{33610396806596622668103854 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =3\right)^{-n +3}}{25847555963427144292137851}+\frac{33610396806596622668103854 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =4\right)^{-n +3}}{25847555963427144292137851}+\frac{33610396806596622668103854 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =5\right)^{-n +3}}{25847555963427144292137851}+\frac{33610396806596622668103854 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =6\right)^{-n +3}}{25847555963427144292137851}+\frac{33610396806596622668103854 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =7\right)^{-n +3}}{25847555963427144292137851}+\frac{33610396806596622668103854 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =8\right)^{-n +3}}{25847555963427144292137851}+\frac{33610396806596622668103854 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =9\right)^{-n +3}}{25847555963427144292137851}+\frac{33610396806596622668103854 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =10\right)^{-n +3}}{25847555963427144292137851}+\frac{33610396806596622668103854 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =11\right)^{-n +3}}{25847555963427144292137851}+\frac{335029404311882004118863888 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =1\right)^{-n +4}}{25847555963427144292137851}+\frac{335029404311882004118863888 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =2\right)^{-n +4}}{25847555963427144292137851}+\frac{335029404311882004118863888 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =3\right)^{-n +4}}{25847555963427144292137851}+\frac{335029404311882004118863888 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =4\right)^{-n +4}}{25847555963427144292137851}+\frac{335029404311882004118863888 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =5\right)^{-n +4}}{25847555963427144292137851}+\frac{335029404311882004118863888 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =6\right)^{-n +4}}{25847555963427144292137851}+\frac{335029404311882004118863888 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =7\right)^{-n +4}}{25847555963427144292137851}+\frac{335029404311882004118863888 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =8\right)^{-n +4}}{25847555963427144292137851}+\frac{335029404311882004118863888 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =9\right)^{-n +4}}{25847555963427144292137851}+\frac{335029404311882004118863888 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =10\right)^{-n +4}}{25847555963427144292137851}+\frac{335029404311882004118863888 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =11\right)^{-n +4}}{25847555963427144292137851}-\frac{426362764365855984715125692 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =1\right)^{-n +5}}{25847555963427144292137851}-\frac{426362764365855984715125692 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =2\right)^{-n +5}}{25847555963427144292137851}-\frac{426362764365855984715125692 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =3\right)^{-n +5}}{25847555963427144292137851}-\frac{426362764365855984715125692 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =4\right)^{-n +5}}{25847555963427144292137851}-\frac{426362764365855984715125692 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =5\right)^{-n +5}}{25847555963427144292137851}-\frac{426362764365855984715125692 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =6\right)^{-n 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Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =9\right)^{-n +6}}{25847555963427144292137851}+\frac{564895053415438109396083696 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =10\right)^{-n +6}}{25847555963427144292137851}+\frac{564895053415438109396083696 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =11\right)^{-n +6}}{25847555963427144292137851}-\frac{194858590028832416637382680 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =1\right)^{-n +7}}{25847555963427144292137851}-\frac{194858590028832416637382680 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =2\right)^{-n 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Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =5\right)^{-n +8}}{25847555963427144292137851}-\frac{220277342393811668450291328 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =6\right)^{-n +8}}{25847555963427144292137851}-\frac{220277342393811668450291328 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =7\right)^{-n +8}}{25847555963427144292137851}-\frac{220277342393811668450291328 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =8\right)^{-n +8}}{25847555963427144292137851}-\frac{220277342393811668450291328 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =9\right)^{-n 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Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =3\right)^{-n +9}}{25847555963427144292137851}-\frac{129461531057692943803628832 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =4\right)^{-n +9}}{25847555963427144292137851}-\frac{129461531057692943803628832 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =5\right)^{-n +9}}{25847555963427144292137851}-\frac{129461531057692943803628832 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =6\right)^{-n +9}}{25847555963427144292137851}-\frac{129461531057692943803628832 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =7\right)^{-n +9}}{25847555963427144292137851}-\frac{129461531057692943803628832 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =8\right)^{-n +9}}{25847555963427144292137851}-\frac{129461531057692943803628832 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =9\right)^{-n +9}}{25847555963427144292137851}-\frac{129461531057692943803628832 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =10\right)^{-n +9}}{25847555963427144292137851}-\frac{129461531057692943803628832 \mathit{RootOf} \left(24 Z^{11}+32 Z^{10}+22 Z^{9}-116 Z^{8}+120 Z^{7}-94 Z^{6}+18 Z^{5}+69 Z^{4}-80 Z^{3}+40 Z^{2}-10 Z +1, \mathit{index} =11\right)^{-n +9}}{25847555963427144292137851}\)
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This specification was found using the strategy pack "Regular Insertion Encoding Bottom" and has 451 rules.

Finding the specification took 355 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_{14}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{14}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{21}\! \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_{14}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{15}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x \right)\\ F_{14}\! \left(x \right) &= x\\ F_{15}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{16}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{14}\! \left(x \right) F_{18}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{14}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{16}\! \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_{24}\! \left(x \right)+F_{34}\! \left(x \right)\\ F_{23}\! \left(x \right) &= 0\\ F_{24}\! \left(x \right) &= F_{14}\! \left(x \right) F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{27}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{16}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{24}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{14}\! \left(x \right) F_{31}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{28}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{29}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{14}\! \left(x \right) F_{35}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{37}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{29}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{269}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{14}\! \left(x \right) F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{43}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{14}\! \left(x \right) F_{44}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)+F_{48}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{14}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{43}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{14}\! \left(x \right) F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{54}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{46}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{50}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{14}\! \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_{10}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)+F_{84}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{60}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{14}\! \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_{10}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= x^{2}\\ F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{14}\! \left(x \right) F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{71}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{64}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{67}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{14}\! \left(x \right) F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)+F_{75}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{66}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{59}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{76}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{77}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{14}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{16}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{14}\! \left(x \right) F_{80}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{67}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{77}\! \left(x \right)+F_{79}\! \left(x \right)\\ F_{84}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{85}\! \left(x \right)+F_{97}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{14}\! \left(x \right) F_{86}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)+F_{90}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{14}\! \left(x \right) F_{46}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{14}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{89}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{92}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{14}\! \left(x \right) F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{121}\! \left(x \right)\\ F_{101}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{102}\! \left(x \right)+F_{108}\! \left(x \right)\\ F_{102}\! \left(x \right) &= F_{103}\! \left(x \right) F_{14}\! \left(x \right)\\ F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{106}\! \left(x \right)\\ F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{89}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)\\ F_{107}\! \left(x \right) &= F_{92}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{109}\! \left(x \right) F_{14}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{111}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{113}\! \left(x \right)\\ F_{112}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{102}\! \left(x \right)+F_{108}\! \left(x \right)\\ F_{113}\! \left(x \right) &= 3 F_{23}\! \left(x \right)+F_{114}\! \left(x \right)+F_{116}\! \left(x \right)\\ F_{114}\! \left(x \right) &= F_{115}\! \left(x \right) F_{14}\! \left(x \right)\\ F_{115}\! \left(x \right) &= F_{50}\! \left(x \right)\\ F_{116}\! \left(x \right) &= F_{117}\! \left(x \right) F_{14}\! \left(x \right)\\ F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{119}\! \left(x \right)\\ F_{118}\! \left(x \right) &= F_{92}\! \left(x \right)\\ F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)\\ F_{120}\! \left(x \right) &= 3 F_{23}\! \left(x \right)+F_{114}\! \left(x \right)+F_{116}\! \left(x \right)\\ F_{121}\! \left(x \right) &= 3 F_{23}\! \left(x \right)+F_{114}\! \left(x \right)+F_{116}\! \left(x \right)\\ F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{202}\! \left(x \right)\\ F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{144}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{124}\! \left(x \right) &= F_{125}\! \left(x \right) F_{14}\! \left(x \right)\\ F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{127}\! \left(x \right)\\ F_{126}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{129}\! \left(x \right)\\ F_{128}\! \left(x \right) &= F_{124}\! \left(x \right)\\ F_{129}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{130}\! \left(x \right)+F_{140}\! \left(x \right)\\ F_{130}\! \left(x \right) &= F_{131}\! \left(x \right) F_{14}\! \left(x \right)\\ F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)+F_{133}\! \left(x \right)\\ F_{132}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)+F_{135}\! \left(x \right)\\ F_{134}\! \left(x \right) &= F_{130}\! \left(x \right)\\ F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)\\ F_{136}\! \left(x \right) &= F_{137}\! \left(x \right) F_{14}\! \left(x \right)\\ F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{139}\! \left(x \right)\\ F_{138}\! \left(x \right) &= F_{134}\! \left(x \right)\\ F_{139}\! \left(x \right) &= F_{135}\! \left(x \right)\\ F_{140}\! \left(x \right) &= F_{14}\! \left(x \right) F_{141}\! \left(x \right)\\ F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{143}\! \left(x \right)\\ F_{142}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{134}\! \left(x \right)\\ F_{143}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{135}\! \left(x \right)\\ F_{144}\! \left(x \right) &= F_{14}\! \left(x \right) F_{145}\! \left(x \right)\\ F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)+F_{147}\! \left(x \right)\\ F_{146}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{168}\! \left(x \right)\\ F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{156}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{149}\! \left(x \right) &= F_{14}\! \left(x \right) F_{150}\! \left(x \right)\\ F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{153}\! \left(x \right)\\ F_{151}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{152}\! \left(x \right)\\ F_{152}\! \left(x \right) &= F_{17}\! \left(x \right)\\ F_{153}\! \left(x \right) &= F_{154}\! \left(x \right)+F_{155}\! \left(x \right)\\ F_{154}\! \left(x \right) &= F_{24}\! \left(x \right)\\ F_{155}\! \left(x \right) &= F_{30}\! \left(x \right)\\ F_{156}\! \left(x \right) &= F_{14}\! \left(x \right) F_{157}\! \left(x \right)\\ F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)+F_{159}\! \left(x \right)\\ F_{158}\! \left(x \right) &= F_{154}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{159}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{160}\! \left(x \right)\\ F_{160}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{161}\! \left(x \right)+F_{163}\! \left(x \right)\\ F_{161}\! \left(x \right) &= F_{14}\! \left(x \right) F_{162}\! \left(x \right)\\ F_{162}\! \left(x \right) &= F_{16}\! \left(x \right)\\ F_{163}\! \left(x \right) &= F_{14}\! \left(x \right) F_{164}\! \left(x \right)\\ F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)+F_{166}\! \left(x \right)\\ F_{165}\! \left(x \right) &= F_{28}\! \left(x \right)\\ F_{166}\! \left(x \right) &= F_{167}\! \left(x \right)\\ F_{167}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{161}\! \left(x \right)+F_{163}\! \left(x \right)\\ F_{168}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{169}\! \left(x \right)+F_{176}\! \left(x \right)\\ F_{169}\! \left(x \right) &= F_{14}\! \left(x \right) F_{170}\! \left(x \right)\\ F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)+F_{173}\! \left(x \right)\\ F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{172}\! \left(x \right) &= F_{51}\! \left(x \right)\\ F_{173}\! \left(x \right) &= F_{174}\! \left(x \right)+F_{175}\! \left(x \right)\\ F_{174}\! \left(x \right) &= F_{130}\! \left(x \right)\\ F_{175}\! \left(x \right) &= F_{136}\! \left(x \right)\\ F_{176}\! \left(x \right) &= F_{14}\! \left(x \right) F_{177}\! \left(x \right)\\ F_{177}\! \left(x \right) &= F_{178}\! \left(x \right)+F_{179}\! \left(x \right)\\ F_{178}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{174}\! \left(x \right)\\ F_{179}\! \left(x \right) &= F_{180}\! \left(x \right)+F_{201}\! \left(x \right)\\ F_{180}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{181}\! \left(x \right)+F_{188}\! \left(x \right)\\ F_{181}\! \left(x \right) &= F_{14}\! \left(x \right) F_{182}\! \left(x \right)\\ F_{182}\! \left(x \right) &= F_{183}\! \left(x \right)+F_{185}\! \left(x \right)\\ F_{183}\! \left(x \right) &= F_{184}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{184}\! \left(x \right) &= F_{51}\! \left(x \right)\\ F_{185}\! \left(x \right) &= F_{186}\! \left(x \right)+F_{187}\! \left(x \right)\\ F_{186}\! \left(x \right) &= F_{130}\! \left(x \right)\\ F_{187}\! \left(x \right) &= F_{136}\! \left(x \right)\\ F_{188}\! \left(x \right) &= F_{14}\! \left(x \right) F_{189}\! \left(x \right)\\ F_{189}\! \left(x \right) &= F_{190}\! \left(x \right)+F_{191}\! \left(x \right)\\ F_{190}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{186}\! \left(x \right)\\ F_{191}\! \left(x \right) &= F_{192}\! \left(x \right)+F_{193}\! \left(x \right)\\ F_{192}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{181}\! \left(x \right)+F_{188}\! \left(x \right)\\ F_{193}\! \left(x \right) &= 3 F_{23}\! \left(x \right)+F_{194}\! \left(x \right)+F_{196}\! \left(x \right)\\ F_{194}\! \left(x \right) &= F_{14}\! \left(x \right) F_{195}\! \left(x \right)\\ F_{195}\! \left(x \right) &= F_{50}\! \left(x \right)\\ F_{196}\! \left(x \right) &= F_{14}\! \left(x \right) F_{197}\! \left(x \right)\\ F_{197}\! \left(x \right) &= F_{198}\! \left(x \right)+F_{199}\! \left(x \right)\\ F_{198}\! \left(x \right) &= F_{134}\! \left(x \right)\\ F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)\\ F_{200}\! \left(x \right) &= 3 F_{23}\! \left(x \right)+F_{194}\! \left(x \right)+F_{196}\! \left(x \right)\\ F_{201}\! \left(x \right) &= 3 F_{23}\! \left(x \right)+F_{194}\! \left(x \right)+F_{196}\! \left(x \right)\\ F_{202}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{140}\! \left(x \right)+F_{203}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{203}\! \left(x \right) &= F_{14}\! \left(x \right) F_{204}\! \left(x \right)\\ F_{204}\! \left(x \right) &= F_{205}\! \left(x \right)+F_{206}\! \left(x \right)\\ F_{205}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{206}\! \left(x \right) &= F_{207}\! \left(x \right)+F_{231}\! \left(x \right)\\ F_{207}\! \left(x \right) &= F_{208}\! \left(x \right)+F_{210}\! \left(x \right)+F_{222}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{208}\! \left(x \right) &= F_{14}\! \left(x \right) F_{209}\! \left(x \right)\\ F_{209}\! \left(x \right) &= F_{63}\! \left(x \right)\\ F_{210}\! \left(x \right) &= F_{14}\! \left(x \right) F_{211}\! \left(x \right)\\ F_{211}\! \left(x \right) &= F_{212}\! \left(x \right)+F_{213}\! \left(x \right)\\ F_{212}\! \left(x \right) &= F_{154}\! \left(x \right)\\ F_{213}\! \left(x \right) &= F_{214}\! \left(x \right)\\ F_{214}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{215}\! \left(x \right)+F_{217}\! \left(x \right)\\ F_{215}\! \left(x \right) &= F_{14}\! \left(x \right) F_{216}\! \left(x \right)\\ F_{216}\! \left(x \right) &= F_{70}\! \left(x \right)\\ F_{217}\! \left(x \right) &= F_{14}\! \left(x \right) F_{218}\! \left(x \right)\\ F_{218}\! \left(x \right) &= F_{219}\! \left(x \right)+F_{220}\! \left(x \right)\\ F_{219}\! \left(x \right) &= F_{28}\! \left(x \right)\\ F_{220}\! \left(x \right) &= F_{221}\! \left(x \right)\\ F_{221}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{215}\! \left(x \right)+F_{217}\! \left(x \right)\\ F_{222}\! \left(x \right) &= F_{14}\! \left(x \right) F_{223}\! \left(x \right)\\ F_{223}\! \left(x \right) &= F_{224}\! \left(x \right)+F_{225}\! \left(x \right)\\ F_{224}\! \left(x \right) &= F_{214}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{225}\! \left(x \right) &= F_{207}\! \left(x \right)+F_{226}\! \left(x \right)\\ F_{226}\! \left(x \right) &= F_{227}\! \left(x \right)\\ F_{227}\! \left(x \right) &= F_{14}\! \left(x \right) F_{228}\! \left(x \right)\\ F_{228}\! \left(x \right) &= F_{229}\! \left(x \right)+F_{230}\! \left(x \right)\\ F_{229}\! \left(x \right) &= F_{221}\! \left(x \right)\\ F_{230}\! \left(x \right) &= F_{227}\! \left(x \right)\\ F_{231}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{232}\! \left(x \right)+F_{234}\! \left(x \right)+F_{246}\! \left(x \right)\\ F_{232}\! \left(x \right) &= F_{14}\! \left(x \right) F_{233}\! \left(x \right)\\ F_{233}\! \left(x \right) &= F_{88}\! \left(x \right)\\ F_{234}\! \left(x \right) &= F_{14}\! \left(x \right) F_{235}\! \left(x \right)\\ F_{235}\! \left(x \right) &= F_{236}\! \left(x \right)+F_{237}\! \left(x \right)\\ F_{236}\! \left(x \right) &= F_{174}\! \left(x \right)\\ F_{237}\! \left(x \right) &= F_{238}\! \left(x \right)\\ F_{238}\! \left(x \right) &= 3 F_{23}\! \left(x \right)+F_{239}\! \left(x \right)+F_{241}\! \left(x \right)\\ F_{239}\! \left(x \right) &= F_{14}\! \left(x \right) F_{240}\! \left(x \right)\\ F_{240}\! \left(x \right) &= F_{95}\! \left(x \right)\\ F_{241}\! \left(x \right) &= F_{14}\! \left(x \right) F_{242}\! \left(x \right)\\ F_{242}\! \left(x \right) &= F_{243}\! \left(x \right)+F_{244}\! \left(x \right)\\ F_{243}\! \left(x \right) &= F_{134}\! \left(x \right)\\ F_{244}\! \left(x \right) &= F_{245}\! \left(x \right)\\ F_{245}\! \left(x \right) &= 3 F_{23}\! \left(x \right)+F_{239}\! \left(x \right)+F_{241}\! \left(x \right)\\ F_{246}\! \left(x \right) &= F_{14}\! \left(x \right) F_{247}\! \left(x \right)\\ F_{247}\! \left(x \right) &= F_{248}\! \left(x \right)+F_{249}\! \left(x \right)\\ F_{248}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{238}\! \left(x \right)\\ F_{249}\! \left(x \right) &= F_{250}\! \left(x \right)+F_{268}\! \left(x \right)\\ F_{250}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{251}\! \left(x \right)+F_{253}\! \left(x \right)+F_{258}\! \left(x \right)\\ F_{251}\! \left(x \right) &= F_{14}\! \left(x \right) F_{252}\! \left(x \right)\\ F_{252}\! \left(x \right) &= F_{105}\! \left(x \right)\\ F_{253}\! \left(x \right) &= F_{14}\! \left(x \right) F_{254}\! \left(x \right)\\ F_{254}\! \left(x \right) &= F_{255}\! \left(x \right)+F_{256}\! \left(x \right)\\ F_{255}\! \left(x \right) &= F_{186}\! \left(x \right)\\ F_{256}\! \left(x \right) &= F_{257}\! \left(x \right)\\ F_{257}\! \left(x \right) &= 3 F_{23}\! \left(x \right)+F_{239}\! \left(x \right)+F_{241}\! \left(x \right)\\ F_{258}\! \left(x \right) &= F_{14}\! \left(x \right) F_{259}\! \left(x \right)\\ F_{259}\! \left(x \right) &= F_{260}\! \left(x \right)+F_{261}\! \left(x \right)\\ F_{260}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{257}\! \left(x \right)\\ F_{261}\! \left(x \right) &= F_{262}\! \left(x \right)+F_{263}\! \left(x \right)\\ F_{262}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{251}\! \left(x \right)+F_{253}\! \left(x \right)+F_{258}\! \left(x \right)\\ F_{263}\! \left(x \right) &= F_{264}\! \left(x \right)\\ F_{264}\! \left(x \right) &= F_{14}\! \left(x \right) F_{265}\! \left(x \right)\\ F_{265}\! \left(x \right) &= F_{266}\! \left(x \right)+F_{267}\! \left(x \right)\\ F_{266}\! \left(x \right) &= F_{245}\! \left(x \right)\\ F_{267}\! \left(x \right) &= F_{264}\! \left(x \right)\\ F_{268}\! \left(x \right) &= F_{264}\! \left(x \right)\\ F_{269}\! \left(x \right) &= F_{14}\! \left(x \right) F_{270}\! \left(x \right)\\ F_{270}\! \left(x \right) &= F_{271}\! \left(x \right)+F_{272}\! \left(x \right)\\ F_{271}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{272}\! \left(x \right) &= F_{273}\! \left(x \right)+F_{316}\! \left(x \right)\\ F_{273}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{274}\! \left(x \right)+F_{295}\! \left(x \right)\\ F_{274}\! \left(x \right) &= F_{14}\! \left(x \right) F_{275}\! \left(x \right)\\ F_{275}\! \left(x \right) &= F_{276}\! \left(x \right)+F_{285}\! \left(x \right)\\ F_{276}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{277}\! \left(x \right)\\ F_{277}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{23}\! \left(x \right)+F_{278}\! \left(x \right)\\ F_{278}\! \left(x \right) &= F_{14}\! \left(x \right) F_{279}\! \left(x \right)\\ F_{279}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{280}\! \left(x \right)\\ F_{280}\! \left(x \right) &= F_{277}\! \left(x \right)+F_{281}\! \left(x \right)\\ F_{281}\! \left(x \right) &= F_{282}\! \left(x \right)\\ F_{282}\! \left(x \right) &= F_{14}\! \left(x \right) F_{283}\! \left(x \right)\\ F_{283}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{284}\! \left(x \right)\\ F_{284}\! \left(x \right) &= F_{281}\! \left(x \right)\\ F_{285}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{286}\! \left(x \right)\\ F_{286}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{287}\! \left(x \right)+F_{288}\! \left(x \right)+F_{30}\! \left(x \right)\\ F_{287}\! \left(x \right) &= 0\\ F_{288}\! \left(x \right) &= F_{14}\! \left(x \right) F_{289}\! \left(x \right)\\ F_{289}\! \left(x \right) &= F_{290}\! \left(x \right)+F_{37}\! \left(x \right)\\ F_{290}\! \left(x \right) &= F_{286}\! \left(x \right)+F_{291}\! \left(x \right)\\ F_{291}\! \left(x \right) &= F_{292}\! \left(x \right)\\ F_{292}\! \left(x \right) &= F_{14}\! \left(x \right) F_{293}\! \left(x \right)\\ F_{293}\! \left(x \right) &= F_{294}\! \left(x \right)+F_{33}\! \left(x \right)\\ F_{294}\! \left(x \right) &= F_{291}\! \left(x \right)\\ F_{295}\! \left(x \right) &= F_{14}\! \left(x \right) F_{296}\! \left(x \right)\\ F_{296}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{297}\! \left(x \right)\\ F_{297}\! \left(x \right) &= F_{273}\! \left(x \right)+F_{298}\! \left(x \right)\\ F_{298}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{299}\! \left(x \right)+F_{303}\! \left(x \right)+F_{312}\! \left(x \right)\\ F_{299}\! \left(x \right) &= F_{14}\! \left(x \right) F_{300}\! \left(x \right)\\ F_{300}\! \left(x \right) &= F_{301}\! \left(x \right)+F_{302}\! \left(x \right)\\ F_{301}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{281}\! \left(x \right)\\ F_{302}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{291}\! \left(x \right)\\ F_{303}\! \left(x \right) &= F_{14}\! \left(x \right) F_{304}\! \left(x \right)\\ F_{304}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{305}\! \left(x \right)\\ F_{305}\! \left(x \right) &= F_{306}\! \left(x \right)+F_{307}\! \left(x \right)\\ F_{306}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{299}\! \left(x \right)+F_{303}\! \left(x \right)\\ F_{307}\! \left(x \right) &= F_{308}\! \left(x \right)\\ F_{308}\! \left(x \right) &= F_{14}\! \left(x \right) F_{309}\! \left(x \right)\\ F_{309}\! \left(x \right) &= F_{310}\! \left(x \right)+F_{311}\! \left(x \right)\\ F_{310}\! \left(x \right) &= F_{306}\! \left(x \right)\\ F_{311}\! \left(x \right) &= F_{307}\! \left(x \right)\\ F_{312}\! \left(x \right) &= F_{14}\! \left(x \right) F_{313}\! \left(x \right)\\ F_{313}\! \left(x \right) &= F_{314}\! \left(x \right)+F_{315}\! \left(x \right)\\ F_{314}\! \left(x \right) &= F_{273}\! \left(x \right)+F_{306}\! \left(x \right)\\ F_{315}\! \left(x \right) &= F_{298}\! \left(x \right)+F_{307}\! \left(x \right)\\ F_{316}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{317}\! \left(x \right)+F_{341}\! \left(x \right)+F_{373}\! \left(x \right)\\ F_{317}\! \left(x \right) &= F_{14}\! \left(x \right) F_{318}\! \left(x \right)\\ F_{318}\! \left(x \right) &= F_{319}\! \left(x \right)+F_{329}\! \left(x \right)\\ F_{319}\! \left(x \right) &= F_{320}\! \left(x \right)+F_{42}\! \left(x \right)\\ F_{320}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{321}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{321}\! \left(x \right) &= F_{14}\! \left(x \right) F_{322}\! \left(x \right)\\ F_{322}\! \left(x \right) &= F_{323}\! \left(x \right)+F_{48}\! \left(x \right)\\ F_{323}\! \left(x \right) &= F_{324}\! \left(x \right)+F_{325}\! \left(x \right)\\ F_{324}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{321}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{325}\! \left(x \right) &= F_{326}\! \left(x \right)\\ F_{326}\! \left(x \right) &= F_{14}\! \left(x \right) F_{327}\! \left(x \right)\\ F_{327}\! \left(x \right) &= F_{328}\! \left(x \right)+F_{54}\! \left(x \right)\\ F_{328}\! \left(x \right) &= F_{325}\! \left(x \right)\\ F_{329}\! \left(x \right) &= F_{330}\! \left(x \right)+F_{331}\! \left(x \right)\\ F_{330}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{130}\! \left(x \right)+F_{140}\! \left(x \right)\\ F_{331}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{136}\! \left(x \right)+F_{332}\! \left(x \right)+F_{333}\! \left(x \right)\\ F_{332}\! \left(x \right) &= 0\\ F_{333}\! \left(x \right) &= F_{14}\! \left(x \right) F_{334}\! \left(x \right)\\ F_{334}\! \left(x \right) &= F_{143}\! \left(x \right)+F_{335}\! \left(x \right)\\ F_{335}\! \left(x \right) &= F_{336}\! \left(x \right)+F_{337}\! \left(x \right)\\ F_{336}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{136}\! \left(x \right)+F_{332}\! \left(x \right)+F_{333}\! \left(x \right)\\ F_{337}\! \left(x \right) &= F_{338}\! \left(x \right)\\ F_{338}\! \left(x \right) &= F_{14}\! \left(x \right) F_{339}\! \left(x \right)\\ F_{339}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{340}\! \left(x \right)\\ F_{340}\! \left(x \right) &= F_{337}\! \left(x \right)\\ F_{341}\! \left(x \right) &= F_{14}\! \left(x \right) F_{342}\! \left(x \right)\\ F_{342}\! \left(x \right) &= F_{343}\! \left(x \right)+F_{344}\! \left(x \right)\\ F_{343}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{330}\! \left(x \right)\\ F_{344}\! \left(x \right) &= F_{345}\! \left(x \right)+F_{372}\! \left(x \right)\\ F_{345}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{346}\! \left(x \right)+F_{350}\! \left(x \right)\\ F_{346}\! \left(x \right) &= F_{14}\! \left(x \right) F_{347}\! \left(x \right)\\ F_{347}\! \left(x \right) &= F_{348}\! \left(x \right)+F_{349}\! \left(x \right)\\ F_{348}\! \left(x \right) &= F_{324}\! \left(x \right)+F_{49}\! \left(x \right)\\ F_{349}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{336}\! \left(x \right)\\ F_{350}\! \left(x \right) &= F_{14}\! \left(x \right) F_{351}\! \left(x \right)\\ F_{351}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{352}\! \left(x \right)\\ F_{352}\! \left(x \right) &= F_{353}\! \left(x \right)+F_{354}\! \left(x \right)\\ F_{353}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{346}\! \left(x \right)+F_{350}\! \left(x \right)\\ F_{354}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{355}\! \left(x \right)+F_{359}\! \left(x \right)+F_{368}\! \left(x \right)\\ F_{355}\! \left(x \right) &= F_{14}\! \left(x \right) F_{356}\! \left(x \right)\\ F_{356}\! \left(x \right) &= F_{357}\! \left(x \right)+F_{358}\! \left(x \right)\\ F_{357}\! \left(x \right) &= F_{325}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{358}\! \left(x \right) &= F_{135}\! \left(x \right)+F_{337}\! \left(x \right)\\ F_{359}\! \left(x \right) &= F_{14}\! \left(x \right) F_{360}\! \left(x \right)\\ F_{360}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{361}\! \left(x \right)\\ F_{361}\! \left(x \right) &= F_{362}\! \left(x \right)+F_{363}\! \left(x \right)\\ F_{362}\! \left(x \right) &= 3 F_{23}\! \left(x \right)+F_{355}\! \left(x \right)+F_{359}\! \left(x \right)\\ F_{363}\! \left(x \right) &= F_{364}\! \left(x \right)\\ F_{364}\! \left(x \right) &= F_{14}\! \left(x \right) F_{365}\! \left(x \right)\\ F_{365}\! \left(x \right) &= F_{366}\! \left(x \right)+F_{367}\! \left(x \right)\\ F_{366}\! \left(x \right) &= F_{362}\! \left(x \right)\\ F_{367}\! \left(x \right) &= F_{363}\! \left(x \right)\\ F_{368}\! \left(x \right) &= F_{14}\! \left(x \right) F_{369}\! \left(x \right)\\ F_{369}\! \left(x \right) &= F_{370}\! \left(x \right)+F_{371}\! \left(x \right)\\ F_{370}\! \left(x \right) &= F_{353}\! \left(x \right)+F_{362}\! \left(x \right)\\ F_{371}\! \left(x \right) &= F_{354}\! \left(x \right)+F_{363}\! \left(x \right)\\ F_{372}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{355}\! \left(x \right)+F_{359}\! \left(x \right)+F_{368}\! \left(x \right)\\ F_{373}\! \left(x \right) &= F_{14}\! \left(x \right) F_{374}\! \left(x \right)\\ F_{374}\! \left(x \right) &= F_{375}\! \left(x \right)+F_{376}\! \left(x \right)\\ F_{375}\! \left(x \right) &= F_{273}\! \left(x \right)+F_{345}\! \left(x \right)\\ F_{376}\! \left(x \right) &= F_{377}\! \left(x \right)+F_{404}\! \left(x \right)\\ F_{377}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{378}\! \left(x \right)+F_{385}\! \left(x \right)+F_{391}\! \left(x \right)\\ F_{378}\! \left(x \right) &= F_{14}\! \left(x \right) F_{379}\! \left(x \right)\\ F_{379}\! \left(x \right) &= F_{380}\! \left(x \right)+F_{382}\! \left(x \right)\\ F_{380}\! \left(x \right) &= F_{277}\! \left(x \right)+F_{381}\! \left(x \right)\\ F_{381}\! \left(x \right) &= F_{282}\! \left(x \right)\\ F_{382}\! \left(x \right) &= F_{383}\! \left(x \right)+F_{384}\! \left(x \right)\\ F_{383}\! \left(x \right) &= F_{30}\! \left(x \right)\\ F_{384}\! \left(x \right) &= F_{292}\! \left(x \right)\\ F_{385}\! \left(x \right) &= F_{14}\! \left(x \right) F_{386}\! \left(x \right)\\ F_{386}\! \left(x \right) &= F_{387}\! \left(x \right)+F_{388}\! \left(x \right)\\ F_{387}\! \left(x \right) &= F_{154}\! \left(x \right)+F_{383}\! \left(x \right)\\ F_{388}\! \left(x \right) &= F_{389}\! \left(x \right)+F_{390}\! \left(x \right)\\ F_{389}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{299}\! \left(x \right)+F_{303}\! \left(x \right)\\ F_{390}\! \left(x \right) &= F_{308}\! \left(x \right)\\ F_{391}\! \left(x \right) &= F_{14}\! \left(x \right) F_{392}\! \left(x \right)\\ F_{392}\! \left(x \right) &= F_{393}\! \left(x \right)+F_{394}\! \left(x \right)\\ F_{393}\! \left(x \right) &= F_{273}\! \left(x \right)+F_{389}\! \left(x \right)\\ F_{394}\! \left(x \right) &= F_{377}\! \left(x \right)+F_{395}\! \left(x \right)\\ F_{395}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{396}\! \left(x \right)+F_{398}\! \left(x \right)+F_{399}\! \left(x \right)\\ F_{396}\! \left(x \right) &= F_{14}\! \left(x \right) F_{397}\! \left(x \right)\\ F_{397}\! \left(x \right) &= F_{281}\! \left(x \right)\\ F_{398}\! \left(x \right) &= 0\\ F_{399}\! \left(x \right) &= F_{14}\! \left(x \right) F_{400}\! \left(x \right)\\ F_{400}\! \left(x \right) &= F_{401}\! \left(x \right)+F_{402}\! \left(x \right)\\ F_{401}\! \left(x \right) &= F_{306}\! \left(x \right)\\ F_{402}\! \left(x \right) &= F_{403}\! \left(x \right)\\ F_{403}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{396}\! \left(x \right)+F_{398}\! \left(x \right)+F_{399}\! \left(x \right)\\ F_{404}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{405}\! \left(x \right)+F_{412}\! \left(x \right)+F_{418}\! \left(x \right)\\ F_{405}\! \left(x \right) &= F_{14}\! \left(x \right) F_{406}\! \left(x \right)\\ F_{406}\! \left(x \right) &= F_{407}\! \left(x \right)+F_{409}\! \left(x \right)\\ F_{407}\! \left(x \right) &= F_{320}\! \left(x \right)+F_{408}\! \left(x \right)\\ F_{408}\! \left(x \right) &= F_{326}\! \left(x \right)\\ F_{409}\! \left(x \right) &= F_{410}\! \left(x \right)+F_{411}\! \left(x \right)\\ F_{410}\! \left(x \right) &= F_{136}\! \left(x \right)\\ F_{411}\! \left(x \right) &= F_{338}\! \left(x \right)\\ F_{412}\! \left(x \right) &= F_{14}\! \left(x \right) F_{413}\! \left(x \right)\\ F_{413}\! \left(x \right) &= F_{414}\! \left(x \right)+F_{415}\! \left(x \right)\\ F_{414}\! \left(x \right) &= F_{174}\! \left(x \right)+F_{410}\! \left(x \right)\\ F_{415}\! \left(x \right) &= F_{416}\! \left(x \right)+F_{417}\! \left(x \right)\\ F_{416}\! \left(x \right) &= 3 F_{23}\! \left(x \right)+F_{355}\! \left(x \right)+F_{359}\! \left(x \right)\\ F_{417}\! \left(x \right) &= F_{364}\! \left(x \right)\\ F_{418}\! \left(x \right) &= F_{14}\! \left(x \right) F_{419}\! \left(x \right)\\ F_{419}\! \left(x \right) &= F_{420}\! \left(x \right)+F_{421}\! \left(x \right)\\ F_{420}\! \left(x \right) &= F_{353}\! \left(x \right)+F_{416}\! \left(x \right)\\ F_{421}\! \left(x \right) &= F_{422}\! \left(x \right)+F_{450}\! \left(x \right)\\ F_{422}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{423}\! \left(x \right)+F_{430}\! \left(x \right)+F_{436}\! \left(x \right)\\ F_{423}\! \left(x \right) &= F_{14}\! \left(x \right) F_{424}\! \left(x \right)\\ F_{424}\! \left(x \right) &= F_{425}\! \left(x \right)+F_{427}\! \left(x \right)\\ F_{425}\! \left(x \right) &= F_{324}\! \left(x \right)+F_{426}\! \left(x \right)\\ F_{426}\! \left(x \right) &= F_{326}\! \left(x \right)\\ F_{427}\! \left(x \right) &= F_{428}\! \left(x \right)+F_{429}\! \left(x \right)\\ F_{428}\! \left(x \right) &= F_{136}\! \left(x \right)\\ F_{429}\! \left(x \right) &= F_{338}\! \left(x \right)\\ F_{430}\! \left(x \right) &= F_{14}\! \left(x \right) F_{431}\! \left(x \right)\\ F_{431}\! \left(x \right) &= F_{432}\! \left(x \right)+F_{433}\! \left(x \right)\\ F_{432}\! \left(x \right) &= F_{186}\! \left(x \right)+F_{428}\! \left(x \right)\\ F_{433}\! \left(x \right) &= F_{434}\! \left(x \right)+F_{435}\! \left(x \right)\\ F_{434}\! \left(x \right) &= 3 F_{23}\! \left(x \right)+F_{355}\! \left(x \right)+F_{359}\! \left(x \right)\\ F_{435}\! \left(x \right) &= F_{364}\! \left(x \right)\\ F_{436}\! \left(x \right) &= F_{14}\! \left(x \right) F_{437}\! \left(x \right)\\ F_{437}\! \left(x \right) &= F_{438}\! \left(x \right)+F_{439}\! \left(x \right)\\ F_{438}\! \left(x \right) &= F_{353}\! \left(x \right)+F_{434}\! \left(x \right)\\ F_{439}\! \left(x \right) &= F_{440}\! \left(x \right)+F_{441}\! \left(x \right)\\ F_{440}\! \left(x \right) &= 2 F_{23}\! \left(x \right)+F_{423}\! \left(x \right)+F_{430}\! \left(x \right)+F_{436}\! \left(x \right)\\ F_{441}\! \left(x \right) &= 3 F_{23}\! \left(x \right)+F_{442}\! \left(x \right)+F_{444}\! \left(x \right)+F_{445}\! \left(x \right)\\ F_{442}\! \left(x \right) &= F_{14}\! \left(x \right) F_{443}\! \left(x \right)\\ F_{443}\! \left(x \right) &= F_{325}\! \left(x \right)\\ F_{444}\! \left(x \right) &= 0\\ F_{445}\! \left(x \right) &= F_{14}\! \left(x \right) F_{446}\! \left(x \right)\\ F_{446}\! \left(x \right) &= F_{447}\! \left(x \right)+F_{448}\! \left(x \right)\\ F_{447}\! \left(x \right) &= F_{362}\! \left(x \right)\\ F_{448}\! \left(x \right) &= F_{449}\! \left(x \right)\\ F_{449}\! \left(x \right) &= 3 F_{23}\! \left(x \right)+F_{442}\! \left(x \right)+F_{444}\! \left(x \right)+F_{445}\! \left(x \right)\\ F_{450}\! \left(x \right) &= 3 F_{23}\! \left(x \right)+F_{442}\! \left(x \right)+F_{444}\! \left(x \right)+F_{445}\! \left(x \right)\\ \end{align*}\)