Av(12435, 12453, 12543, 14235, 14253, 14325, 14352, 14523, 14532, 15243, 15423, 15432, 21435, 21453, 21543, 24135, 24153, 24315, 41235, 41253, 41325, 41352, 41523, 41532, 42135, 42153, 42315, 43125, 43152, 43215)
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Generating Function
\(\displaystyle -\frac{\left(x +1\right) \left(x -1\right)^{4}}{2 x^{11}-6 x^{10}+x^{9}+15 x^{8}-17 x^{7}+9 x^{6}+6 x^{5}+11 x^{4}-4 x^{2}+4 x -1}\)
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Counting Sequence
1, 1, 2, 6, 24, 90, 301, 914, 2768, 8586, 27262, 87054, 276635, 873829, 2754021, ...
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Implicit Equation for the Generating Function
\(\displaystyle \left(2 x^{11}-6 x^{10}+x^{9}+15 x^{8}-17 x^{7}+9 x^{6}+6 x^{5}+11 x^{4}-4 x^{2}+4 x -1\right) F \! \left(x \right)+\left(x +1\right) \left(x -1\right)^{4} = 0\)
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Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 90\)
\(\displaystyle a(6) = 301\)
\(\displaystyle a(7) = 914\)
\(\displaystyle a(8) = 2768\)
\(\displaystyle a(9) = 8586\)
\(\displaystyle a(10) = 27262\)
\(\displaystyle a{\left(n + 7 \right)} = - \frac{2 a{\left(n \right)}}{11} + \frac{6 a{\left(n + 1 \right)}}{11} - \frac{a{\left(n + 2 \right)}}{11} - \frac{15 a{\left(n + 3 \right)}}{11} + \frac{17 a{\left(n + 4 \right)}}{11} - \frac{9 a{\left(n + 5 \right)}}{11} - \frac{6 a{\left(n + 6 \right)}}{11} + \frac{4 a{\left(n + 9 \right)}}{11} - \frac{4 a{\left(n + 10 \right)}}{11} + \frac{a{\left(n + 11 \right)}}{11}, \quad n \geq 11\)
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Explicit Closed Form
\(\displaystyle \frac{4875982745861363303076 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =1\right)^{-n -1}}{132542220237166367582119}+\frac{4875982745861363303076 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =2\right)^{-n -1}}{132542220237166367582119}+\frac{4875982745861363303076 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =3\right)^{-n -1}}{132542220237166367582119}+\frac{4875982745861363303076 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =4\right)^{-n -1}}{132542220237166367582119}+\frac{4875982745861363303076 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =5\right)^{-n -1}}{132542220237166367582119}+\frac{4875982745861363303076 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =6\right)^{-n -1}}{132542220237166367582119}+\frac{4875982745861363303076 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =7\right)^{-n -1}}{132542220237166367582119}+\frac{4875982745861363303076 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =8\right)^{-n -1}}{132542220237166367582119}+\frac{4875982745861363303076 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =9\right)^{-n -1}}{132542220237166367582119}+\frac{4875982745861363303076 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =10\right)^{-n -1}}{132542220237166367582119}+\frac{4875982745861363303076 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =11\right)^{-n -1}}{132542220237166367582119}+\frac{1693668961635534542409 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =1\right)^{-n}}{12049292748833306143829}+\frac{1693668961635534542409 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =2\right)^{-n}}{12049292748833306143829}+\frac{1693668961635534542409 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =3\right)^{-n}}{12049292748833306143829}+\frac{1693668961635534542409 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =4\right)^{-n}}{12049292748833306143829}+\frac{1693668961635534542409 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =5\right)^{-n}}{12049292748833306143829}+\frac{1693668961635534542409 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =6\right)^{-n}}{12049292748833306143829}+\frac{1693668961635534542409 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =7\right)^{-n}}{12049292748833306143829}+\frac{1693668961635534542409 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =8\right)^{-n}}{12049292748833306143829}+\frac{1693668961635534542409 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =9\right)^{-n}}{12049292748833306143829}+\frac{1693668961635534542409 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =10\right)^{-n}}{12049292748833306143829}+\frac{1693668961635534542409 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =11\right)^{-n}}{12049292748833306143829}+\frac{1055494516522092784614 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =1\right)^{-n +9}}{132542220237166367582119}+\frac{1055494516522092784614 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =2\right)^{-n +9}}{132542220237166367582119}+\frac{1055494516522092784614 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =3\right)^{-n +9}}{132542220237166367582119}+\frac{1055494516522092784614 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =4\right)^{-n +9}}{132542220237166367582119}+\frac{1055494516522092784614 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =5\right)^{-n +9}}{132542220237166367582119}+\frac{1055494516522092784614 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =6\right)^{-n +9}}{132542220237166367582119}+\frac{1055494516522092784614 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =7\right)^{-n +9}}{132542220237166367582119}+\frac{1055494516522092784614 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =8\right)^{-n +9}}{132542220237166367582119}+\frac{1055494516522092784614 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =9\right)^{-n +9}}{132542220237166367582119}+\frac{1055494516522092784614 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =10\right)^{-n +9}}{132542220237166367582119}+\frac{1055494516522092784614 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =11\right)^{-n +9}}{132542220237166367582119}-\frac{228560591535504506580 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =1\right)^{-n +8}}{12049292748833306143829}-\frac{228560591535504506580 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =2\right)^{-n +8}}{12049292748833306143829}-\frac{228560591535504506580 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =3\right)^{-n +8}}{12049292748833306143829}-\frac{228560591535504506580 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =4\right)^{-n +8}}{12049292748833306143829}-\frac{228560591535504506580 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =5\right)^{-n +8}}{12049292748833306143829}-\frac{228560591535504506580 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =6\right)^{-n +8}}{12049292748833306143829}-\frac{228560591535504506580 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =7\right)^{-n +8}}{12049292748833306143829}-\frac{228560591535504506580 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =8\right)^{-n +8}}{12049292748833306143829}-\frac{228560591535504506580 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =9\right)^{-n +8}}{12049292748833306143829}-\frac{228560591535504506580 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =10\right)^{-n +8}}{12049292748833306143829}-\frac{228560591535504506580 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =11\right)^{-n +8}}{12049292748833306143829}-\frac{38288506857387265873 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =1\right)^{-n +7}}{132542220237166367582119}-\frac{38288506857387265873 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =2\right)^{-n +7}}{132542220237166367582119}-\frac{38288506857387265873 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =3\right)^{-n +7}}{132542220237166367582119}-\frac{38288506857387265873 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =4\right)^{-n +7}}{132542220237166367582119}-\frac{38288506857387265873 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =5\right)^{-n +7}}{132542220237166367582119}-\frac{38288506857387265873 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =6\right)^{-n +7}}{132542220237166367582119}-\frac{38288506857387265873 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =7\right)^{-n +7}}{132542220237166367582119}-\frac{38288506857387265873 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =8\right)^{-n +7}}{132542220237166367582119}-\frac{38288506857387265873 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =9\right)^{-n +7}}{132542220237166367582119}-\frac{38288506857387265873 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =10\right)^{-n +7}}{132542220237166367582119}-\frac{38288506857387265873 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =11\right)^{-n +7}}{132542220237166367582119}+\frac{5489029391660671373080 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =1\right)^{-n +6}}{132542220237166367582119}+\frac{5489029391660671373080 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =2\right)^{-n +6}}{132542220237166367582119}+\frac{5489029391660671373080 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =3\right)^{-n +6}}{132542220237166367582119}+\frac{5489029391660671373080 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =4\right)^{-n +6}}{132542220237166367582119}+\frac{5489029391660671373080 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =5\right)^{-n +6}}{132542220237166367582119}+\frac{5489029391660671373080 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =6\right)^{-n +6}}{132542220237166367582119}+\frac{5489029391660671373080 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =7\right)^{-n +6}}{132542220237166367582119}+\frac{5489029391660671373080 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =8\right)^{-n +6}}{132542220237166367582119}+\frac{5489029391660671373080 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =9\right)^{-n +6}}{132542220237166367582119}+\frac{5489029391660671373080 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =10\right)^{-n +6}}{132542220237166367582119}+\frac{5489029391660671373080 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =11\right)^{-n +6}}{132542220237166367582119}-\frac{7042054926032733464047 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =1\right)^{-n +5}}{132542220237166367582119}-\frac{7042054926032733464047 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =2\right)^{-n +5}}{132542220237166367582119}-\frac{7042054926032733464047 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =3\right)^{-n +5}}{132542220237166367582119}-\frac{7042054926032733464047 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =4\right)^{-n +5}}{132542220237166367582119}-\frac{7042054926032733464047 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =5\right)^{-n +5}}{132542220237166367582119}-\frac{7042054926032733464047 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =6\right)^{-n +5}}{132542220237166367582119}-\frac{7042054926032733464047 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =7\right)^{-n +5}}{132542220237166367582119}-\frac{7042054926032733464047 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =8\right)^{-n +5}}{132542220237166367582119}-\frac{7042054926032733464047 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =9\right)^{-n +5}}{132542220237166367582119}-\frac{7042054926032733464047 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =10\right)^{-n +5}}{132542220237166367582119}-\frac{7042054926032733464047 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =11\right)^{-n +5}}{132542220237166367582119}+\frac{8199308629935038168430 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =1\right)^{-n +4}}{132542220237166367582119}+\frac{8199308629935038168430 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =2\right)^{-n +4}}{132542220237166367582119}+\frac{8199308629935038168430 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =3\right)^{-n 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+3}}{132542220237166367582119}+\frac{6487351935007053008498 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =3\right)^{-n +3}}{132542220237166367582119}+\frac{6487351935007053008498 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =4\right)^{-n +3}}{132542220237166367582119}+\frac{6487351935007053008498 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =5\right)^{-n +3}}{132542220237166367582119}+\frac{6487351935007053008498 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =6\right)^{-n +3}}{132542220237166367582119}+\frac{6487351935007053008498 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =7\right)^{-n +3}}{132542220237166367582119}+\frac{6487351935007053008498 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =8\right)^{-n +3}}{132542220237166367582119}+\frac{6487351935007053008498 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =9\right)^{-n +3}}{132542220237166367582119}+\frac{6487351935007053008498 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =10\right)^{-n +3}}{132542220237166367582119}+\frac{6487351935007053008498 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =11\right)^{-n +3}}{132542220237166367582119}+\frac{5370284572333289189951 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =1\right)^{-n +2}}{132542220237166367582119}+\frac{5370284572333289189951 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =2\right)^{-n +2}}{132542220237166367582119}+\frac{5370284572333289189951 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =3\right)^{-n +2}}{132542220237166367582119}+\frac{5370284572333289189951 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =4\right)^{-n +2}}{132542220237166367582119}+\frac{5370284572333289189951 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =5\right)^{-n +2}}{132542220237166367582119}+\frac{5370284572333289189951 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =6\right)^{-n +2}}{132542220237166367582119}+\frac{5370284572333289189951 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =7\right)^{-n +2}}{132542220237166367582119}+\frac{5370284572333289189951 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =8\right)^{-n +2}}{132542220237166367582119}+\frac{5370284572333289189951 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =9\right)^{-n +2}}{132542220237166367582119}+\frac{5370284572333289189951 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =10\right)^{-n +2}}{132542220237166367582119}+\frac{5370284572333289189951 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =11\right)^{-n +2}}{132542220237166367582119}+\frac{6714256973921379638392 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =1\right)^{-n +1}}{132542220237166367582119}+\frac{6714256973921379638392 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =2\right)^{-n +1}}{132542220237166367582119}+\frac{6714256973921379638392 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =3\right)^{-n +1}}{132542220237166367582119}+\frac{6714256973921379638392 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =4\right)^{-n +1}}{132542220237166367582119}+\frac{6714256973921379638392 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =5\right)^{-n +1}}{132542220237166367582119}+\frac{6714256973921379638392 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =6\right)^{-n +1}}{132542220237166367582119}+\frac{6714256973921379638392 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =7\right)^{-n +1}}{132542220237166367582119}+\frac{6714256973921379638392 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =8\right)^{-n +1}}{132542220237166367582119}+\frac{6714256973921379638392 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =9\right)^{-n +1}}{132542220237166367582119}+\frac{6714256973921379638392 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =10\right)^{-n +1}}{132542220237166367582119}+\frac{6714256973921379638392 \mathit{RootOf} \left(2 Z^{11}-6 Z^{10}+Z^{9}+15 Z^{8}-17 Z^{7}+9 Z^{6}+6 Z^{5}+11 Z^{4}-4 Z^{2}+4 Z -1, \mathit{index} =11\right)^{-n +1}}{132542220237166367582119}\)
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This specification was found using the strategy pack "Regular Insertion Encoding Bottom" and has 111 rules.

Finding the specification took 133 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_{33}\! \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_{16}\! \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_{14}\! \left(x \right)\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{18}\! \left(x \right) &= 0\\ F_{19}\! \left(x \right) &= F_{14}\! \left(x \right) F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{27}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{23}\! \left(x \right)+F_{25}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{14}\! \left(x \right) F_{24}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{14}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{14}\! \left(x \right) F_{26}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{15}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{14}\! \left(x \right) F_{30}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{22}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{28}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{34}\! \left(x \right)+F_{70}\! \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_{52}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{37}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{38}\! \left(x \right)+F_{44}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{14}\! \left(x \right) F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{14}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{41}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{14}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{47}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{41}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{10}\! \left(x \right) F_{14}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{14}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{54}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{34}\! \left(x \right)+F_{44}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{55}\! \left(x \right)+F_{61}\! \left(x \right)+F_{63}\! \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_{64}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{59}\! \left(x \right)+F_{61}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{14}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{41}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{14}\! \left(x \right) F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{43}\! \left(x \right)\\ F_{63}\! \left(x \right) &= 0\\ F_{64}\! \left(x \right) &= F_{54}\! \left(x \right)+F_{65}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{14}\! \left(x \right) F_{67}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)+F_{69}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{58}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{65}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{14}\! \left(x \right) F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)+F_{73}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)+F_{87}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{75}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{14}\! \left(x \right) F_{76}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{77}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{74}\! \left(x \right)+F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{29}\! \left(x \right)+F_{79}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{14}\! \left(x \right) F_{80}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{81}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{78}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{14}\! \left(x \right) F_{84}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{85}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{82}\! \left(x \right)\\ F_{86}\! \left(x \right) &= 0\\ F_{87}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{18}\! \left(x \right)+F_{55}\! \left(x \right)+F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{14}\! \left(x \right) F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{90}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)+F_{92}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{55}\! \left(x \right)+F_{63}\! \left(x \right)+F_{88}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{101}\! \left(x \right)+F_{18}\! \left(x \right)+F_{66}\! \left(x \right)+F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{14}\! \left(x \right) F_{94}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{64}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{92}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{14}\! \left(x \right) F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{99}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{96}\! \left(x \right)\\ F_{100}\! \left(x \right) &= 0\\ F_{101}\! \left(x \right) &= 0\\ 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_{48}\! \left(x \right)\\ F_{105}\! \left(x \right) &= F_{51}\! \left(x \right)\\ F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{109}\! \left(x \right)\\ F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)\\ F_{108}\! \left(x \right) &= F_{14}\! \left(x \right) F_{22}\! \left(x \right)\\ F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)\\ F_{110}\! \left(x \right) &= F_{14}\! \left(x \right) F_{58}\! \left(x \right)\\ \end{align*}\)