Av(12435, 12453, 12543, 14235, 14253, 14325, 14352, 14523, 14532, 15243, 15423, 15432, 21435, 21453, 21543, 24135, 24153, 41235, 41253, 41325, 41352, 41523, 41532, 42135, 42153)
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Generating Function
\(\displaystyle -\frac{\left(2 x -1\right) \left(x +1\right) \left(x^{2}+x -1\right) \left(x^{2}-3 x +1\right)^{2}}{2 x^{11}-3 x^{10}-33 x^{9}+21 x^{8}+23 x^{7}+20 x^{6}-64 x^{5}+22 x^{4}+29 x^{3}-28 x^{2}+9 x -1}\)
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Counting Sequence
1, 1, 2, 6, 24, 95, 359, 1305, 4678, 16681, 59432, 211727, 754259, 2686639, 9568421, ...
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Implicit Equation for the Generating Function
\(\displaystyle \left(2 x^{11}-3 x^{10}-33 x^{9}+21 x^{8}+23 x^{7}+20 x^{6}-64 x^{5}+22 x^{4}+29 x^{3}-28 x^{2}+9 x -1\right) F \! \left(x \right)+\left(2 x -1\right) \left(x +1\right) \left(x^{2}+x -1\right) \left(x^{2}-3 x +1\right)^{2} = 0\)
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Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 95\)
\(\displaystyle a(6) = 359\)
\(\displaystyle a(7) = 1305\)
\(\displaystyle a(8) = 4678\)
\(\displaystyle a(9) = 16681\)
\(\displaystyle a(10) = 59432\)
\(\displaystyle a{\left(n + 11 \right)} = 2 a{\left(n \right)} - 3 a{\left(n + 1 \right)} - 33 a{\left(n + 2 \right)} + 21 a{\left(n + 3 \right)} + 23 a{\left(n + 4 \right)} + 20 a{\left(n + 5 \right)} - 64 a{\left(n + 6 \right)} + 22 a{\left(n + 7 \right)} + 29 a{\left(n + 8 \right)} - 28 a{\left(n + 9 \right)} + 9 a{\left(n + 10 \right)}, \quad n \geq 11\)
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Explicit Closed Form
\(\displaystyle -\frac{67232386368790989182 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =1\right)^{-n +9}}{34776577476254551473663}-\frac{67232386368790989182 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =2\right)^{-n +9}}{34776577476254551473663}-\frac{67232386368790989182 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =3\right)^{-n +9}}{34776577476254551473663}-\frac{67232386368790989182 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =4\right)^{-n +9}}{34776577476254551473663}-\frac{67232386368790989182 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =5\right)^{-n +9}}{34776577476254551473663}-\frac{67232386368790989182 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =6\right)^{-n +9}}{34776577476254551473663}-\frac{67232386368790989182 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =7\right)^{-n +9}}{34776577476254551473663}-\frac{67232386368790989182 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =8\right)^{-n +9}}{34776577476254551473663}-\frac{67232386368790989182 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =9\right)^{-n +9}}{34776577476254551473663}-\frac{67232386368790989182 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =10\right)^{-n +9}}{34776577476254551473663}-\frac{67232386368790989182 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =11\right)^{-n +9}}{34776577476254551473663}-\frac{1493311543146371858555 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =1\right)^{-n +8}}{11592192492084850491221}-\frac{1493311543146371858555 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =2\right)^{-n +8}}{11592192492084850491221}-\frac{1493311543146371858555 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =3\right)^{-n +8}}{11592192492084850491221}-\frac{1493311543146371858555 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =4\right)^{-n +8}}{11592192492084850491221}-\frac{1493311543146371858555 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =5\right)^{-n +8}}{11592192492084850491221}-\frac{1493311543146371858555 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =6\right)^{-n +8}}{11592192492084850491221}-\frac{1493311543146371858555 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =7\right)^{-n +8}}{11592192492084850491221}-\frac{1493311543146371858555 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =8\right)^{-n +8}}{11592192492084850491221}-\frac{1493311543146371858555 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =9\right)^{-n +8}}{11592192492084850491221}-\frac{1493311543146371858555 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =10\right)^{-n +8}}{11592192492084850491221}-\frac{1493311543146371858555 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =11\right)^{-n +8}}{11592192492084850491221}+\frac{1309906661299992630808 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =1\right)^{-n +7}}{11592192492084850491221}+\frac{1309906661299992630808 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =2\right)^{-n +7}}{11592192492084850491221}+\frac{1309906661299992630808 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =3\right)^{-n +7}}{11592192492084850491221}+\frac{1309906661299992630808 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =4\right)^{-n +7}}{11592192492084850491221}+\frac{1309906661299992630808 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =5\right)^{-n +7}}{11592192492084850491221}+\frac{1309906661299992630808 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =6\right)^{-n +7}}{11592192492084850491221}+\frac{1309906661299992630808 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =7\right)^{-n +7}}{11592192492084850491221}+\frac{1309906661299992630808 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =8\right)^{-n +7}}{11592192492084850491221}+\frac{1309906661299992630808 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =9\right)^{-n +7}}{11592192492084850491221}+\frac{1309906661299992630808 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =10\right)^{-n +7}}{11592192492084850491221}+\frac{1309906661299992630808 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =11\right)^{-n +7}}{11592192492084850491221}+\frac{78705117872669700038008 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =1\right)^{-n +6}}{34776577476254551473663}+\frac{78705117872669700038008 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =2\right)^{-n +6}}{34776577476254551473663}+\frac{78705117872669700038008 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =3\right)^{-n +6}}{34776577476254551473663}+\frac{78705117872669700038008 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =4\right)^{-n +6}}{34776577476254551473663}+\frac{78705117872669700038008 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =5\right)^{-n +6}}{34776577476254551473663}+\frac{78705117872669700038008 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =6\right)^{-n +6}}{34776577476254551473663}+\frac{78705117872669700038008 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =7\right)^{-n +6}}{34776577476254551473663}+\frac{78705117872669700038008 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =8\right)^{-n +6}}{34776577476254551473663}+\frac{78705117872669700038008 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =9\right)^{-n +6}}{34776577476254551473663}+\frac{78705117872669700038008 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =10\right)^{-n +6}}{34776577476254551473663}+\frac{78705117872669700038008 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =11\right)^{-n +6}}{34776577476254551473663}-\frac{102690397115418918154813 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =1\right)^{-n +3}}{34776577476254551473663}-\frac{102690397115418918154813 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =2\right)^{-n +3}}{34776577476254551473663}-\frac{102690397115418918154813 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =3\right)^{-n +3}}{34776577476254551473663}-\frac{102690397115418918154813 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =4\right)^{-n +3}}{34776577476254551473663}-\frac{102690397115418918154813 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =5\right)^{-n +3}}{34776577476254551473663}-\frac{102690397115418918154813 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =6\right)^{-n +3}}{34776577476254551473663}-\frac{102690397115418918154813 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =7\right)^{-n +3}}{34776577476254551473663}-\frac{102690397115418918154813 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =8\right)^{-n +3}}{34776577476254551473663}-\frac{102690397115418918154813 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =9\right)^{-n +3}}{34776577476254551473663}-\frac{102690397115418918154813 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =10\right)^{-n +3}}{34776577476254551473663}-\frac{102690397115418918154813 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =11\right)^{-n +3}}{34776577476254551473663}+\frac{21860303915089563872247 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =1\right)^{-n +2}}{11592192492084850491221}+\frac{21860303915089563872247 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =2\right)^{-n +2}}{11592192492084850491221}+\frac{21860303915089563872247 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =3\right)^{-n +2}}{11592192492084850491221}+\frac{21860303915089563872247 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =4\right)^{-n +2}}{11592192492084850491221}+\frac{21860303915089563872247 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =5\right)^{-n +2}}{11592192492084850491221}+\frac{21860303915089563872247 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =6\right)^{-n +2}}{11592192492084850491221}+\frac{21860303915089563872247 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =7\right)^{-n +2}}{11592192492084850491221}+\frac{21860303915089563872247 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =8\right)^{-n +2}}{11592192492084850491221}+\frac{21860303915089563872247 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =9\right)^{-n +2}}{11592192492084850491221}+\frac{21860303915089563872247 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =10\right)^{-n +2}}{11592192492084850491221}+\frac{21860303915089563872247 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =11\right)^{-n +2}}{11592192492084850491221}+\frac{20675141565257312982655 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =1\right)^{-n +5}}{34776577476254551473663}+\frac{20675141565257312982655 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =2\right)^{-n +5}}{34776577476254551473663}+\frac{20675141565257312982655 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =3\right)^{-n +5}}{34776577476254551473663}+\frac{20675141565257312982655 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =4\right)^{-n +5}}{34776577476254551473663}+\frac{20675141565257312982655 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =5\right)^{-n 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Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =4\right)^{-n +4}}{34776577476254551473663}-\frac{57411730984020716171540 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =5\right)^{-n +4}}{34776577476254551473663}-\frac{57411730984020716171540 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =6\right)^{-n +4}}{34776577476254551473663}-\frac{57411730984020716171540 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =7\right)^{-n +4}}{34776577476254551473663}-\frac{57411730984020716171540 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =8\right)^{-n 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Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =7\right)^{-n +1}}{34776577476254551473663}+\frac{39082144107977402291285 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =8\right)^{-n +1}}{34776577476254551473663}+\frac{39082144107977402291285 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =9\right)^{-n +1}}{34776577476254551473663}+\frac{39082144107977402291285 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =10\right)^{-n +1}}{34776577476254551473663}+\frac{39082144107977402291285 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =11\right)^{-n +1}}{34776577476254551473663}+\frac{3310586748277873273562 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-1}}{11592192492084850491221}+\frac{3310586748277873273562 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =6\right)^{-n -1}}{11592192492084850491221}+\frac{3310586748277873273562 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =7\right)^{-n -1}}{11592192492084850491221}+\frac{3310586748277873273562 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =8\right)^{-n -1}}{11592192492084850491221}+\frac{3310586748277873273562 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =9\right)^{-n -1}}{11592192492084850491221}+\frac{3310586748277873273562 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =10\right)^{-n -1}}{11592192492084850491221}+\frac{3310586748277873273562 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =11\right)^{-n -1}}{11592192492084850491221}-\frac{14211615375838688236788 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =1\right)^{-n}}{11592192492084850491221}-\frac{14211615375838688236788 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =2\right)^{-n}}{11592192492084850491221}-\frac{14211615375838688236788 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =3\right)^{-n}}{11592192492084850491221}-\frac{14211615375838688236788 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =4\right)^{-n}}{11592192492084850491221}-\frac{14211615375838688236788 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =5\right)^{-n}}{11592192492084850491221}-\frac{14211615375838688236788 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =6\right)^{-n}}{11592192492084850491221}-\frac{14211615375838688236788 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =7\right)^{-n}}{11592192492084850491221}-\frac{14211615375838688236788 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =8\right)^{-n}}{11592192492084850491221}-\frac{14211615375838688236788 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =9\right)^{-n}}{11592192492084850491221}-\frac{14211615375838688236788 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =10\right)^{-n}}{11592192492084850491221}-\frac{14211615375838688236788 \mathit{RootOf} \left(2 Z^{11}-3 Z^{10}-33 Z^{9}+21 Z^{8}+23 Z^{7}+20 Z^{6}-64 Z^{5}+22 Z^{4}+29 Z^{3}-28 Z^{2}+9 Z -1, \mathit{index} =11\right)^{-n}}{11592192492084850491221}\)
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This specification was found using the strategy pack "Regular Insertion Encoding Left" and has 104 rules.

Finding the specification took 113 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_{15}\! \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_{22}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{15}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{13}\! \left(x \right)+F_{16}\! \left(x \right)\\ F_{12}\! \left(x \right) &= 0\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{6}\! \left(x \right)\\ F_{15}\! \left(x \right) &= x\\ F_{16}\! \left(x \right) &= F_{15}\! \left(x \right) F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{19}\! \left(x \right)\\ F_{18}\! \left(x \right) &= F_{15}\! \left(x \right)\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{16}\! \left(x \right)+F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{15}\! \left(x \right) F_{6}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{23}\! \left(x \right)+F_{92}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{15}\! \left(x \right) F_{24}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{22}\! \left(x \right)\\ F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{70}\! \left(x \right)\\ F_{27}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{28}\! \left(x \right)+F_{67}\! \left(x \right)\\ F_{28}\! \left(x \right) &= F_{15}\! \left(x \right) F_{29}\! \left(x \right)\\ F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{31}\! \left(x \right)\\ F_{30}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{27}\! \left(x \right)\\ F_{31}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{33}\! \left(x \right)+F_{35}\! \left(x \right)+F_{64}\! \left(x \right)\\ F_{33}\! \left(x \right) &= F_{15}\! \left(x \right) F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= F_{27}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{15}\! \left(x \right) F_{36}\! \left(x \right)\\ F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{44}\! \left(x \right)\\ F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{39}\! \left(x \right)+F_{40}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{15}\! \left(x \right) F_{2}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{15}\! \left(x \right) F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{39}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{35}\! \left(x \right)+F_{46}\! \left(x \right)+F_{47}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{15}\! \left(x \right) F_{27}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{15}\! \left(x \right) F_{48}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= 2 F_{12}\! \left(x \right)+F_{51}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{15}\! \left(x \right) F_{52}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{15}\! \left(x \right) F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)+F_{56}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{52}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{57}\! \left(x \right) &= 2 F_{12}\! \left(x \right)+F_{58}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{15}\! \left(x \right) F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{52}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{15}\! \left(x \right) F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)+F_{63}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{43}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{50}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{15}\! \left(x \right) F_{65}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{67}\! \left(x \right) &= F_{15}\! \left(x \right) F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{71}\! \left(x \right)+F_{73}\! \left(x \right)+F_{77}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{15}\! \left(x \right) F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{22}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{15}\! \left(x \right) F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{75}\! \left(x \right) &= F_{38}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{45}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{15}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{80}\! \left(x \right)\\ F_{80}\! \left(x \right) &= 2 F_{12}\! \left(x \right)+F_{81}\! \left(x \right)+F_{88}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{15}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{40}\! \left(x \right)+F_{84}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{15}\! \left(x \right) F_{85}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)+F_{87}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{80}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{15}\! \left(x \right) F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{43}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{50}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{15}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)+F_{95}\! \left(x \right)\\ F_{94}\! \left(x \right) &= F_{6}\! \left(x \right)+F_{83}\! \left(x \right)\\ F_{95}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{96}\! \left(x \right)\\ F_{96}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{73}\! \left(x \right)+F_{97}\! \left(x \right)+F_{99}\! \left(x \right)\\ F_{97}\! \left(x \right) &= F_{15}\! \left(x \right) F_{98}\! \left(x \right)\\ F_{98}\! \left(x \right) &= F_{22}\! \left(x \right)\\ F_{99}\! \left(x \right) &= F_{100}\! \left(x \right) F_{15}\! \left(x \right)\\ F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)\\ F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{20}\! \left(x \right)\\ F_{102}\! \left(x \right) &= 2 F_{12}\! \left(x \right)+F_{103}\! \left(x \right)+F_{88}\! \left(x \right)\\ F_{103}\! \left(x \right) &= F_{15}\! \left(x \right) F_{83}\! \left(x \right)\\ \end{align*}\)