Av(12354, 13254, 21354, 23154, 23514, 31254, 32154, 32514)
Counting Sequence
1, 1, 2, 6, 24, 112, 568, 3028, 16684, 94108, 540220, 3143716, 18495860, 109804748, 656833516, ...
Implicit Equation for the Generating Function
\(\displaystyle F \left(x
\right)^{4}+\left(2 x^{2}-x -5\right) F \left(x
\right)^{3}+\left(6 x^{3}-13 x^{2}+7 x +9\right) F \left(x
\right)^{2}+\left(-5 x^{3}+15 x^{2}-11 x -7\right) F \! \left(x \right)+x^{3}-4 x^{2}+5 x +2 = 0\)
Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 112\)
\(\displaystyle a(6) = 568\)
\(\displaystyle a(7) = 3028\)
\(\displaystyle a(8) = 16684\)
\(\displaystyle a(9) = 94108\)
\(\displaystyle a(10) = 540220\)
\(\displaystyle a(11) = 3143716\)
\(\displaystyle a(12) = 18495860\)
\(\displaystyle a(13) = 109804748\)
\(\displaystyle a(14) = 656833516\)
\(\displaystyle a(15) = 3954548404\)
\(\displaystyle a{\left(n + 16 \right)} = - \frac{3888 n \left(n - 2\right) \left(n - 1\right) a{\left(n \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{432 n \left(n - 1\right) \left(263 n + 284\right) a{\left(n + 1 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} - \frac{72 n \left(17081 n^{2} + 48989 n + 30852\right) a{\left(n + 2 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{11 \left(5 n + 68\right) a{\left(n + 15 \right)}}{n + 16} - \frac{\left(949 n^{2} + 25405 n + 169548\right) a{\left(n + 14 \right)}}{\left(n + 15\right) \left(n + 16\right)} + \frac{\left(947 n^{3} + 68187 n^{2} + 1247248 n + 6772704\right) a{\left(n + 13 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{3 \left(55053 n^{3} + 1699075 n^{2} + 17295196 n + 57989872\right) a{\left(n + 12 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{24 \left(264784 n^{3} + 1436297 n^{2} + 2426893 n + 1255902\right) a{\left(n + 3 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} - \frac{3 \left(776913 n^{3} + 22648409 n^{2} + 219096974 n + 703443040\right) a{\left(n + 11 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{12 \left(1225132 n^{3} + 8633313 n^{2} + 13205959 n - 5474884\right) a{\left(n + 5 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} - \frac{12 \left(1348919 n^{3} + 10200551 n^{2} + 25136474 n + 20250164\right) a{\left(n + 4 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{6 \left(4315071 n^{3} + 86386017 n^{2} + 529773610 n + 1020351820\right) a{\left(n + 6 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{\left(15354911 n^{3} + 409446561 n^{2} + 3627823594 n + 10683287184\right) a{\left(n + 10 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} - \frac{4 \left(22222414 n^{3} + 431906652 n^{2} + 2767672229 n + 5843547774\right) a{\left(n + 7 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{2 \left(51986113 n^{3} + 1118463078 n^{2} + 7994045393 n + 18974233176\right) a{\left(n + 8 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} - \frac{\left(55019999 n^{3} + 1323166683 n^{2} + 10578047320 n + 28115446560\right) a{\left(n + 9 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)}, \quad n \geq 16\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 112\)
\(\displaystyle a(6) = 568\)
\(\displaystyle a(7) = 3028\)
\(\displaystyle a(8) = 16684\)
\(\displaystyle a(9) = 94108\)
\(\displaystyle a(10) = 540220\)
\(\displaystyle a(11) = 3143716\)
\(\displaystyle a(12) = 18495860\)
\(\displaystyle a(13) = 109804748\)
\(\displaystyle a(14) = 656833516\)
\(\displaystyle a(15) = 3954548404\)
\(\displaystyle a{\left(n + 16 \right)} = - \frac{3888 n \left(n - 2\right) \left(n - 1\right) a{\left(n \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{432 n \left(n - 1\right) \left(263 n + 284\right) a{\left(n + 1 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} - \frac{72 n \left(17081 n^{2} + 48989 n + 30852\right) a{\left(n + 2 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{11 \left(5 n + 68\right) a{\left(n + 15 \right)}}{n + 16} - \frac{\left(949 n^{2} + 25405 n + 169548\right) a{\left(n + 14 \right)}}{\left(n + 15\right) \left(n + 16\right)} + \frac{\left(947 n^{3} + 68187 n^{2} + 1247248 n + 6772704\right) a{\left(n + 13 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{3 \left(55053 n^{3} + 1699075 n^{2} + 17295196 n + 57989872\right) a{\left(n + 12 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{24 \left(264784 n^{3} + 1436297 n^{2} + 2426893 n + 1255902\right) a{\left(n + 3 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} - \frac{3 \left(776913 n^{3} + 22648409 n^{2} + 219096974 n + 703443040\right) a{\left(n + 11 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{12 \left(1225132 n^{3} + 8633313 n^{2} + 13205959 n - 5474884\right) a{\left(n + 5 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} - \frac{12 \left(1348919 n^{3} + 10200551 n^{2} + 25136474 n + 20250164\right) a{\left(n + 4 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{6 \left(4315071 n^{3} + 86386017 n^{2} + 529773610 n + 1020351820\right) a{\left(n + 6 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{\left(15354911 n^{3} + 409446561 n^{2} + 3627823594 n + 10683287184\right) a{\left(n + 10 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} - \frac{4 \left(22222414 n^{3} + 431906652 n^{2} + 2767672229 n + 5843547774\right) a{\left(n + 7 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} + \frac{2 \left(51986113 n^{3} + 1118463078 n^{2} + 7994045393 n + 18974233176\right) a{\left(n + 8 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)} - \frac{\left(55019999 n^{3} + 1323166683 n^{2} + 10578047320 n + 28115446560\right) a{\left(n + 9 \right)}}{\left(n + 14\right) \left(n + 15\right) \left(n + 16\right)}, \quad n \geq 16\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 130 rules.
Finding the specification took 3238 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_{16}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2\\
F_{6}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{7}\! \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_{10}\! \left(x \right)+F_{126}\! \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_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{82}\! \left(x \right)\\
F_{13}\! \left(x \right) &= -F_{17}\! \left(x \right)+F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= \frac{F_{15}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{15}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{16}\! \left(x \right) &= x\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= \frac{F_{19}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{16}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{16}\! \left(x \right) F_{23}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{23}\! \left(x \right) &= \frac{F_{24}\! \left(x \right)}{F_{16}\! \left(x \right) F_{79}\! \left(x \right)}\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= -F_{116}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= \frac{F_{27}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= -F_{108}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{16}\! \left(x \right) F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{16}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{36}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{16}\! \left(x \right) F_{43}\! \left(x \right) F_{79}\! \left(x \right)\\
F_{43}\! \left(x \right) &= -F_{55}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= -F_{50}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= \frac{F_{46}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= \frac{F_{49}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{49}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{50}\! \left(x \right) &= -F_{55}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= \frac{F_{52}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= -F_{54}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{54}\! \left(x \right) x +F_{54} \left(x \right)^{2}+x\\
F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{16}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{48}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{16}\! \left(x \right) F_{5}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{5}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{16}\! \left(x \right) F_{59}\! \left(x \right) F_{65}\! \left(x \right) F_{76}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{16}\! \left(x \right) F_{5}\! \left(x \right) F_{65}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{16}\! \left(x \right) F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{16}\! \left(x \right) F_{71}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{16}\! \left(x \right) F_{68}\! \left(x \right) F_{70}\! \left(x \right) F_{71}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{71}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{16}\! \left(x \right) F_{68}\! \left(x \right) F_{71}\! \left(x \right) F_{76}\! \left(x \right)\\
F_{79}\! \left(x \right) &= \frac{F_{80}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= -F_{89}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= -F_{86}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= \frac{F_{85}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{85}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{86}\! \left(x \right) &= -F_{89}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= \frac{F_{88}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{88}\! \left(x \right) &= F_{53}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{2}\! \left(x \right) F_{71}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{16}\! \left(x \right) F_{74}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{16}\! \left(x \right) F_{79}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{16}\! \left(x \right) F_{79}\! \left(x \right) F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{2}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right) F_{103}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{54}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{103}\! \left(x \right) &= \frac{F_{104}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)\\
F_{105}\! \left(x \right) &= -F_{98}\! \left(x \right)+F_{106}\! \left(x \right)\\
F_{106}\! \left(x \right) &= \frac{F_{107}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{107}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{111}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{2}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{102}\! \left(x \right) F_{113}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{113}\! \left(x \right) &= \frac{F_{114}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{118}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{108}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right) F_{16}\! \left(x \right) F_{79}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{122}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{0}\! \left(x \right) F_{43}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right) F_{16}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{124}\! \left(x \right) &= \frac{F_{125}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{125}\! \left(x \right) &= F_{13}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)+F_{128}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{16}\! \left(x \right) F_{21}\! \left(x \right) F_{82}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 129 rules.
Finding the specification took 1648 seconds.
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Copy 129 equations to clipboard:
\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{16}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2\\
F_{6}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{7}\! \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_{10}\! \left(x \right)+F_{126}\! \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_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{83}\! \left(x \right)\\
F_{13}\! \left(x \right) &= -F_{17}\! \left(x \right)+F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= \frac{F_{15}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{15}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{16}\! \left(x \right) &= x\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= \frac{F_{19}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{16}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{16}\! \left(x \right) F_{23}\! \left(x \right) F_{69}\! \left(x \right)\\
F_{23}\! \left(x \right) &= \frac{F_{24}\! \left(x \right)}{F_{16}\! \left(x \right) F_{80}\! \left(x \right)}\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= -F_{116}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= \frac{F_{27}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= -F_{109}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{16}\! \left(x \right) F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{16}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{36}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{16}\! \left(x \right) F_{43}\! \left(x \right) F_{80}\! \left(x \right)\\
F_{43}\! \left(x \right) &= -F_{56}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= -F_{53}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= \frac{F_{46}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{48}\! \left(x \right) x +F_{48} \left(x \right)^{2}+x\\
F_{49}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= \frac{F_{52}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{52}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{53}\! \left(x \right) &= -F_{56}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= \frac{F_{55}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{55}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{16}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{51}\! \left(x \right) F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{16}\! \left(x \right) F_{5}\! \left(x \right) F_{60}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{5}\! \left(x \right) F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{16}\! \left(x \right) F_{60}\! \left(x \right) F_{66}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{16}\! \left(x \right) F_{5}\! \left(x \right) F_{66}\! \left(x \right) F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{16}\! \left(x \right) F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{16}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{16}\! \left(x \right) F_{69}\! \left(x \right) F_{71}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{72}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{16}\! \left(x \right) F_{69}\! \left(x \right) F_{72}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{80}\! \left(x \right) &= \frac{F_{81}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= -F_{90}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= -F_{87}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= \frac{F_{86}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{86}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{87}\! \left(x \right) &= -F_{90}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= \frac{F_{89}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{89}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{2}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{16}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{16}\! \left(x \right) F_{80}\! \left(x \right) F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{16}\! \left(x \right) F_{80}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{101}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{2}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right) F_{104}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{104}\! \left(x \right) &= \frac{F_{105}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\
F_{106}\! \left(x \right) &= -F_{99}\! \left(x \right)+F_{107}\! \left(x \right)\\
F_{107}\! \left(x \right) &= \frac{F_{108}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{108}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{111}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{0}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{103}\! \left(x \right) F_{114}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{114}\! \left(x \right) &= \frac{F_{115}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{115}\! \left(x \right) &= F_{50}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{118}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{109}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right) F_{16}\! \left(x \right) F_{80}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{122}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{0}\! \left(x \right) F_{43}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right) F_{16}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{124}\! \left(x \right) &= \frac{F_{125}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{125}\! \left(x \right) &= F_{13}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{127}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{16}\! \left(x \right) F_{21}\! \left(x \right) F_{83}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 109 rules.
Finding the specification took 4056 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_{16}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2\\
F_{6}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{7}\! \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_{10}\! \left(x \right)+F_{106}\! \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_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{13}\! \left(x \right) &= -F_{17}\! \left(x \right)+F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= \frac{F_{15}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{15}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{16}\! \left(x \right) &= x\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= \frac{F_{19}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{16}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{16}\! \left(x \right) F_{23}\! \left(x \right) F_{70}\! \left(x \right)\\
F_{23}\! \left(x \right) &= \frac{F_{24}\! \left(x \right)}{F_{16}\! \left(x \right) F_{45}\! \left(x \right)}\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= -F_{96}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= \frac{F_{27}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= -F_{89}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{16}\! \left(x \right) F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{72}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{16}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{37}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{16}\! \left(x \right) F_{44}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= \frac{F_{46}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= -F_{61}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= -F_{58}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= \frac{F_{51}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{51}\! \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_{53}\! \left(x \right) x +F_{53} \left(x \right)^{2}+x\\
F_{54}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= \frac{F_{57}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{57}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{58}\! \left(x \right) &= -F_{61}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= \frac{F_{60}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{60}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{2}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{16}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{16}\! \left(x \right) F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{16}\! \left(x \right) F_{63}\! \left(x \right) F_{69}\! \left(x \right) F_{70}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{63}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{16}\! \left(x \right) F_{69}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{16}\! \left(x \right) F_{45}\! \left(x \right) F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{16}\! \left(x \right) F_{45}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{2}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{16}\! \left(x \right) F_{83}\! \left(x \right) F_{84}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{84}\! \left(x \right) &= \frac{F_{85}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= -F_{79}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= \frac{F_{88}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{88}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{0}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{6}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{16}\! \left(x \right) F_{83}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= \frac{F_{95}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{95}\! \left(x \right) &= F_{55}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{36}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right) F_{16}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{102}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{0}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right) F_{16}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{104}\! \left(x \right) &= \frac{F_{105}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{105}\! \left(x \right) &= F_{13}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{16}\! \left(x \right) F_{21}\! \left(x \right) F_{48}\! \left(x \right)\\
\end{align*}\)