Av(12354, 12453, 12543, 13254, 21354, 21453, 21543)
Counting Sequence
1, 1, 2, 6, 24, 113, 582, 3164, 17838, 103276, 610304, 3665958, 22316734, 137375886, 853661444, ...
Implicit Equation for the Generating Function
\(\displaystyle \left(3 x -2\right) F \left(x
\right)^{4}+\left(-6 x +4\right) F \left(x
\right)^{3}+2 x F \left(x
\right)^{2}-3 F \! \left(x \right)+1 = 0\)
Recurrence
\(\displaystyle a(0) = 1\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 113\)
\(\displaystyle a(6) = 582\)
\(\displaystyle a(7) = 3164\)
\(\displaystyle a(8) = 17838\)
\(\displaystyle a{\left(n + 9 \right)} = \frac{192 n \left(n + 1\right) \left(2 n + 1\right) a{\left(n \right)}}{407 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)} - \frac{16 \left(n + 1\right) \left(230 n^{2} + 1174 n + 1257\right) a{\left(n + 1 \right)}}{407 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)} + \frac{3 \left(12405 n + 89393\right) a{\left(n + 8 \right)}}{3256 \left(n + 9\right)} - \frac{\left(134687 n^{2} + 1707842 n + 5457366\right) a{\left(n + 7 \right)}}{3256 \left(n + 8\right) \left(n + 9\right)} - \frac{16 \left(1231 n^{3} + 6990 n^{2} + 13499 n + 8859\right) a{\left(n + 2 \right)}}{1221 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)} + \frac{\left(3617 n^{3} + 98316 n^{2} + 572425 n + 929190\right) a{\left(n + 3 \right)}}{1221 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)} + \frac{\left(223387 n^{3} + 2190678 n^{2} + 6755264 n + 6261150\right) a{\left(n + 4 \right)}}{2442 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)} - \frac{\left(418159 n^{3} + 5275516 n^{2} + 21635794 n + 28540429\right) a{\left(n + 5 \right)}}{3256 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)} + \frac{\left(3441661 n^{3} + 55226586 n^{2} + 294989687 n + 525100746\right) a{\left(n + 6 \right)}}{39072 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)}, \quad n \geq 9\)
\(\displaystyle a(1) = 1\)
\(\displaystyle a(2) = 2\)
\(\displaystyle a(3) = 6\)
\(\displaystyle a(4) = 24\)
\(\displaystyle a(5) = 113\)
\(\displaystyle a(6) = 582\)
\(\displaystyle a(7) = 3164\)
\(\displaystyle a(8) = 17838\)
\(\displaystyle a{\left(n + 9 \right)} = \frac{192 n \left(n + 1\right) \left(2 n + 1\right) a{\left(n \right)}}{407 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)} - \frac{16 \left(n + 1\right) \left(230 n^{2} + 1174 n + 1257\right) a{\left(n + 1 \right)}}{407 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)} + \frac{3 \left(12405 n + 89393\right) a{\left(n + 8 \right)}}{3256 \left(n + 9\right)} - \frac{\left(134687 n^{2} + 1707842 n + 5457366\right) a{\left(n + 7 \right)}}{3256 \left(n + 8\right) \left(n + 9\right)} - \frac{16 \left(1231 n^{3} + 6990 n^{2} + 13499 n + 8859\right) a{\left(n + 2 \right)}}{1221 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)} + \frac{\left(3617 n^{3} + 98316 n^{2} + 572425 n + 929190\right) a{\left(n + 3 \right)}}{1221 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)} + \frac{\left(223387 n^{3} + 2190678 n^{2} + 6755264 n + 6261150\right) a{\left(n + 4 \right)}}{2442 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)} - \frac{\left(418159 n^{3} + 5275516 n^{2} + 21635794 n + 28540429\right) a{\left(n + 5 \right)}}{3256 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)} + \frac{\left(3441661 n^{3} + 55226586 n^{2} + 294989687 n + 525100746\right) a{\left(n + 6 \right)}}{39072 \left(n + 7\right) \left(n + 8\right) \left(n + 9\right)}, \quad n \geq 9\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 158 rules.
Finding the specification took 46661 seconds.
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Copy 158 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_{20}\! \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_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{20}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{156}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{14}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{0}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right) F_{20}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{18}\! \left(x \right) &= \frac{F_{19}\! \left(x \right)}{F_{20}\! \left(x \right)}\\
F_{19}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{20}\! \left(x \right) &= x\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{16}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{17}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{20}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= \frac{F_{29}\! \left(x \right)}{F_{18}\! \left(x \right) F_{20}\! \left(x \right)}\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= -F_{35}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= \frac{F_{32}\! \left(x \right)}{F_{20}\! \left(x \right)}\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{2}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{20}\! \left(x \right) F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{28}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= -F_{50}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= \frac{F_{42}\! \left(x \right)}{F_{20}\! \left(x \right)}\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= -F_{44}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{18}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{20}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{45}\! \left(x \right)\\
F_{51}\! \left(x \right) &= \frac{F_{52}\! \left(x \right)}{F_{20}\! \left(x \right)}\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= -F_{14}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{154}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{20}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= -F_{152}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= \frac{F_{59}\! \left(x \right)}{F_{20}\! \left(x \right)}\\
F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{20}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{150}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{19}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{20}\! \left(x \right) F_{68}\! \left(x \right) F_{76}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{20}\! \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_{1}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{20}\! \left(x \right) F_{69}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{149}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= -F_{140}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= \frac{F_{80}\! \left(x \right)}{F_{20}\! \left(x \right)}\\
F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= -F_{84}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= \frac{F_{83}\! \left(x \right)}{F_{20}\! \left(x \right)}\\
F_{83}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{122}\! \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_{0}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{20}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{4}\! \left(x \right) F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= \frac{F_{95}\! \left(x \right)}{F_{20}\! \left(x \right)}\\
F_{95}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{18}\! \left(x \right) F_{20}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= \frac{F_{99}\! \left(x \right)}{F_{105}\! \left(x \right) F_{20}\! \left(x \right)}\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)\\
F_{100}\! \left(x \right) &= -F_{103}\! \left(x \right)+F_{101}\! \left(x \right)\\
F_{101}\! \left(x \right) &= \frac{F_{102}\! \left(x \right)}{F_{20}\! \left(x \right)}\\
F_{102}\! \left(x \right) &= F_{92}\! \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_{2}\! \left(x \right)\\
F_{105}\! \left(x \right) &= x^{2} F_{105} \left(x \right)^{3}-x^{2} F_{105} \left(x \right)^{2}+x F_{105} \left(x \right)^{2}+1\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{118}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{111}\! \left(x \right) &= -F_{117}\! \left(x \right)+F_{112}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{115}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{116}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{112}\! \left(x \right)\\
F_{117}\! \left(x \right) &= x^{2} F_{117} \left(x \right)^{3}+2 x^{2} F_{117} \left(x \right)^{2}+x^{2} F_{117}\! \left(x \right)+x F_{117} \left(x \right)^{2}+2 x F_{117}\! \left(x \right)+x\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right) F_{20}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{120}\! \left(x \right) &= \frac{F_{121}\! \left(x \right)}{F_{20}\! \left(x \right)}\\
F_{121}\! \left(x \right) &= F_{110}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{129}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{126}\! \left(x \right) &= \frac{F_{127}\! \left(x \right)}{F_{20}\! \left(x \right)}\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)\\
F_{128}\! \left(x \right) &= -F_{117}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{136}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{132}\! \left(x \right) F_{134}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{117}\! \left(x \right)+F_{133}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{134}\! \left(x \right) &= \frac{F_{135}\! \left(x \right)}{F_{20}\! \left(x \right)}\\
F_{135}\! \left(x \right) &= F_{78}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{134}\! \left(x \right) F_{138}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{141}\! \left(x \right) &= \frac{F_{142}\! \left(x \right)}{F_{0}\! \left(x \right)}\\
F_{142}\! \left(x \right) &= -F_{145}\! \left(x \right)+F_{143}\! \left(x \right)\\
F_{143}\! \left(x \right) &= \frac{F_{144}\! \left(x \right)}{F_{20}\! \left(x \right)}\\
F_{144}\! \left(x \right) &= F_{112}\! \left(x \right)\\
F_{145}\! \left(x \right) &= -F_{148}\! \left(x \right)+F_{146}\! \left(x \right)\\
F_{146}\! \left(x \right) &= \frac{F_{147}\! \left(x \right)}{F_{20}\! \left(x \right)}\\
F_{147}\! \left(x \right) &= F_{111}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{141}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{20}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{134}\! \left(x \right) F_{18}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{153}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{23}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{155}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{20}\! \left(x \right) F_{23}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{157}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{16}\! \left(x \right) F_{20}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 166 rules.
Finding the specification took 17716 seconds.
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Copy 166 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_{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_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{14}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{15}\! \left(x \right)\\
F_{12}\! \left(x \right) &= \frac{F_{13}\! \left(x \right)}{F_{14}\! \left(x \right)}\\
F_{13}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{14}\! \left(x \right) &= x\\
F_{15}\! \left(x \right) &= F_{13}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{14}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{164}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{0}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{14}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= -F_{70}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= \frac{F_{27}\! \left(x \right)}{F_{14}\! \left(x \right)}\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= -F_{29}\! \left(x \right)+F_{12}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{31}\! \left(x \right) &= x^{2} F_{31} \left(x \right)^{3}-x^{2} F_{31} \left(x \right)^{2}+x F_{31} \left(x \right)^{2}+1\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{14}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= \frac{F_{35}\! \left(x \right)}{F_{14}\! \left(x \right)}\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= -F_{31}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{14}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{2}\! \left(x \right) F_{31}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{14}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{36}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= \frac{F_{49}\! \left(x \right)}{F_{14}\! \left(x \right)}\\
F_{49}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{14}\! \left(x \right) F_{34}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= \frac{F_{53}\! \left(x \right)}{F_{14}\! \left(x \right) F_{31}\! \left(x \right)}\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= -F_{42}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= \frac{F_{56}\! \left(x \right)}{F_{14}\! \left(x \right)}\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)\\
F_{57}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{48}\! \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_{14}\! \left(x \right) F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{14}\! \left(x \right) F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{14}\! \left(x \right) F_{64}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{14}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{60}\! \left(x \right)+F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{73}\! \left(x \right) &= x^{2} F_{73} \left(x \right)^{3}+2 x^{2} F_{73} \left(x \right)^{2}+x^{2} F_{73}\! \left(x \right)+x F_{73} \left(x \right)^{2}+2 x F_{73}\! \left(x \right)+x\\
F_{74}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{14}\! \left(x \right) F_{64}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{14}\! \left(x \right) F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= \frac{F_{81}\! \left(x \right)}{F_{14}\! \left(x \right) F_{85}\! \left(x \right)}\\
F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{14}\! \left(x \right) F_{77}\! \left(x \right) F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= \frac{F_{86}\! \left(x \right)}{F_{0}\! \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_{14}\! \left(x \right)}\\
F_{88}\! \left(x \right) &= F_{38}\! \left(x \right)\\
F_{89}\! \left(x \right) &= -F_{93}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= \frac{F_{91}\! \left(x \right)}{F_{14}\! \left(x \right)}\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{2}\! \left(x \right) F_{85}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{14}\! \left(x \right) F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{14}\! \left(x \right) F_{52}\! \left(x \right) F_{85}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right) F_{14}\! \left(x \right) F_{85}\! \left(x \right)\\
F_{101}\! \left(x \right) &= \frac{F_{102}\! \left(x \right)}{F_{14}\! \left(x \right)}\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\
F_{103}\! \left(x \right) &= -F_{132}\! \left(x \right)+F_{104}\! \left(x \right)\\
F_{104}\! \left(x \right) &= \frac{F_{105}\! \left(x \right)}{F_{14}\! \left(x \right)}\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\
F_{106}\! \left(x \right) &= -F_{110}\! \left(x \right)+F_{107}\! \left(x \right)\\
F_{107}\! \left(x \right) &= \frac{F_{108}\! \left(x \right)}{F_{14}\! \left(x \right)}\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{119}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{113}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{0}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{117}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{4}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{12}\! \left(x \right) F_{14}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{125}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{123}\! \left(x \right) &= \frac{F_{124}\! \left(x \right)}{F_{14}\! \left(x \right)}\\
F_{124}\! \left(x \right) &= F_{74}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{129}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{101}\! \left(x \right) F_{128}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{101}\! \left(x \right) F_{131}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{77}\! \left(x \right) F_{85}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{135}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)+F_{137}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{25}\! \left(x \right) F_{80}\! \left(x \right)\\
F_{137}\! \left(x \right) &= \frac{F_{138}\! \left(x \right)}{F_{14}\! \left(x \right)}\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{14}\! \left(x \right) F_{140}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)\\
F_{141}\! \left(x \right) &= -F_{163}\! \left(x \right)+F_{142}\! \left(x \right)\\
F_{142}\! \left(x \right) &= \frac{F_{143}\! \left(x \right)}{F_{14}\! \left(x \right)}\\
F_{143}\! \left(x \right) &= F_{144}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{14}\! \left(x \right) F_{145}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{146}\! \left(x \right)+F_{161}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{11}\! \left(x \right) F_{147}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{148}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{14}\! \left(x \right) F_{150}\! \left(x \right) F_{158}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{151}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{152}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{14}\! \left(x \right) F_{153}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{154}\! \left(x \right)+F_{155}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{151}\! \left(x \right)+F_{156}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{157}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{14}\! \left(x \right) F_{151}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{159}\! \left(x \right)+F_{160}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{14}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{162}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{101}\! \left(x \right) F_{12}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{64}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{14}\! \left(x \right) F_{154}\! \left(x \right) F_{64}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 80 rules.
Finding the specification took 759 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_{12}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{12}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x , 1\right)\\
F_{7}\! \left(x , y\right) &= F_{4}\! \left(x \right)+F_{8}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{76}\! \left(x , y\right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= 0\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{12}\! \left(x \right)\\
F_{11}\! \left(x , y\right) &= -\frac{y \left(F_{8}\! \left(x , 1\right)-F_{8}\! \left(x , y\right)\right)}{-1+y}\\
F_{12}\! \left(x \right) &= x\\
F_{13}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{14}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= -\frac{y \left(F_{15}\! \left(x , 1\right)-F_{15}\! \left(x , y\right)\right)}{-1+y}\\
F_{15}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{16}\! \left(x , y\right)+F_{73}\! \left(x , y\right)+F_{9}\! \left(x \right)\\
F_{16}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{17}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{24}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)+F_{26}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)+F_{42}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)+F_{25}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{22}\! \left(x , y\right) F_{24}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= y x\\
F_{25}\! \left(x , y\right) &= F_{26}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{41}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{29}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{29}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= F_{32}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{33}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{31}\! \left(x , y\right)+F_{34}\! \left(x , y\right)+F_{38}\! \left(x , y\right)+F_{40}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{35}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{36}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= F_{8}\! \left(x , y\right)\\
F_{38}\! \left(x , y\right) &= F_{39}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{26}\! \left(x , y\right)\\
F_{40}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{33}\! \left(x , y\right)\\
F_{41}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{26}\! \left(x , y\right)\\
F_{42}\! \left(x , y\right) &= y F_{43}\! \left(x , y\right)\\
F_{43}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)+F_{44}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{45}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{46}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)+F_{63}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= F_{49}\! \left(x , y\right)+F_{57}\! \left(x , y\right)+F_{69}\! \left(x , y\right)\\
F_{49}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)+F_{50}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= F_{50}\! \left(x , y\right)+F_{54}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x , 1\right)\\
F_{53}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)+F_{4}\! \left(x \right)\\
F_{54}\! \left(x , y\right) &= F_{55}\! \left(x , y\right)\\
F_{56}\! \left(x , y\right) &= F_{53}\! \left(x , y\right)+F_{55}\! \left(x , y\right)\\
F_{56}\! \left(x , y\right) &= -\frac{-y F_{53}\! \left(x , y\right)+F_{53}\! \left(x , 1\right)}{-1+y}\\
F_{57}\! \left(x , y\right) &= F_{58}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{59}\! \left(x , y\right)\\
F_{59}\! \left(x , y\right) &= F_{60}\! \left(x , y\right)+F_{68}\! \left(x , y\right)\\
F_{61}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{60}\! \left(x , y\right)\\
F_{61}\! \left(x , y\right) &= F_{62}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= F_{50}\! \left(x , y\right)+F_{62}\! \left(x , y\right)+F_{66}\! \left(x , y\right)\\
F_{64}\! \left(x , y\right) &= F_{42}\! \left(x , y\right)+F_{63}\! \left(x , y\right)\\
F_{65}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{64}\! \left(x , y\right)\\
F_{65}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)\\
F_{66}\! \left(x , y\right) &= F_{67}\! \left(x , y\right)\\
F_{67}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{19}\! \left(x , y\right)\\
F_{68}\! \left(x , y\right) &= F_{46}\! \left(x , y\right)\\
F_{69}\! \left(x , y\right) &= F_{70}\! \left(x , y\right)\\
F_{70}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{71}\! \left(x , y\right)\\
F_{71}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)+F_{72}\! \left(x , y\right)\\
F_{72}\! \left(x , y\right) &= F_{43}\! \left(x , y\right)\\
F_{73}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{74}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= F_{50}\! \left(x , y\right)+F_{75}\! \left(x , y\right)\\
F_{75}\! \left(x , y\right) &= y F_{27}\! \left(x , y\right)\\
F_{76}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{77}\! \left(x , y\right)\\
F_{77}\! \left(x , y\right) &= F_{50}\! \left(x , y\right)+F_{78}\! \left(x , y\right)\\
F_{78}\! \left(x , y\right) &= y F_{34}\! \left(x , y\right)\\
F_{79}\! \left(x \right) &= F_{12}\! \left(x \right) F_{52}\! \left(x \right)\\
\end{align*}\)