Av(12453, 12543, 15243, 21453, 21543, 25143, 51243, 52143)
Counting Sequence
1, 1, 2, 6, 24, 112, 568, 3024, 16600, 93008, 528632, 3036016, 17572504, 102318256, 598547640, ...
This specification was found using the strategy pack "Point Placements Req Corrob" and has 139 rules.
Finding the specification took 4933 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_{13}\! \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_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{13}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{14}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{12}\! \left(x \right)\\
F_{11}\! \left(x \right) &= x^{2} F_{11} \left(x \right)^{2}+4 x^{2} F_{11}\! \left(x \right)+4 x F_{11} \left(x \right)^{2}+4 x^{2}-5 x F_{11}\! \left(x \right)-F_{11} \left(x \right)^{2}-x +2 F_{11}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{13}\! \left(x \right) &= x\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{13}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{19}\! \left(x \right) &= -F_{32}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= -F_{29}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= \frac{F_{22}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= -F_{28}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= \frac{F_{27}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{27}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{28}\! \left(x \right) &= x^{2} F_{28} \left(x \right)^{2}+2 x^{2} F_{28}\! \left(x \right)+4 x F_{28} \left(x \right)^{2}+x^{2}-13 x F_{28}\! \left(x \right)-F_{28} \left(x \right)^{2}+8 x +4 F_{28}\! \left(x \right)-2\\
F_{29}\! \left(x \right) &= -F_{32}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= \frac{F_{31}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{31}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34} \left(x \right)^{2} F_{2}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{13}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{13}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{13}\! \left(x \right) F_{34}\! \left(x \right) F_{36}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{42}\! \left(x \right) x +F_{42} \left(x \right)^{2}+x\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{13}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{13}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{51}\! \left(x \right) &= \frac{F_{52}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{2}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{13}\! \left(x \right) F_{57}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{57}\! \left(x \right) &= \frac{F_{58}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{58}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= -F_{73}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= \frac{F_{62}\! \left(x \right)}{F_{28}\! \left(x \right)}\\
F_{62}\! \left(x \right) &= -F_{68}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= \frac{F_{64}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= -F_{28}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= \frac{F_{67}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{67}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{68}\! \left(x \right) &= -F_{72}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= \frac{F_{70}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= -F_{42}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{11}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{73}\! \left(x \right) x +F_{73} \left(x \right)^{2}-2 F_{73}\! \left(x \right)+2\\
F_{74}\! \left(x \right) &= F_{60}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= \frac{F_{76}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{76}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)+F_{97}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{42}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= -F_{73}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{82}\! \left(x \right) &= -F_{47}\! \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_{13}\! \left(x \right)}\\
F_{85}\! \left(x \right) &= F_{80}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{13}\! \left(x \right) F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= \frac{F_{89}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= -F_{93}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= \frac{F_{92}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{92}\! \left(x \right) &= F_{80}\! \left(x \right)\\
F_{93}\! \left(x \right) &= -F_{96}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= \frac{F_{95}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{95}\! \left(x \right) &= F_{79}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{11}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{100}\! \left(x \right) &= \frac{F_{101}\! \left(x \right)}{F_{112}\! \left(x \right) F_{13}\! \left(x \right)}\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\
F_{102}\! \left(x \right) &= -F_{81}\! \left(x \right)+F_{103}\! \left(x \right)\\
F_{103}\! \left(x \right) &= -F_{111}\! \left(x \right)+F_{104}\! \left(x \right)\\
F_{104}\! \left(x \right) &= -F_{107}\! \left(x \right)+F_{105}\! \left(x \right)\\
F_{105}\! \left(x \right) &= \frac{F_{106}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{106}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{109}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{5}\! \left(x \right) F_{73}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{55}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{0}\! \left(x \right) F_{73}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{120}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right) F_{13}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{100}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{112}\! \left(x \right) F_{123}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{123}\! \left(x \right) &= -F_{137}\! \left(x \right)+F_{124}\! \left(x \right)\\
F_{124}\! \left(x \right) &= \frac{F_{125}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{117}\! \left(x \right) F_{127}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{127}\! \left(x \right) &= -F_{134}\! \left(x \right)+F_{128}\! \left(x \right)\\
F_{128}\! \left(x \right) &= -F_{131}\! \left(x \right)+F_{129}\! \left(x \right)\\
F_{129}\! \left(x \right) &= \frac{F_{130}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{130}\! \left(x \right) &= F_{79}\! \left(x \right)\\
F_{131}\! \left(x \right) &= -F_{134}\! \left(x \right)+F_{132}\! \left(x \right)\\
F_{132}\! \left(x \right) &= \frac{F_{133}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{133}\! \left(x \right) &= F_{80}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{135}\! \left(x \right)+F_{136}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{2}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{13}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{137}\! \left(x \right) &= \frac{F_{138}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{138}\! \left(x \right) &= F_{60}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion" and has 37 rules.
Finding the specification took 1155 seconds.
Copy 37 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_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \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_{11}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{10}\! \left(x \right) x +F_{10} \left(x \right)^{2}+x\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{18}\! \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_{2}\! \left(x \right)\\
F_{16}\! \left(x \right) &= x\\
F_{17}\! \left(x \right) &= F_{17}\! \left(x \right) x +F_{17} \left(x \right)^{2}-2 F_{17}\! \left(x \right)+2\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{16}\! \left(x \right) F_{20}\! \left(x \right) F_{26}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{21}\! \left(x \right) &= x^{2} F_{21} \left(x \right)^{2}+4 x^{2} F_{21}\! \left(x \right)+4 x F_{21} \left(x \right)^{2}+4 x^{2}-5 x F_{21}\! \left(x \right)-F_{21} \left(x \right)^{2}-x +2 F_{21}\! \left(x \right)\\
F_{22}\! \left(x \right) &= -F_{25}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= \frac{F_{24}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{24}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{25}\! \left(x \right) &= x^{2} F_{25} \left(x \right)^{2}+2 x^{2} F_{25}\! \left(x \right)+4 x F_{25} \left(x \right)^{2}+x^{2}-13 x F_{25}\! \left(x \right)-F_{25} \left(x \right)^{2}+8 x +4 F_{25}\! \left(x \right)-2\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x , 1\right)\\
F_{27}\! \left(x , y\right) &= -\frac{-y F_{28}\! \left(x , y\right)+F_{28}\! \left(x , 1\right)}{-1+y}\\
F_{29}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{31}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= x F_{30}\! \left(x , y\right) y +y x +F_{30}\! \left(x , y\right)^{2}\\
F_{31}\! \left(x , y\right) &= y x\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{16}\! \left(x \right) F_{34}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{34}\! \left(x \right) &= \frac{F_{35}\! \left(x \right)}{F_{16}\! \left(x \right)}\\
F_{35}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{28}\! \left(x , 1\right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 142 rules.
Finding the specification took 13327 seconds.
This tree is too big to show here. Click to view tree on new page.
Copy 142 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_{13}\! \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_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{13}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{14}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{12}\! \left(x \right)\\
F_{11}\! \left(x \right) &= x^{2} F_{11} \left(x \right)^{2}+4 x^{2} F_{11}\! \left(x \right)+4 x F_{11} \left(x \right)^{2}+4 x^{2}-5 x F_{11}\! \left(x \right)-F_{11} \left(x \right)^{2}-x +2 F_{11}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{13}\! \left(x \right) &= x\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{13}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{77}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{19}\! \left(x \right) &= -F_{30}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= -F_{26}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= \frac{F_{22}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= \frac{F_{25}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{25}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{26}\! \left(x \right) &= -F_{30}\! \left(x \right)+F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= \frac{F_{28}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= -F_{11}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32} \left(x \right)^{2} F_{2}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{13}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{13}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{13}\! \left(x \right) F_{32}\! \left(x \right) F_{34}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{40}\! \left(x \right) x +F_{40} \left(x \right)^{2}+x\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{13}\! \left(x \right) F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{13}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{49}\! \left(x \right) &= \frac{F_{50}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{2}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{13}\! \left(x \right) F_{55}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{55}\! \left(x \right) &= \frac{F_{56}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{56}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= -F_{68}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= \frac{F_{60}\! \left(x \right)}{F_{73}\! \left(x \right)}\\
F_{60}\! \left(x \right) &= -F_{69}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= \frac{F_{62}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= -F_{11}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= -F_{68}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= \frac{F_{67}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{67}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{68}\! \left(x \right) x +F_{68} \left(x \right)^{2}-2 F_{68}\! \left(x \right)+2\\
F_{69}\! \left(x \right) &= -F_{72}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= \frac{F_{71}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{71}\! \left(x \right) &= F_{64}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{11}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{73}\! \left(x \right) &= x^{2} F_{73} \left(x \right)^{2}+2 x^{2} F_{73}\! \left(x \right)+4 x F_{73} \left(x \right)^{2}+x^{2}-13 x F_{73}\! \left(x \right)-F_{73} \left(x \right)^{2}+8 x +4 F_{73}\! \left(x \right)-2\\
F_{74}\! \left(x \right) &= F_{58}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= \frac{F_{76}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{76}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{79}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{80}\! \left(x \right) &= -F_{45}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= -F_{85}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= \frac{F_{83}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= -F_{40}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{13}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= \frac{F_{88}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= -F_{92}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= \frac{F_{91}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{91}\! \left(x \right) &= F_{84}\! \left(x \right)\\
F_{92}\! \left(x \right) &= -F_{95}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= \frac{F_{94}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{94}\! \left(x \right) &= F_{79}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{44}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{11}\! \left(x \right) F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{13}\! \left(x \right) F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= \frac{F_{100}\! \left(x \right)}{F_{113}\! \left(x \right) F_{13}\! \left(x \right)}\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)\\
F_{101}\! \left(x \right) &= -F_{112}\! \left(x \right)+F_{102}\! \left(x \right)\\
F_{102}\! \left(x \right) &= -F_{111}\! \left(x \right)+F_{103}\! \left(x \right)\\
F_{103}\! \left(x \right) &= -F_{106}\! \left(x \right)+F_{104}\! \left(x \right)\\
F_{104}\! \left(x \right) &= \frac{F_{105}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{105}\! \left(x \right) &= F_{5}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{108}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{5}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)+F_{110}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{56}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{0}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{114}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{122}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{117}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{114}\! \left(x \right) F_{119}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{13}\! \left(x \right) F_{99}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{124}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{108}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{113}\! \left(x \right) F_{126}\! \left(x \right) F_{13}\! \left(x \right)\\
F_{126}\! \left(x \right) &= -F_{140}\! \left(x \right)+F_{127}\! \left(x \right)\\
F_{127}\! \left(x \right) &= \frac{F_{128}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{119}\! \left(x \right) F_{13}\! \left(x \right) F_{130}\! \left(x \right)\\
F_{130}\! \left(x \right) &= -F_{137}\! \left(x \right)+F_{131}\! \left(x \right)\\
F_{131}\! \left(x \right) &= -F_{134}\! \left(x \right)+F_{132}\! \left(x \right)\\
F_{132}\! \left(x \right) &= \frac{F_{133}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{133}\! \left(x \right) &= F_{79}\! \left(x \right)\\
F_{134}\! \left(x \right) &= -F_{137}\! \left(x \right)+F_{135}\! \left(x \right)\\
F_{135}\! \left(x \right) &= \frac{F_{136}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{136}\! \left(x \right) &= F_{84}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{139}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{2}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{13}\! \left(x \right) F_{38}\! \left(x \right)\\
F_{140}\! \left(x \right) &= \frac{F_{141}\! \left(x \right)}{F_{13}\! \left(x \right)}\\
F_{141}\! \left(x \right) &= F_{58}\! \left(x \right)\\
\end{align*}\)