Av(14523, 14532, 41523, 41532)
Counting Sequence
1, 1, 2, 6, 24, 116, 632, 3716, 22980, 147200, 967544, 6486420, 44169636, 304620752, 2123140000, ...
This specification was found using the strategy pack "Point Placements Req Corrob" and has 143 rules.
Finding the specification took 17198 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_{28}\! \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_{28}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{139}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{15}\! \left(x \right) &= -F_{135}\! \left(x \right)+F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= \frac{F_{17}\! \left(x \right)}{F_{28}\! \left(x \right)}\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= -F_{94}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= \frac{F_{20}\! \left(x \right)}{F_{28}\! \left(x \right)}\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{25}\! \left(x \right) &= -F_{29}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= \frac{F_{27}\! \left(x \right)}{F_{28}\! \left(x \right)}\\
F_{27}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{28}\! \left(x \right) &= x\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{28}\! \left(x \right) F_{31}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{31}\! \left(x \right) &= \frac{F_{32}\! \left(x \right)}{F_{28}\! \left(x \right)}\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= \frac{F_{35}\! \left(x \right)}{F_{28}\! \left(x \right)}\\
F_{35}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{43}\! \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_{28}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{28}\! \left(x \right) F_{37}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{28}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= \frac{F_{46}\! \left(x \right)}{F_{28}\! \left(x \right)}\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= -F_{37}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= \frac{F_{49}\! \left(x \right)}{F_{0}\! \left(x \right)}\\
F_{49}\! \left(x \right) &= -F_{59}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= \frac{F_{51}\! \left(x \right)}{F_{28}\! \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_{58}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= \frac{F_{57}\! \left(x \right)}{F_{28}\! \left(x \right)}\\
F_{57}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{58}\! \left(x \right) x +F_{58} \left(x \right)^{2}-2 F_{58}\! \left(x \right)+2\\
F_{59}\! \left(x \right) &= -F_{62}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= \frac{F_{61}\! \left(x \right)}{F_{28}\! \left(x \right)}\\
F_{61}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{2}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{28}\! \left(x \right) F_{65}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{65}\! \left(x \right) &= \frac{F_{66}\! \left(x \right)}{F_{28}\! \left(x \right)}\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{68}\! \left(x \right) &= \frac{F_{69}\! \left(x \right)}{F_{81}\! \left(x \right)}\\
F_{69}\! \left(x \right) &= -F_{78}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{28}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= \frac{F_{73}\! \left(x \right)}{F_{28}\! \left(x \right)}\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= -F_{77}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= \frac{F_{76}\! \left(x \right)}{F_{28}\! \left(x \right)}\\
F_{76}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{4}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{2}\! \left(x \right) F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= \frac{F_{80}\! \left(x \right)}{F_{28}\! \left(x \right)}\\
F_{80}\! \left(x \right) &= F_{55}\! \left(x \right)\\
F_{81}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{28}\! \left(x \right) F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{31}\! \left(x \right) F_{36}\! \left(x \right) F_{56}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{40}\! \left(x \right) F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{28}\! \left(x \right) F_{31}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{31}\! \left(x \right) F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{28}\! \left(x \right) F_{45}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{28}\! \left(x \right) F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= \frac{F_{98}\! \left(x \right)}{F_{28}\! \left(x \right)}\\
F_{98}\! \left(x \right) &= F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{122}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{117}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{111}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{107}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{0}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right) F_{33}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{105}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{114}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{108}\! \left(x \right) F_{115}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{28}\! \left(x \right) F_{31}\! \left(x \right) F_{38}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{108}\! \left(x \right) F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= -F_{121}\! \left(x \right)+F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= \frac{F_{120}\! \left(x \right)}{F_{28}\! \left(x \right)}\\
F_{120}\! \left(x \right) &= F_{81}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{126}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{101}\! \left(x \right) F_{79}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{127}\! \left(x \right) &= -F_{130}\! \left(x \right)+F_{128}\! \left(x \right)\\
F_{128}\! \left(x \right) &= \frac{F_{129}\! \left(x \right)}{F_{28}\! \left(x \right)}\\
F_{129}\! \left(x \right) &= F_{101}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{131}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{132}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{103}\! \left(x \right) F_{28}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right) F_{28}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{137}\! \left(x \right) &= \frac{F_{138}\! \left(x \right)}{F_{28}\! \left(x \right)}\\
F_{138}\! \left(x \right) &= F_{9}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{28}\! \left(x \right) F_{97}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{103}\! \left(x \right) F_{28}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 143 rules.
Finding the specification took 54182 seconds.
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Copy 143 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_{29}\! \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_{29}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{11}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{2}\! \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_{29}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right) F_{29}\! \left(x \right)\\
F_{16}\! \left(x \right) &= -F_{135}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= \frac{F_{18}\! \left(x \right)}{F_{29}\! \left(x \right)}\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= -F_{94}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= \frac{F_{21}\! \left(x \right)}{F_{29}\! \left(x \right)}\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right) F_{29}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right) F_{55}\! \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_{29}\! \left(x \right)}\\
F_{28}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{29}\! \left(x \right) &= x\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{29}\! \left(x \right) F_{32}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{32}\! \left(x \right) &= \frac{F_{33}\! \left(x \right)}{F_{29}\! \left(x \right)}\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= \frac{F_{38}\! \left(x \right)}{F_{29}\! \left(x \right)}\\
F_{38}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{29}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{29}\! \left(x \right) F_{40}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{29}\! \left(x \right) F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= \frac{F_{48}\! \left(x \right)}{F_{29}\! \left(x \right)}\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= -F_{40}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= \frac{F_{51}\! \left(x \right)}{F_{0}\! \left(x \right)}\\
F_{51}\! \left(x \right) &= -F_{57}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= \frac{F_{53}\! \left(x \right)}{F_{29}\! \left(x \right)}\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= \frac{F_{56}\! \left(x \right)}{F_{29}\! \left(x \right)}\\
F_{56}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{57}\! \left(x \right) &= -F_{62}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= \frac{F_{59}\! \left(x \right)}{F_{29}\! \left(x \right)}\\
F_{59}\! \left(x \right) &= F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= -F_{61}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{61}\! \left(x \right) x +F_{61} \left(x \right)^{2}+x\\
F_{62}\! \left(x \right) &= F_{2}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{29}\! \left(x \right) F_{65}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{65}\! \left(x \right) &= \frac{F_{66}\! \left(x \right)}{F_{29}\! \left(x \right)}\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= -F_{10}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{68}\! \left(x \right) &= \frac{F_{69}\! \left(x \right)}{F_{35}\! \left(x \right)}\\
F_{69}\! \left(x \right) &= -F_{78}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{29}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= \frac{F_{73}\! \left(x \right)}{F_{29}\! \left(x \right)}\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= -F_{77}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= \frac{F_{76}\! \left(x \right)}{F_{29}\! \left(x \right)}\\
F_{76}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{4}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{2}\! \left(x \right) F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= \frac{F_{80}\! \left(x \right)}{F_{29}\! \left(x \right)}\\
F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{60}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{29}\! \left(x \right) F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)+F_{90}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{86}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{32}\! \left(x \right) F_{39}\! \left(x \right) F_{55}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{42}\! \left(x \right) F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{29}\! \left(x \right) F_{32}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{32}\! \left(x \right) F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{29}\! \left(x \right) F_{47}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{29}\! \left(x \right) F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= \frac{F_{98}\! \left(x \right)}{F_{29}\! \left(x \right)}\\
F_{98}\! \left(x \right) &= F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{122}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right) F_{121}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right) F_{29}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{117}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{111}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{107}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{0}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{105}\! \left(x \right) F_{29}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{113}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{4}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{108}\! \left(x \right) F_{114}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right) F_{29}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{108}\! \left(x \right) F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= -F_{116}\! \left(x \right)+F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= \frac{F_{120}\! \left(x \right)}{F_{29}\! \left(x \right)}\\
F_{120}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{121}\! \left(x \right) x +F_{121} \left(x \right)^{2}-2 F_{121}\! \left(x \right)+2\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right) F_{29}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{125}\! \left(x \right)+F_{126}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{101}\! \left(x \right) F_{79}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{127}\! \left(x \right) &= -F_{130}\! \left(x \right)+F_{128}\! \left(x \right)\\
F_{128}\! \left(x \right) &= \frac{F_{129}\! \left(x \right)}{F_{29}\! \left(x \right)}\\
F_{129}\! \left(x \right) &= F_{101}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{131}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{132}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{103}\! \left(x \right) F_{29}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right) F_{29}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{137}\! \left(x \right) &= \frac{F_{138}\! \left(x \right)}{F_{29}\! \left(x \right)}\\
F_{138}\! \left(x \right) &= F_{9}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{29}\! \left(x \right) F_{97}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{103}\! \left(x \right) F_{29}\! \left(x \right)\\
\end{align*}\)