Av(13452, 14352, 14523, 14532, 41352, 41523, 41532, 45123, 45132)
Counting Sequence
1, 1, 2, 6, 24, 111, 547, 2782, 14445, 76241, 407978, 2208844, 12078881, 66620529, 370177307, ...
This specification was found using the strategy pack "Point And Col Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 228 rules.
Finding the specification took 3855 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_{10}\! \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_{222}\! \left(x \right)+F_{6}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{6}\! \left(x \right) &= 0\\
F_{7}\! \left(x \right) &= F_{10}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{218}\! \left(x \right)+F_{219}\! \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) &= x\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x , 1\right)\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)+F_{217}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x \right)+F_{37}\! \left(x , y\right)\\
F_{14}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x \right)+F_{216}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{10}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{20}\! \left(x \right)+F_{22}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{10}\! \left(x \right) F_{17}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{10}\! \left(x \right) F_{17}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{10}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{207}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{204}\! \left(x \right)+F_{205}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{10}\! \left(x \right) F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x , 1\right)\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{31}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= F_{202}\! \left(x , y\right)+F_{32}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{32}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)+F_{144}\! \left(x , y\right)+F_{34}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{35}\! \left(x , y\right) F_{56}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{37}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= F_{200}\! \left(x , y\right)+F_{201}\! \left(x , y\right)+F_{38}\! \left(x , y\right)+F_{6}\! \left(x \right)\\
F_{38}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{39}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= F_{113}\! \left(x , y\right)+F_{40}\! \left(x , y\right)+F_{42}\! \left(x , y\right)+F_{43}\! \left(x , y\right)+F_{6}\! \left(x \right)\\
F_{40}\! \left(x , y\right) &= F_{41}\! \left(x , y\right)\\
F_{41}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{39}\! \left(x , y\right)\\
F_{42}\! \left(x , y\right) &= F_{38}\! \left(x , y\right)\\
F_{43}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{44}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{23}\! \left(x \right)+F_{44}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{133}\! \left(x , y\right)+F_{190}\! \left(x , y\right)+F_{192}\! \left(x , y\right)+F_{197}\! \left(x , y\right)+F_{46}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{47}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= -\frac{-F_{48}\! \left(x , y\right) y +F_{48}\! \left(x , 1\right)}{-1+y}\\
F_{49}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{48}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{180}\! \left(x , y\right)+F_{188}\! \left(x , y\right)+F_{189}\! \left(x , y\right)+F_{49}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{179}\! \left(x , y\right)+F_{51}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= F_{52}\! \left(x , y\right)+F_{64}\! \left(x , y\right)\\
F_{52}\! \left(x , y\right) &= F_{53}\! \left(x , y\right)+F_{57}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{54}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= F_{55}\! \left(x , y\right)\\
F_{55}\! \left(x , y\right) &= F_{53}\! \left(x , y\right) F_{56}\! \left(x , y\right)\\
F_{56}\! \left(x , y\right) &= y x\\
F_{57}\! \left(x , y\right) &= F_{58}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{53}\! \left(x , y\right) F_{59}\! \left(x , y\right)\\
F_{59}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{60}\! \left(x , y\right)+F_{61}\! \left(x , y\right)+F_{63}\! \left(x , y\right)\\
F_{60}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{12}\! \left(x , y\right)\\
F_{61}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{62}\! \left(x , y\right)\\
F_{62}\! \left(x , y\right) &= F_{16}\! \left(x \right)+F_{39}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= F_{56}\! \left(x , y\right) F_{59}\! \left(x , y\right)\\
F_{64}\! \left(x , y\right) &= F_{65}\! \left(x , y\right)\\
F_{65}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{66}\! \left(x , y\right)\\
F_{66}\! \left(x , y\right) &= F_{172}\! \left(x , y\right)+F_{67}\! \left(x , y\right)\\
F_{68}\! \left(x , y\right) &= F_{165}\! \left(x , y\right)+F_{67}\! \left(x , y\right)\\
F_{69}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{68}\! \left(x , y\right)\\
F_{69}\! \left(x , y\right) &= F_{70}\! \left(x , y\right)\\
F_{70}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{71}\! \left(x , y\right)\\
F_{71}\! \left(x , y\right) &= F_{164}\! \left(x , y\right)+F_{72}\! \left(x \right)+F_{79}\! \left(x , y\right)+F_{88}\! \left(x , y\right)+F_{92}\! \left(x , y\right)\\
F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{10}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{10}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{79}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{80}\! \left(x , y\right)\\
F_{80}\! \left(x , y\right) &= F_{81}\! \left(x , y\right)+F_{82}\! \left(x , y\right)\\
F_{81}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{72}\! \left(x \right)\\
F_{82}\! \left(x , y\right) &= F_{78}\! \left(x \right) F_{83}\! \left(x , y\right)\\
F_{83}\! \left(x , y\right) &= F_{84}\! \left(x , y\right)\\
F_{84}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{85}\! \left(x , y\right)\\
F_{86}\! \left(x , y\right) &= F_{56}\! \left(x , y\right) F_{85}\! \left(x , y\right)\\
F_{86}\! \left(x , y\right) &= F_{87}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{24}\! \left(x \right)+F_{87}\! \left(x , y\right)\\
F_{88}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{89}\! \left(x , y\right)\\
F_{89}\! \left(x , y\right) &= F_{90}\! \left(x , y\right)+F_{91}\! \left(x , y\right)\\
F_{90}\! \left(x , y\right) &= F_{62}\! \left(x , y\right) F_{72}\! \left(x \right)\\
F_{91}\! \left(x , y\right) &= F_{29}\! \left(x , y\right) F_{78}\! \left(x \right)\\
F_{92}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{93}\! \left(x , y\right)\\
F_{93}\! \left(x , y\right) &= F_{115}\! \left(x , y\right)+F_{94}\! \left(x , y\right)\\
F_{94}\! \left(x , y\right) &= F_{72}\! \left(x \right) F_{95}\! \left(x , y\right)\\
F_{95}\! \left(x , y\right) &= F_{114}\! \left(x , y\right)+F_{96}\! \left(x , y\right)\\
F_{97}\! \left(x , y\right) &= F_{100}\! \left(x , y\right)+F_{96}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= F_{97}\! \left(x , y\right)+F_{98}\! \left(x , y\right)\\
F_{98}\! \left(x , y\right) &= F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{5}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{100}\! \left(x , y\right) &= F_{101}\! \left(x , y\right)+F_{103}\! \left(x , y\right)+F_{109}\! \left(x , y\right)+F_{110}\! \left(x , y\right)+F_{6}\! \left(x \right)\\
F_{101}\! \left(x , y\right) &= F_{102}\! \left(x , y\right)\\
F_{102}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{100}\! \left(x , y\right)\\
F_{103}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{104}\! \left(x , y\right)\\
F_{104}\! \left(x , y\right) &= F_{105}\! \left(x , y\right)+F_{107}\! \left(x , y\right)+F_{108}\! \left(x , y\right)+F_{109}\! \left(x , y\right)+F_{6}\! \left(x \right)\\
F_{105}\! \left(x , y\right) &= F_{106}\! \left(x , y\right)\\
F_{106}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{104}\! \left(x , y\right)\\
F_{107}\! \left(x , y\right) &= F_{103}\! \left(x , y\right)\\
F_{108}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{45}\! \left(x , y\right)\\
F_{109}\! \left(x , y\right) &= F_{100}\! \left(x , y\right) F_{56}\! \left(x , y\right)\\
F_{97}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{110}\! \left(x , y\right)+F_{111}\! \left(x , y\right)+F_{112}\! \left(x , y\right)+F_{113}\! \left(x , y\right)\\
F_{111}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{48}\! \left(x , y\right)\\
F_{112}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{62}\! \left(x , y\right)\\
F_{113}\! \left(x , y\right) &= F_{56}\! \left(x , y\right) F_{97}\! \left(x , y\right)\\
F_{114}\! \left(x , y\right) &= F_{99}\! \left(x \right)\\
F_{115}\! \left(x , y\right) &= F_{116}\! \left(x , y\right)\\
F_{117}\! \left(x , y\right) &= F_{116}\! \left(x , y\right)+F_{163}\! \left(x , y\right)\\
F_{117}\! \left(x , y\right) &= F_{118}\! \left(x , y\right)+F_{162}\! \left(x , y\right)\\
F_{119}\! \left(x , y\right) &= F_{118}\! \left(x , y\right)+F_{162}\! \left(x , y\right)\\
F_{120}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{119}\! \left(x , y\right)\\
F_{121}\! \left(x , y\right) &= F_{120}\! \left(x , y\right)+F_{160}\! \left(x , y\right)+F_{161}\! \left(x , y\right)+F_{6}\! \left(x \right)\\
F_{122}\! \left(x , y\right) &= F_{121}\! \left(x , y\right)+F_{158}\! \left(x , y\right)\\
F_{122}\! \left(x , y\right) &= F_{123}\! \left(x , y\right)+F_{156}\! \left(x , y\right)\\
F_{123}\! \left(x , y\right) &= F_{124}\! \left(x , y\right)+F_{51}\! \left(x , y\right)\\
F_{124}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{125}\! \left(x , y\right) F_{78}\! \left(x \right)\\
F_{125}\! \left(x , y\right) &= F_{126}\! \left(x , y\right)+F_{52}\! \left(x , y\right)\\
F_{126}\! \left(x , y\right) &= 2 F_{6}\! \left(x \right)+F_{127}\! \left(x , y\right)+F_{155}\! \left(x , y\right)\\
F_{127}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{128}\! \left(x , y\right)\\
F_{128}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{129}\! \left(x , y\right)+F_{154}\! \left(x , y\right)+F_{60}\! \left(x , y\right)+F_{61}\! \left(x , y\right)\\
F_{129}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{130}\! \left(x , y\right)\\
F_{131}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{130}\! \left(x , y\right)\\
F_{132}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{131}\! \left(x , y\right)+F_{133}\! \left(x , y\right)+F_{134}\! \left(x , y\right)+F_{136}\! \left(x , y\right)+F_{148}\! \left(x , y\right)\\
F_{110}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{132}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{133}\! \left(x , y\right)+F_{134}\! \left(x , y\right)+F_{136}\! \left(x , y\right)+F_{147}\! \left(x , y\right)\\
F_{134}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{135}\! \left(x , y\right)\\
F_{135}\! \left(x , y\right) &= -\frac{-y F_{12}\! \left(x , y\right)+F_{12}\! \left(x , 1\right)}{-1+y}\\
F_{136}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{137}\! \left(x , y\right)\\
F_{137}\! \left(x , y\right) &= -\frac{-F_{138}\! \left(x , y\right) y +F_{138}\! \left(x , 1\right)}{-1+y}\\
F_{138}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)+F_{139}\! \left(x , y\right)\\
F_{139}\! \left(x , y\right) &= F_{140}\! \left(x , y\right)\\
F_{140}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{141}\! \left(x , y\right)\\
F_{141}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)+F_{142}\! \left(x , y\right)+F_{144}\! \left(x , y\right)+F_{146}\! \left(x , y\right)\\
F_{142}\! \left(x , y\right) &= F_{143}\! \left(x , y\right)\\
F_{143}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{31}\! \left(x , y\right)\\
F_{144}\! \left(x , y\right) &= F_{145}\! \left(x , y\right)\\
F_{145}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{85}\! \left(x , y\right)\\
F_{146}\! \left(x , y\right) &= F_{141}\! \left(x , y\right) F_{56}\! \left(x , y\right)\\
F_{147}\! \left(x , y\right) &= F_{138}\! \left(x , y\right) F_{56}\! \left(x , y\right)\\
F_{148}\! \left(x , y\right) &= F_{149}\! \left(x , y\right) F_{56}\! \left(x , y\right)\\
F_{149}\! \left(x , y\right) &= F_{150}\! \left(x , y\right)+F_{153}\! \left(x , y\right)\\
F_{150}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)+F_{151}\! \left(x , y\right)\\
F_{151}\! \left(x , y\right) &= 3 F_{6}\! \left(x \right)+F_{131}\! \left(x , y\right)+F_{152}\! \left(x , y\right)\\
F_{152}\! \left(x , y\right) &= F_{151}\! \left(x , y\right) F_{56}\! \left(x , y\right)\\
F_{153}\! \left(x , y\right) &= F_{139}\! \left(x , y\right)\\
F_{154}\! \left(x , y\right) &= F_{128}\! \left(x , y\right) F_{56}\! \left(x , y\right)\\
F_{155}\! \left(x , y\right) &= F_{126}\! \left(x , y\right) F_{56}\! \left(x , y\right)\\
F_{156}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{157}\! \left(x , y\right)\\
F_{157}\! \left(x , y\right) &= F_{124}\! \left(x , y\right)+F_{156}\! \left(x , y\right)+F_{51}\! \left(x , y\right)\\
F_{158}\! \left(x , y\right) &= F_{159}\! \left(x \right) F_{52}\! \left(x , y\right)\\
F_{159}\! \left(x \right) &= F_{74}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{160}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{139}\! \left(x , y\right) F_{78}\! \left(x \right)\\
F_{161}\! \left(x , y\right) &= F_{121}\! \left(x , y\right) F_{56}\! \left(x , y\right)\\
F_{162}\! \left(x , y\right) &= F_{150}\! \left(x , y\right) F_{76}\! \left(x \right)\\
F_{163}\! \left(x , y\right) &= F_{72}\! \left(x \right) F_{96}\! \left(x , y\right)\\
F_{164}\! \left(x , y\right) &= F_{56}\! \left(x , y\right) F_{71}\! \left(x , y\right)\\
F_{165}\! \left(x , y\right) &= F_{166}\! \left(x , y\right)+F_{167}\! \left(x , y\right)\\
F_{166}\! \left(x , y\right) &= F_{50}\! \left(x , y\right) F_{76}\! \left(x \right)\\
F_{167}\! \left(x , y\right) &= F_{128}\! \left(x , y\right) F_{168}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{169}\! \left(x \right)+F_{170}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{10}\! \left(x \right) F_{76}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{10}\! \left(x \right) F_{171}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{168}\! \left(x \right)\\
F_{172}\! \left(x , y\right) &= F_{173}\! \left(x , y\right)+F_{174}\! \left(x , y\right)\\
F_{173}\! \left(x , y\right) &= F_{50}\! \left(x , y\right) F_{54}\! \left(x , y\right)\\
F_{174}\! \left(x , y\right) &= F_{128}\! \left(x , y\right) F_{175}\! \left(x , y\right)\\
F_{175}\! \left(x , y\right) &= F_{176}\! \left(x , y\right)+F_{177}\! \left(x , y\right)+F_{6}\! \left(x \right)\\
F_{176}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{54}\! \left(x , y\right)\\
F_{177}\! \left(x , y\right) &= F_{178}\! \left(x , y\right) F_{56}\! \left(x , y\right)\\
F_{178}\! \left(x , y\right) &= F_{10}\! \left(x \right)+F_{175}\! \left(x , y\right)\\
F_{179}\! \left(x , y\right) &= F_{180}\! \left(x , y\right)+F_{182}\! \left(x , y\right)+F_{185}\! \left(x , y\right)+F_{187}\! \left(x , y\right)+F_{6}\! \left(x \right)\\
F_{180}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{181}\! \left(x , y\right)\\
F_{181}\! \left(x , y\right) &= F_{12}\! \left(x , y\right)+F_{83}\! \left(x , y\right)\\
F_{182}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{183}\! \left(x , y\right)\\
F_{184}\! \left(x , y\right) &= F_{138}\! \left(x , y\right)+F_{183}\! \left(x , y\right)\\
F_{184}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)+F_{62}\! \left(x , y\right)\\
F_{185}\! \left(x , y\right) &= F_{186}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{10}\! \left(x \right) F_{5}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{187}\! \left(x , y\right) &= F_{179}\! \left(x , y\right) F_{56}\! \left(x , y\right)\\
F_{188}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{184}\! \left(x , y\right)\\
F_{189}\! \left(x , y\right) &= F_{50}\! \left(x , y\right) F_{56}\! \left(x , y\right)\\
F_{190}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{191}\! \left(x , y\right)\\
F_{191}\! \left(x , y\right) &= -\frac{-F_{132}\! \left(x , y\right) y +F_{132}\! \left(x , 1\right)}{-1+y}\\
F_{192}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{193}\! \left(x , y\right)\\
F_{193}\! \left(x , y\right) &= F_{194}\! \left(x , y\right)+F_{195}\! \left(x , y\right)\\
F_{194}\! \left(x , y\right) &= -\frac{-F_{97}\! \left(x , y\right) y +F_{97}\! \left(x , 1\right)}{-1+y}\\
F_{195}\! \left(x , y\right) &= F_{196}\! \left(x , y\right)\\
F_{196}\! \left(x , y\right) &= -\frac{-y F_{139}\! \left(x , y\right)+F_{139}\! \left(x , 1\right)}{-1+y}\\
F_{197}\! \left(x , y\right) &= F_{198}\! \left(x , y\right) F_{56}\! \left(x , y\right)\\
F_{198}\! \left(x , y\right) &= F_{199}\! \left(x , y\right)+F_{97}\! \left(x , y\right)\\
F_{199}\! \left(x , y\right) &= F_{139}\! \left(x , y\right)\\
F_{200}\! \left(x , y\right) &= F_{10}\! \left(x \right) F_{87}\! \left(x , y\right)\\
F_{201}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{56}\! \left(x , y\right)\\
F_{202}\! \left(x , y\right) &= F_{203}\! \left(x , y\right)\\
F_{141}\! \left(x , y\right) &= F_{203}\! \left(x , y\right)+F_{35}\! \left(x , y\right)\\
F_{204}\! \left(x \right) &= F_{10}\! \left(x \right) F_{11}\! \left(x \right)\\
F_{205}\! \left(x \right) &= F_{10}\! \left(x \right) F_{206}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{138}\! \left(x , 1\right)\\
F_{207}\! \left(x \right) &= 2 F_{6}\! \left(x \right)+F_{208}\! \left(x \right)+F_{210}\! \left(x \right)+F_{213}\! \left(x \right)\\
F_{208}\! \left(x \right) &= F_{10}\! \left(x \right) F_{209}\! \left(x \right)\\
F_{209}\! \left(x \right) &= F_{48}\! \left(x , 1\right)\\
F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)\\
F_{211}\! \left(x \right) &= F_{10}\! \left(x \right) F_{212}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{151}\! \left(x , 1\right)\\
F_{213}\! \left(x \right) &= F_{214}\! \left(x \right)\\
F_{214}\! \left(x \right) &= F_{10}\! \left(x \right) F_{215}\! \left(x \right)\\
F_{215}\! \left(x \right) &= F_{207}\! \left(x \right)\\
F_{216}\! \left(x \right) &= F_{10}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{217}\! \left(x , y\right) &= F_{196}\! \left(x , y\right)\\
F_{218}\! \left(x \right) &= F_{10}\! \left(x \right) F_{26}\! \left(x \right)\\
F_{219}\! \left(x \right) &= F_{10}\! \left(x \right) F_{220}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{221}\! \left(x \right)+F_{8}\! \left(x \right)\\
F_{221}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{222}\! \left(x \right) &= F_{10}\! \left(x \right) F_{223}\! \left(x \right)\\
F_{223}\! \left(x \right) &= F_{224}\! \left(x \right)+F_{225}\! \left(x \right)+F_{226}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{224}\! \left(x \right) &= F_{10}\! \left(x \right) F_{206}\! \left(x \right)\\
F_{225}\! \left(x \right) &= F_{10}\! \left(x \right) F_{207}\! \left(x \right)\\
F_{226}\! \left(x \right) &= F_{227}\! \left(x \right)\\
F_{227}\! \left(x \right) &= F_{10}\! \left(x \right) F_{223}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 137 rules.
Finding the specification took 35220 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_{4}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{4}\! \left(x \right) &= x\\
F_{5}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{4}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{11}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{15}\! \left(x \right) F_{25}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{0}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{15}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{15}\! \left(x \right) F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= \frac{F_{20}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{20}\! \left(x \right) &= -F_{24}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{15}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{16}\! \left(x \right) F_{19}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{0}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{33}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{32}\! \left(x \right) &= 0\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{4}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{31}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{26}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{0}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= x^{2} F_{40} \left(x \right)^{3}+2 x^{2} F_{40} \left(x \right)^{2}+x^{2} F_{40}\! \left(x \right)+x F_{40} \left(x \right)^{2}+2 x F_{40}\! \left(x \right)+x\\
F_{41}\! \left(x \right) &= F_{112}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{4}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{15}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{4}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{102}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= \frac{F_{51}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= -F_{58}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= \frac{F_{54}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= -F_{57}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{57}\! \left(x \right) &= x^{2} F_{57} \left(x \right)^{3}-x^{2} F_{57} \left(x \right)^{2}+x F_{57} \left(x \right)^{2}+1\\
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_{4}\! \left(x \right)}\\
F_{60}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{4}\! \left(x \right) F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{46}\! \left(x \right) F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= \frac{F_{70}\! \left(x \right)}{F_{0}\! \left(x \right)}\\
F_{70}\! \left(x \right) &= -F_{71}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= -F_{73}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{2}\! \left(x \right) F_{69}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{4}\! \left(x \right) F_{46}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{4}\! \left(x \right) F_{62}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= \frac{F_{79}\! \left(x \right)}{F_{4}\! \left(x \right) F_{9}\! \left(x \right)}\\
F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= -F_{98}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= \frac{F_{82}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= -F_{38}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= -F_{85}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{62}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{2}\! \left(x \right) F_{57}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{4}\! \left(x \right) F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{2}\! \left(x \right) F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{47}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{15}\! \left(x \right) F_{62}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{21}\! \left(x \right) F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{93}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{15}\! \left(x \right) F_{4}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{38}\! \left(x \right) F_{69}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{38}\! \left(x \right) F_{4}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{103}\! \left(x \right) &= \frac{F_{104}\! \left(x \right)}{F_{2}\! \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_{4}\! \left(x \right)}\\
F_{106}\! \left(x \right) &= F_{72}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x \right)+F_{109}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{2}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{103}\! \left(x \right) F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{111}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{16}\! \left(x \right) F_{2}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right)+F_{116}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{2}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{103}\! \left(x \right) F_{15}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{135}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{125}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{57}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)+F_{132}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right) F_{15}\! \left(x \right) F_{95}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)+F_{21}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{16}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{4}\! \left(x \right) F_{8}\! \left(x \right) F_{95}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point And Col Placements Req Corrob" and has 293 rules.
Finding the specification took 90148 seconds.
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Copy 293 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_{15}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{15}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{257}\! \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_{0}\! \left(x \right) F_{10}\! \left(x \right)\\
F_{10}\! \left(x \right) &= x^{2} F_{10} \left(x \right)^{3}-x^{2} F_{10} \left(x \right)^{2}+x F_{10} \left(x \right)^{2}+1\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{248}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{14}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{13}\! \left(x \right) &= 0\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right) F_{16}\! \left(x \right)\\
F_{15}\! \left(x \right) &= x\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{12}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{21}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{15}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{15}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{20}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{15}\! \left(x \right) F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{15}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{191}\! \left(x \right)+F_{32}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{15}\! \left(x \right) F_{31}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{15}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{36}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{15}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{31}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{15}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{10}\! \left(x \right) F_{15}\! \left(x \right) F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{45}\! \left(x \right)+F_{46}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{10}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{15}\! \left(x \right) F_{43}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{15}\! \left(x \right) F_{43}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{49}\! \left(x \right) &= \frac{F_{50}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{50}\! \left(x \right) &= -F_{101}\! \left(x \right)-F_{13}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= -F_{10}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{100}\! \left(x \right)+F_{13}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{15}\! \left(x \right) F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{53}\! \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_{60}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{15}\! \left(x \right) F_{55}\! \left(x \right)\\
F_{59}\! \left(x \right) &= 0\\
F_{60}\! \left(x \right) &= F_{15}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= 2 F_{13}\! \left(x \right)+F_{62}\! \left(x \right)+F_{91}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{15}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{15}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= -F_{81}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= \frac{F_{70}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= -F_{52}\! \left(x \right)+F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= \frac{F_{73}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{73}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{76}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= \frac{F_{75}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{75}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{76}\! \left(x \right) &= F_{15}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{79}\! \left(x \right)\\
F_{79}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{73}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{15}\! \left(x \right) F_{78}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{82}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{15}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{61}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{79}\! \left(x \right) F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{15}\! \left(x \right) F_{88}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{15}\! \left(x \right) F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= 3 F_{13}\! \left(x \right)+F_{92}\! \left(x \right)+F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{15}\! \left(x \right) F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{96}\! \left(x \right)+F_{97}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{65}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{87}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{15}\! \left(x \right) F_{85}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{15}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{104}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)+F_{233}\! \left(x \right)+F_{246}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{216}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{108}\! \left(x \right)+F_{111}\! \left(x \right)+F_{112}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{107}\! \left(x \right)+F_{110}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{111}\! \left(x \right) &= F_{15}\! \left(x \right) F_{17}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{114}\! \left(x \right) &= \frac{F_{115}\! \left(x \right)}{F_{10}\! \left(x \right)}\\
F_{115}\! \left(x \right) &= -F_{119}\! \left(x \right)+F_{116}\! \left(x \right)\\
F_{116}\! \left(x \right) &= \frac{F_{117}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= -F_{12}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{13}\! \left(x \right)+F_{213}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{186}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{113}\! \left(x \right) F_{124}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{125}\! \left(x \right)+F_{126}\! \left(x \right)+F_{127}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{124}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{124}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{128}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{131}\! \left(x \right)\\
F_{129}\! \left(x \right) &= \frac{F_{130}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{130}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{126}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right) F_{15}\! \left(x \right) F_{164}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{135}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{136}\! \left(x \right) &= -F_{160}\! \left(x \right)+F_{137}\! \left(x \right)\\
F_{137}\! \left(x \right) &= \frac{F_{138}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{138}\! \left(x \right) &= F_{139}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{144}\! \left(x \right)\\
F_{140}\! \left(x \right) &= -F_{10}\! \left(x \right)+F_{141}\! \left(x \right)\\
F_{141}\! \left(x \right) &= \frac{F_{142}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{142}\! \left(x \right) &= F_{143}\! \left(x \right)\\
F_{143}\! \left(x \right) &= x^{2} F_{143} \left(x \right)^{3}+2 x^{2} F_{143} \left(x \right)^{2}+x^{2} F_{143}\! \left(x \right)+x F_{143} \left(x \right)^{2}+2 x F_{143}\! \left(x \right)+x\\
F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)\\
F_{145}\! \left(x \right) &= -F_{156}\! \left(x \right)+F_{146}\! \left(x \right)\\
F_{146}\! \left(x \right) &= -F_{157}\! \left(x \right)+F_{147}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{148}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{149}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{150}\! \left(x \right)+F_{152}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{10}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{152}\! \left(x \right) &= 2 F_{13}\! \left(x \right)+F_{153}\! \left(x \right)+F_{155}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{154}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{149}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{155}\! \left(x \right) &= F_{15}\! \left(x \right) F_{156}\! \left(x \right)\\
F_{156}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{152}\! \left(x \right)\\
F_{157}\! \left(x \right) &= F_{158}\! \left(x \right)\\
F_{158}\! \left(x \right) &= F_{140}\! \left(x \right)+F_{159}\! \left(x \right)\\
F_{159}\! \left(x \right) &= F_{10}\! \left(x \right) F_{88}\! \left(x \right)\\
F_{160}\! \left(x \right) &= F_{161}\! \left(x \right)+F_{162}\! \left(x \right)\\
F_{161}\! \left(x \right) &= F_{139}\! \left(x \right)\\
F_{162}\! \left(x \right) &= F_{163}\! \left(x \right)\\
F_{163}\! \left(x \right) &= F_{15}\! \left(x \right) F_{160}\! \left(x \right)\\
F_{164}\! \left(x \right) &= F_{165}\! \left(x \right)+F_{170}\! \left(x \right)\\
F_{165}\! \left(x \right) &= F_{166}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{166}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{167}\! \left(x \right)\\
F_{167}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{168}\! \left(x \right)+F_{169}\! \left(x \right)\\
F_{168}\! \left(x \right) &= F_{15}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{169}\! \left(x \right) &= F_{15}\! \left(x \right) F_{166}\! \left(x \right)\\
F_{170}\! \left(x \right) &= F_{171}\! \left(x \right)+F_{176}\! \left(x \right)\\
F_{171}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{172}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{173}\! \left(x \right)+F_{175}\! \left(x \right)\\
F_{173}\! \left(x \right) &= F_{15}\! \left(x \right) F_{174}\! \left(x \right)\\
F_{174}\! \left(x \right) &= F_{172}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{175}\! \left(x \right) &= F_{15}\! \left(x \right) F_{171}\! \left(x \right)\\
F_{176}\! \left(x \right) &= F_{177}\! \left(x \right)+F_{181}\! \left(x \right)\\
F_{177}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{178}\! \left(x \right)+F_{180}\! \left(x \right)\\
F_{178}\! \left(x \right) &= F_{15}\! \left(x \right) F_{179}\! \left(x \right)\\
F_{179}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{177}\! \left(x \right)\\
F_{180}\! \left(x \right) &= F_{15}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{181}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{182}\! \left(x \right)+F_{184}\! \left(x \right)+F_{185}\! \left(x \right)\\
F_{182}\! \left(x \right) &= F_{15}\! \left(x \right) F_{183}\! \left(x \right)\\
F_{183}\! \left(x \right) &= F_{167}\! \left(x \right)+F_{181}\! \left(x \right)\\
F_{184}\! \left(x \right) &= F_{15}\! \left(x \right) F_{172}\! \left(x \right)\\
F_{185}\! \left(x \right) &= F_{15}\! \left(x \right) F_{176}\! \left(x \right)\\
F_{186}\! \left(x \right) &= F_{187}\! \left(x \right)\\
F_{187}\! \left(x \right) &= F_{15}\! \left(x \right) F_{17}\! \left(x \right) F_{188}\! \left(x \right) F_{88}\! \left(x \right)\\
F_{188}\! \left(x \right) &= \frac{F_{189}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{189}\! \left(x \right) &= F_{190}\! \left(x \right)\\
F_{190}\! \left(x \right) &= \frac{F_{191}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{191}\! \left(x \right) &= -F_{13}\! \left(x \right)-F_{193}\! \left(x \right)-F_{197}\! \left(x \right)+F_{192}\! \left(x \right)\\
F_{192}\! \left(x \right) &= -F_{52}\! \left(x \right)+F_{102}\! \left(x \right)\\
F_{193}\! \left(x \right) &= F_{15}\! \left(x \right) F_{194}\! \left(x \right)\\
F_{194}\! \left(x \right) &= -F_{102}\! \left(x \right)+F_{195}\! \left(x \right)\\
F_{195}\! \left(x \right) &= \frac{F_{196}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{196}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{197}\! \left(x \right)-F_{212}\! \left(x \right)+F_{102}\! \left(x \right)\\
F_{197}\! \left(x \right) &= F_{15}\! \left(x \right) F_{198}\! \left(x \right)\\
F_{198}\! \left(x \right) &= F_{199}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{199}\! \left(x \right) &= F_{200}\! \left(x \right)\\
F_{200}\! \left(x \right) &= F_{15}\! \left(x \right) F_{201}\! \left(x \right)\\
F_{201}\! \left(x \right) &= F_{202}\! \left(x \right)+F_{210}\! \left(x \right)\\
F_{202}\! \left(x \right) &= F_{203}\! \left(x \right)+F_{204}\! \left(x \right)\\
F_{203}\! \left(x \right) &= F_{39}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{204}\! \left(x \right) &= F_{205}\! \left(x \right)\\
F_{205}\! \left(x \right) &= F_{15}\! \left(x \right) F_{206}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{206}\! \left(x \right) &= F_{207}\! \left(x \right)+F_{209}\! \left(x \right)\\
F_{207}\! \left(x \right) &= \frac{F_{208}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{208}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{209}\! \left(x \right) &= F_{188}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{210}\! \left(x \right) &= F_{211}\! \left(x \right)\\
F_{211}\! \left(x \right) &= F_{15}\! \left(x \right) F_{188}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{212}\! \left(x \right) &= F_{106}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{213}\! \left(x \right) &= F_{214}\! \left(x \right)\\
F_{214}\! \left(x \right) &= F_{113}\! \left(x \right) F_{15}\! \left(x \right) F_{215}\! \left(x \right)\\
F_{215}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{144}\! \left(x \right)\\
F_{216}\! \left(x \right) &= F_{217}\! \left(x \right)\\
F_{217}\! \left(x \right) &= F_{218}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{218}\! \left(x \right) &= F_{219}\! \left(x \right)\\
F_{219}\! \left(x \right) &= F_{15}\! \left(x \right) F_{220}\! \left(x \right)\\
F_{220}\! \left(x \right) &= F_{221}\! \left(x \right)+F_{228}\! \left(x \right)\\
F_{221}\! \left(x \right) &= \frac{F_{222}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{222}\! \left(x \right) &= -F_{13}\! \left(x \right)-F_{227}\! \left(x \right)+F_{223}\! \left(x \right)\\
F_{223}\! \left(x \right) &= F_{224}\! \left(x \right)+F_{225}\! \left(x \right)\\
F_{224}\! \left(x \right) &= F_{35}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{225}\! \left(x \right) &= F_{226}\! \left(x \right)\\
F_{226}\! \left(x \right) &= F_{15}\! \left(x \right) F_{206}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{227}\! \left(x \right) &= F_{15}\! \left(x \right) F_{202}\! \left(x \right)\\
F_{228}\! \left(x \right) &= F_{229}\! \left(x \right)\\
F_{229}\! \left(x \right) &= F_{15}\! \left(x \right) F_{16}\! \left(x \right) F_{230}\! \left(x \right)\\
F_{230}\! \left(x \right) &= \frac{F_{231}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{231}\! \left(x \right) &= F_{232}\! \left(x \right)\\
F_{232}\! \left(x \right) &= -F_{39}\! \left(x \right)+F_{113}\! \left(x \right)\\
F_{233}\! \left(x \right) &= F_{234}\! \left(x \right)\\
F_{234}\! \left(x \right) &= F_{15}\! \left(x \right) F_{235}\! \left(x \right)\\
F_{235}\! \left(x \right) &= F_{236}\! \left(x \right)+F_{237}\! \left(x \right)\\
F_{236}\! \left(x \right) &= F_{106}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{237}\! \left(x \right) &= F_{238}\! \left(x \right)\\
F_{238}\! \left(x \right) &= F_{15}\! \left(x \right) F_{188}\! \left(x \right) F_{239}\! \left(x \right)\\
F_{239}\! \left(x \right) &= F_{240}\! \left(x \right)+F_{245}\! \left(x \right)\\
F_{240}\! \left(x \right) &= F_{241}\! \left(x \right)+F_{87}\! \left(x \right)\\
F_{241}\! \left(x \right) &= F_{242}\! \left(x \right)+F_{243}\! \left(x \right)\\
F_{242}\! \left(x \right) &= F_{0}\! \left(x \right) F_{88}\! \left(x \right)\\
F_{243}\! \left(x \right) &= F_{244}\! \left(x \right) F_{88}\! \left(x \right)\\
F_{244}\! \left(x \right) &= -F_{88}\! \left(x \right)+F_{0}\! \left(x \right)\\
F_{245}\! \left(x \right) &= F_{53}\! \left(x \right) F_{88}\! \left(x \right)\\
F_{246}\! \left(x \right) &= F_{247}\! \left(x \right)\\
F_{247}\! \left(x \right) &= F_{106}\! \left(x \right) F_{15}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{248}\! \left(x \right) &= F_{249}\! \left(x \right)\\
F_{249}\! \left(x \right) &= F_{15}\! \left(x \right) F_{250}\! \left(x \right)\\
F_{250}\! \left(x \right) &= F_{251}\! \left(x \right)+F_{252}\! \left(x \right)\\
F_{251}\! \left(x \right) &= F_{12}\! \left(x \right) F_{74}\! \left(x \right)\\
F_{252}\! \left(x \right) &= F_{253}\! \left(x \right)\\
F_{253}\! \left(x \right) &= F_{15}\! \left(x \right) F_{240}\! \left(x \right) F_{254}\! \left(x \right)\\
F_{254}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{255}\! \left(x \right)+F_{256}\! \left(x \right)\\
F_{255}\! \left(x \right) &= F_{15}\! \left(x \right) F_{254}\! \left(x \right)\\
F_{256}\! \left(x \right) &= F_{15}\! \left(x \right) F_{230}\! \left(x \right)\\
F_{257}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{258}\! \left(x \right)+F_{263}\! \left(x \right)\\
F_{258}\! \left(x \right) &= F_{15}\! \left(x \right) F_{259}\! \left(x \right)\\
F_{259}\! \left(x \right) &= F_{260}\! \left(x \right)\\
F_{260}\! \left(x \right) &= F_{107}\! \left(x \right) F_{15}\! \left(x \right) F_{261}\! \left(x \right)\\
F_{261}\! \left(x \right) &= \frac{F_{262}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{262}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{263}\! \left(x \right) &= F_{264}\! \left(x \right)\\
F_{264}\! \left(x \right) &= F_{15}\! \left(x \right) F_{265}\! \left(x \right)\\
F_{265}\! \left(x \right) &= F_{266}\! \left(x \right)+F_{272}\! \left(x \right)\\
F_{266}\! \left(x \right) &= F_{267}\! \left(x \right)+F_{268}\! \left(x \right)\\
F_{267}\! \left(x \right) &= F_{17}\! \left(x \right) F_{74}\! \left(x \right)\\
F_{268}\! \left(x \right) &= F_{269}\! \left(x \right)\\
F_{269}\! \left(x \right) &= F_{107}\! \left(x \right) F_{15}\! \left(x \right) F_{270}\! \left(x \right)\\
F_{270}\! \left(x \right) &= \frac{F_{271}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{271}\! \left(x \right) &= F_{55}\! \left(x \right)\\
F_{272}\! \left(x \right) &= F_{273}\! \left(x \right)+F_{291}\! \left(x \right)\\
F_{273}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{274}\! \left(x \right)+F_{282}\! \left(x \right)\\
F_{274}\! \left(x \right) &= F_{275}\! \left(x \right)\\
F_{275}\! \left(x \right) &= F_{15}\! \left(x \right) F_{276}\! \left(x \right)\\
F_{276}\! \left(x \right) &= F_{272}\! \left(x \right)+F_{277}\! \left(x \right)\\
F_{277}\! \left(x \right) &= F_{278}\! \left(x \right)\\
F_{278}\! \left(x \right) &= F_{15}\! \left(x \right) F_{279}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{279}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{280}\! \left(x \right)+F_{281}\! \left(x \right)\\
F_{280}\! \left(x \right) &= F_{15}\! \left(x \right) F_{279}\! \left(x \right)\\
F_{281}\! \left(x \right) &= F_{15}\! \left(x \right) F_{188}\! \left(x \right)\\
F_{282}\! \left(x \right) &= F_{283}\! \left(x \right)\\
F_{283}\! \left(x \right) &= F_{15}\! \left(x \right) F_{284}\! \left(x \right)\\
F_{284}\! \left(x \right) &= F_{285}\! \left(x \right)\\
F_{285}\! \left(x \right) &= F_{15}\! \left(x \right) F_{286}\! \left(x \right)\\
F_{286}\! \left(x \right) &= F_{287}\! \left(x \right)+F_{288}\! \left(x \right)\\
F_{287}\! \left(x \right) &= F_{279}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{288}\! \left(x \right) &= F_{254}\! \left(x \right) F_{289}\! \left(x \right)\\
F_{289}\! \left(x \right) &= F_{290}\! \left(x \right)\\
F_{290}\! \left(x \right) &= F_{15}\! \left(x \right) F_{239}\! \left(x \right)\\
F_{291}\! \left(x \right) &= F_{292}\! \left(x \right)\\
F_{292}\! \left(x \right) &= F_{15}\! \left(x \right) F_{279}\! \left(x \right) F_{79}\! \left(x \right) F_{88}\! \left(x \right)\\
\end{align*}\)