Av(13254, 13524, 13542, 14325, 14352, 21354, 21435, 24135, 41325, 41352, 42135)
Counting Sequence
1, 1, 2, 6, 24, 109, 522, 2574, 12964, 66426, 345300, 1816976, 9660732, 51825093, 280168474, ...
This specification was found using the strategy pack "Insertion Point Placements Tracked Fusion Isolated" and has 153 rules.
Found on April 08, 2021.Finding the specification took 10447 seconds.
This tree is too big to show here. Click to view tree on new page.
Copy 153 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_{4}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{51}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{8}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{8}\! \left(x \right) &= x\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{27}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{1}\! \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_{8}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{18}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{19}\! \left(x \right) &= 0\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{14}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{31}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{35}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{35}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{41}\! \left(x \right) &= 2 F_{19}\! \left(x \right)+F_{42}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{37}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{32}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= 2 F_{19}\! \left(x \right)+F_{42}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{122}\! \left(x \right)+F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{119}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{28}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x , 1\right)\\
F_{57}\! \left(x , y\right) &= F_{2}\! \left(x \right)+F_{58}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= F_{59}\! \left(x , y\right)\\
F_{59}\! \left(x , y\right) &= F_{60}\! \left(x , y\right) F_{67}\! \left(x , y\right) F_{68}\! \left(x , y\right)\\
F_{60}\! \left(x , y\right) &= F_{57}\! \left(x , y\right)+F_{61}\! \left(x , y\right)\\
F_{61}\! \left(x , y\right) &= F_{62}\! \left(x , y\right)+F_{71}\! \left(x , y\right)\\
F_{62}\! \left(x , y\right) &= F_{6}\! \left(x \right)+F_{63}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= F_{28}\! \left(x \right) F_{64}\! \left(x , y\right)\\
F_{64}\! \left(x , y\right) &= F_{65}\! \left(x , y\right)\\
F_{65}\! \left(x , y\right) &= F_{66}\! \left(x , y\right) F_{67}\! \left(x , y\right) F_{68}\! \left(x , y\right)\\
F_{66}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{64}\! \left(x , y\right)\\
F_{67}\! \left(x , y\right) &= y x\\
F_{68}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{69}\! \left(x , y\right)\\
F_{69}\! \left(x , y\right) &= F_{70}\! \left(x , y\right)\\
F_{70}\! \left(x , y\right) &= F_{67}\! \left(x , y\right) F_{68}\! \left(x , y\right)\\
F_{71}\! \left(x , y\right) &= F_{51}\! \left(x \right)+F_{72}\! \left(x , y\right)\\
F_{72}\! \left(x , y\right) &= F_{73}\! \left(x , y\right)\\
F_{73}\! \left(x , y\right) &= F_{74}\! \left(x , y\right) F_{8}\! \left(x \right)\\
F_{74}\! \left(x , y\right) &= F_{103}\! \left(x , y\right)+F_{75}\! \left(x , y\right)\\
F_{75}\! \left(x , y\right) &= F_{76}\! \left(x , y\right)+F_{95}\! \left(x , y\right)\\
F_{76}\! \left(x , y\right) &= F_{77}\! \left(x , y\right)+F_{94}\! \left(x , y\right)\\
F_{77}\! \left(x , y\right) &= F_{19}\! \left(x \right)+F_{78}\! \left(x , y\right)+F_{89}\! \left(x , y\right)\\
F_{78}\! \left(x , y\right) &= F_{79}\! \left(x , y\right) F_{8}\! \left(x \right)\\
F_{79}\! \left(x , y\right) &= F_{80}\! \left(x , y\right)+F_{83}\! \left(x , y\right)\\
F_{80}\! \left(x , y\right) &= F_{69}\! \left(x , y\right)+F_{81}\! \left(x , y\right)\\
F_{81}\! \left(x , y\right) &= F_{82}\! \left(x , y\right)\\
F_{82}\! \left(x , y\right) &= F_{8}\! \left(x \right) F_{80}\! \left(x , y\right)\\
F_{83}\! \left(x , y\right) &= F_{84}\! \left(x , y\right)+F_{87}\! \left(x , y\right)\\
F_{84}\! \left(x , y\right) &= F_{85}\! \left(x , y\right)\\
F_{85}\! \left(x , y\right) &= F_{67}\! \left(x , y\right) F_{86}\! \left(x , y\right)\\
F_{86}\! \left(x , y\right) &= F_{28}\! \left(x \right)+F_{84}\! \left(x , y\right)\\
F_{87}\! \left(x , y\right) &= F_{88}\! \left(x , y\right)\\
F_{88}\! \left(x , y\right) &= F_{8}\! \left(x \right) F_{83}\! \left(x , y\right)\\
F_{89}\! \left(x , y\right) &= F_{67}\! \left(x , y\right) F_{90}\! \left(x , y\right)\\
F_{90}\! \left(x , y\right) &= F_{86}\! \left(x , y\right)+F_{91}\! \left(x , y\right)\\
F_{91}\! \left(x , y\right) &= F_{77}\! \left(x , y\right)+F_{92}\! \left(x , y\right)\\
F_{92}\! \left(x , y\right) &= F_{93}\! \left(x , y\right)\\
F_{93}\! \left(x , y\right) &= F_{67}\! \left(x , y\right) F_{91}\! \left(x , y\right)\\
F_{94}\! \left(x , y\right) &= -\frac{y \left(F_{58}\! \left(x , 1\right)-F_{58}\! \left(x , y\right)\right)}{-1+y}\\
F_{95}\! \left(x , y\right) &= F_{102}\! \left(x , y\right)+F_{96}\! \left(x , y\right)\\
F_{96}\! \left(x , y\right) &= -\frac{F_{97}\! \left(x , 1\right) y -F_{97}\! \left(x , y\right)}{-1+y}\\
F_{97}\! \left(x , y\right) &= F_{28}\! \left(x \right) F_{98}\! \left(x , y\right)\\
F_{98}\! \left(x , y\right) &= F_{99}\! \left(x , y\right)\\
F_{99}\! \left(x , y\right) &= F_{100}\! \left(x , y\right) F_{67}\! \left(x , y\right)\\
F_{100}\! \left(x , y\right) &= F_{101}\! \left(x , y\right)+F_{69}\! \left(x , y\right)\\
F_{101}\! \left(x , y\right) &= F_{64}\! \left(x , y\right) F_{68}\! \left(x , y\right)\\
F_{102}\! \left(x , y\right) &= -\frac{y \left(F_{72}\! \left(x , 1\right)-F_{72}\! \left(x , y\right)\right)}{-1+y}\\
F_{103}\! \left(x , y\right) &= F_{104}\! \left(x , y\right)+F_{111}\! \left(x , y\right)\\
F_{104}\! \left(x , y\right) &= F_{105}\! \left(x , y\right)+F_{107}\! \left(x , y\right)\\
F_{105}\! \left(x , y\right) &= -\frac{F_{106}\! \left(x , 1\right) y -F_{106}\! \left(x , y\right)}{-1+y}\\
F_{106}\! \left(x , y\right) &= F_{15}\! \left(x \right) F_{98}\! \left(x , y\right)\\
F_{107}\! \left(x , y\right) &= -\frac{y \left(F_{108}\! \left(x , 1\right)-F_{108}\! \left(x , y\right)\right)}{-1+y}\\
F_{108}\! \left(x , y\right) &= F_{109}\! \left(x , y\right)\\
F_{109}\! \left(x , y\right) &= F_{110}\! \left(x , y\right) F_{8}\! \left(x \right)\\
F_{110}\! \left(x , y\right) &= F_{104}\! \left(x , y\right)+F_{76}\! \left(x , y\right)\\
F_{111}\! \left(x , y\right) &= F_{112}\! \left(x , y\right)+F_{115}\! \left(x , y\right)\\
F_{112}\! \left(x , y\right) &= F_{113}\! \left(x , y\right)\\
F_{113}\! \left(x , y\right) &= -\frac{F_{114}\! \left(x , 1\right) y -F_{114}\! \left(x , y\right)}{-1+y}\\
F_{114}\! \left(x , y\right) &= F_{15}\! \left(x \right) F_{28}\! \left(x \right) F_{98}\! \left(x , y\right)\\
F_{115}\! \left(x , y\right) &= -\frac{y \left(F_{116}\! \left(x , 1\right)-F_{116}\! \left(x , y\right)\right)}{-1+y}\\
F_{116}\! \left(x , y\right) &= F_{117}\! \left(x , y\right)\\
F_{117}\! \left(x , y\right) &= F_{118}\! \left(x , y\right) F_{8}\! \left(x \right)\\
F_{118}\! \left(x , y\right) &= F_{111}\! \left(x , y\right)+F_{95}\! \left(x , y\right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right)+F_{121}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{28} \left(x \right)^{2}\\
F_{121}\! \left(x \right) &= F_{71}\! \left(x , 1\right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right)+F_{129}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{125}\! \left(x \right)\\
F_{124}\! \left(x \right) &= F_{15}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{125}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{126}\! \left(x \right) &= F_{127}\! \left(x \right)\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x , 1\right)\\
F_{128}\! \left(x , y\right) &= F_{108}\! \left(x , y\right)\\
F_{129}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{132}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{131}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{28} \left(x \right)^{2} F_{15}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right)+F_{150}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{135}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right)+F_{140}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{139}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{15}\! \left(x \right) F_{55}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{119}\! \left(x \right) F_{17}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{141}\! \left(x \right)+F_{147}\! \left(x \right)\\
F_{141}\! \left(x \right) &= F_{142}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{142}\! \left(x \right) &= F_{124}\! \left(x \right)+F_{143}\! \left(x \right)\\
F_{143}\! \left(x \right) &= F_{126}\! \left(x \right)+F_{144}\! \left(x \right)\\
F_{144}\! \left(x \right) &= F_{145}\! \left(x \right)\\
F_{145}\! \left(x \right) &= F_{146}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{146}\! \left(x \right) &= F_{142}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{147}\! \left(x \right) &= F_{148}\! \left(x \right) F_{17}\! \left(x \right)\\
F_{148}\! \left(x \right) &= F_{130}\! \left(x \right)+F_{149}\! \left(x \right)\\
F_{149}\! \left(x \right) &= F_{134}\! \left(x \right)+F_{150}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{151}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{152}\! \left(x , 1\right)\\
F_{152}\! \left(x , y\right) &= F_{116}\! \left(x , y\right)\\
\end{align*}\)
This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 49 rules.
Found on April 08, 2021.Finding the specification took 235 seconds.
Copy 49 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_{9}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x , 1\right)\\
F_{6}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{46}\! \left(x , y\right)+F_{7}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= F_{8}\! \left(x , y\right) F_{9}\! \left(x \right)\\
F_{8}\! \left(x , y\right) &= -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}\\
F_{9}\! \left(x \right) &= x\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , 1, y\right)\\
F_{12}\! \left(x , y , z\right) &= F_{13}\! \left(x , y\right) F_{13}\! \left(x , z\right) F_{16}\! \left(x , z\right) F_{17}\! \left(x , z\right)\\
F_{13}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{16}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= y x\\
F_{18}\! \left(x , y , z\right) &= \frac{y F_{17}\! \left(x , y\right)-z F_{17}\! \left(x , z\right)}{-z +y}\\
F_{18}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{19}\! \left(x , y , z\right)+F_{21}\! \left(x , y , z\right)+F_{22}\! \left(x , y , z\right)\\
F_{19}\! \left(x , y , z\right) &= F_{20}\! \left(x , y , z\right)\\
F_{20}\! \left(x , y , z\right) &= F_{13}\! \left(x , y\right) F_{16}\! \left(x , y\right) F_{18}\! \left(x , y , z\right)\\
F_{21}\! \left(x , y , z\right) &= F_{12}\! \left(x , y , z\right)\\
F_{22}\! \left(x , y , z\right) &= F_{23}\! \left(x , y , z\right) F_{9}\! \left(x \right)\\
F_{23}\! \left(x , y , z\right) &= \frac{y F_{24}\! \left(x , y\right)-z F_{24}\! \left(x , z\right)}{-z +y}\\
F_{24}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{44}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{26}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{20}\! \left(x , y , 1\right)\\
F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{9}\! \left(x \right)\\
F_{29}\! \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_{30}\! \left(x , y , 1\right)\\
F_{30}\! \left(x , y , z\right) &= -\frac{-y F_{31}\! \left(x , y , z\right)+F_{31}\! \left(x , 1, z\right)}{-1+y}\\
F_{31}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{32}\! \left(x , y , z\right)+F_{35}\! \left(x , y , z\right)+F_{37}\! \left(x , y , z\right)+F_{42}\! \left(x , y , z\right)\\
F_{32}\! \left(x , y , z\right) &= F_{33}\! \left(x , y , z\right)\\
F_{33}\! \left(x , y , z\right) &= F_{13}\! \left(x , y\right) F_{16}\! \left(x , y\right) F_{34}\! \left(x , y , z\right)\\
F_{34}\! \left(x , y , z\right) &= -\frac{-y F_{18}\! \left(x , y , z\right)+F_{18}\! \left(x , 1, z\right)}{-1+y}\\
F_{35}\! \left(x , y , z\right) &= F_{36}\! \left(x , y , z\right) F_{9}\! \left(x \right)\\
F_{36}\! \left(x , y , z\right) &= -\frac{-z F_{31}\! \left(x , y , z\right)+F_{31}\! \left(x , y , 1\right)}{-1+z}\\
F_{37}\! \left(x , y , z\right) &= F_{38}\! \left(x , y , z\right)\\
F_{38}\! \left(x , y , z\right) &= F_{13}\! \left(x , y\right) F_{13}\! \left(x , z\right) F_{16}\! \left(x , z\right) F_{17}\! \left(x , z\right) F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{39}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{42}\! \left(x , y , z\right) &= F_{43}\! \left(x , y , z\right) F_{9}\! \left(x \right)\\
F_{43}\! \left(x , y , z\right) &= -\frac{-y F_{23}\! \left(x , y , z\right)+F_{23}\! \left(x , 1, z\right)}{-1+y}\\
F_{44}\! \left(x , y\right) &= F_{45}\! \left(x , y\right) F_{9}\! \left(x \right)\\
F_{45}\! \left(x , y\right) &= -\frac{-y F_{24}\! \left(x , y\right)+F_{24}\! \left(x , 1\right)}{-1+y}\\
F_{46}\! \left(x , y\right) &= F_{22}\! \left(x , 1, y\right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x , 1\right)\\
F_{48}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{9}\! \left(x \right)\\
\end{align*}\)