Av(12354, 12453, 12543, 13452, 13542, 14532, 21354, 21453, 21543, 31254)
Counting Sequence
1, 1, 2, 6, 24, 110, 534, 2678, 13748, 71869, 381216, 2046630, 11100266, 60732086, 334799979, ...
This specification was found using the strategy pack "Col Placements Tracked Fusion" and has 57 rules.
Finding the specification took 273 seconds.
Copy 57 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_{4}\! \left(x \right)\\
F_{3}\! \left(x \right) &= x\\
F_{4}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{49}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{3}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x , 1\right)\\
F_{7}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{46}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= F_{3}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= -\frac{-F_{7}\! \left(x , y_{0}\right) y_{0}+F_{7}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{10}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)\\
F_{11}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , 1, y_{0}\right)\\
F_{12}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{38}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}, y_{1}\right)+F_{45}\! \left(x , y_{1}, y_{0}\right)\\
F_{13}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{15}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{15}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{18}\! \left(x , y_{0}, y_{1}\right)+F_{37}\! \left(x , y_{1}, y_{0}\right)\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)\\
F_{17}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{11}\! \left(x , y_{0}\right) y_{0}-F_{11}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{18}\! \left(x , y_{0}, y_{1}\right) &= F_{19}\! \left(x , y_{0}\right) F_{20}\! \left(x , y_{0}, y_{1}\right)\\
F_{19}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{20}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{21}\! \left(x , y_{0}, 1\right) y_{0}-F_{21}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{21}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{22}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{23}\! \left(x , y_{0}, y_{1}\right)+F_{26}\! \left(x , y_{0}, y_{1}\right)+F_{30}\! \left(x , y_{1}\right)\\
F_{23}\! \left(x , y_{0}, y_{1}\right) &= F_{24}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)\\
F_{24}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{25}\! \left(x , y_{0}\right) y_{0}-F_{25}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{25}\! \left(x , y_{0}\right) &= F_{15}\! \left(x , 1, y_{0}\right)\\
F_{26}\! \left(x , y_{0}, y_{1}\right) &= F_{19}\! \left(x , y_{0}\right) F_{27}\! \left(x , y_{0}, y_{1}\right)\\
F_{27}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{28}\! \left(x , y_{0}\right) y_{0}-F_{28}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{28}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{29}\! \left(x , y_{0}\right)+F_{30}\! \left(x , y_{0}\right)\\
F_{29}\! \left(x , y_{0}\right) &= F_{25}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)\\
F_{30}\! \left(x , y_{0}\right) &= F_{19}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}\right)\\
F_{31}\! \left(x , y_{0}\right) &= -\frac{-F_{32}\! \left(x , y_{0}\right) y_{0}+F_{32}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{32}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{33}\! \left(x , y_{0}\right)+F_{36}\! \left(x , y_{0}\right)\\
F_{33}\! \left(x , y_{0}\right) &= F_{3}\! \left(x \right) F_{34}\! \left(x , y_{0}\right)\\
F_{34}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{29}\! \left(x , y_{0}\right)+F_{35}\! \left(x , y_{0}\right)\\
F_{35}\! \left(x , y_{0}\right) &= F_{19}\! \left(x , y_{0}\right) F_{28}\! \left(x , y_{0}\right)\\
F_{36}\! \left(x , y_{0}\right) &= F_{19}\! \left(x , y_{0}\right) F_{32}\! \left(x , y_{0}\right)\\
F_{37}\! \left(x , y_{0}, y_{1}\right) &= F_{19}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{1}, y_{0}\right)\\
F_{38}\! \left(x , y_{0}, y_{1}\right) &= F_{3}\! \left(x \right) F_{39}\! \left(x , y_{0}, y_{1}\right)\\
F_{39}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{12}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{12}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{40}\! \left(x , y_{0}, y_{1}\right) &= F_{19}\! \left(x , y_{0}\right) F_{41}\! \left(x , y_{0}, y_{1}\right)\\
F_{41}\! \left(x , y_{0}, y_{1}\right) &= F_{42}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{43}\! \left(x , y_{0} y_{1}, y_{2}\right) y_{0}+F_{43}\! \left(x , y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{43}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{44}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{44}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{44}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{32}\! \left(x , y_{0}\right) y_{0}-F_{32}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{45}\! \left(x , y_{0}, y_{1}\right) &= F_{19}\! \left(x , y_{0}\right) F_{43}\! \left(x , y_{1}, y_{0}\right)\\
F_{46}\! \left(x , y_{0}\right) &= F_{19}\! \left(x , y_{0}\right) F_{47}\! \left(x , y_{0}\right)\\
F_{47}\! \left(x , y_{0}\right) &= F_{48}\! \left(x , 1, y_{0}\right)\\
F_{48}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{49}\! \left(x \right) &= F_{3}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x , 1\right)\\
F_{51}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{52}\! \left(x , y_{0}\right)+F_{54}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)\\
F_{52}\! \left(x , y_{0}\right) &= F_{3}\! \left(x \right) F_{53}\! \left(x , y_{0}\right)\\
F_{53}\! \left(x , y_{0}\right) &= -\frac{-F_{51}\! \left(x , y_{0}\right) y_{0}+F_{51}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{54}\! \left(x , y_{0}\right) &= F_{19}\! \left(x , y_{0}\right) F_{55}\! \left(x , y_{0}\right)\\
F_{55}\! \left(x , y_{0}\right) &= F_{56}\! \left(x , 1, y_{0}\right)\\
F_{56}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{31}\! \left(x , y_{0} y_{1}\right) y_{0}+F_{31}\! \left(x , y_{1}\right)}{-1+y_{0}}\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 107 rules.
Finding the specification took 35198 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_{9}\! \left(x , 1\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{98}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x \right)+F_{13}\! \left(x , y\right)\\
F_{11}\! \left(x \right) &= \frac{F_{12}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{12}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{21}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)+F_{92}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{26}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)+F_{22}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{19}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{21}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= y x\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x \right)+F_{24}\! \left(x , y\right)\\
F_{23}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{11}\! \left(x \right)\\
F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{26}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)+F_{90}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{31}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{31}\! \left(x , y\right) &= F_{32}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{33}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{33}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)+F_{88}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{35}\! \left(x , y\right)+F_{61}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= F_{36}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{37}\! \left(x , y\right) &= F_{38}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= F_{38}\! \left(x , y\right)+F_{40}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= -\frac{-F_{40}\! \left(x , y\right) y +F_{40}\! \left(x , 1\right)}{-1+y}\\
F_{40}\! \left(x , y\right) &= F_{41}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\
F_{42}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{41}\! \left(x , y\right)\\
F_{42}\! \left(x , y\right) &= F_{43}\! \left(x , y\right)\\
F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{45}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{46}\! \left(x , y\right)+F_{60}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{48}\! \left(x , y\right)\\
F_{49}\! \left(x , y\right) &= F_{48}\! \left(x , y\right)+F_{55}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{49}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{51}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= F_{22}\! \left(x , y\right)+F_{52}\! \left(x , y\right)\\
F_{52}\! \left(x , y\right) &= F_{53}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{54}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= -\frac{-F_{41}\! \left(x , y\right) y +F_{41}\! \left(x , 1\right)}{-1+y}\\
F_{56}\! \left(x , y\right) &= F_{55}\! \left(x , y\right)+F_{58}\! \left(x , y\right)\\
F_{57}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{56}\! \left(x , y\right)\\
F_{57}\! \left(x , y\right) &= F_{51}\! \left(x , y\right)\\
F_{59}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{58}\! \left(x , y\right)\\
F_{59}\! \left(x , y\right) &= F_{22}\! \left(x , y\right)\\
F_{60}\! \left(x , y\right) &= -\frac{y \left(F_{43}\! \left(x , 1\right)-F_{43}\! \left(x , y\right)\right)}{-1+y}\\
F_{61}\! \left(x , y\right) &= y F_{62}\! \left(x , y\right)\\
F_{62}\! \left(x , y\right) &= F_{63}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{64}\! \left(x , y\right)\\
F_{64}\! \left(x , y\right) &= F_{65}\! \left(x , 1, y\right)\\
F_{65}\! \left(x , y , z\right) &= -\frac{-F_{66}\! \left(x , y z \right) y +F_{66}\! \left(x , z\right)}{-1+y}\\
F_{66}\! \left(x , y\right) &= F_{67}\! \left(x , y\right)\\
F_{68}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{67}\! \left(x , y\right)\\
F_{68}\! \left(x , y\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_{4}\! \left(x \right) F_{71}\! \left(x , y\right)\\
F_{71}\! \left(x , y\right) &= -\frac{-F_{72}\! \left(x , y\right) y +F_{72}\! \left(x , 1\right)}{-1+y}\\
F_{72}\! \left(x , y\right) &= F_{73}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{73}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= F_{75}\! \left(x , y\right)\\
F_{76}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{75}\! \left(x , y\right)\\
F_{76}\! \left(x , y\right) &= F_{77}\! \left(x , y\right)\\
F_{77}\! \left(x , y\right) &= F_{78}\! \left(x , y\right)+F_{81}\! \left(x , y\right)\\
F_{78}\! \left(x , y\right) &= F_{79}\! \left(x , y\right)\\
F_{79}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{80}\! \left(x , y\right)\\
F_{80}\! \left(x , y\right) &= -\frac{y \left(F_{19}\! \left(x , 1\right)-F_{19}\! \left(x , y\right)\right)}{-1+y}\\
F_{81}\! \left(x , y\right) &= F_{82}\! \left(x , y\right)\\
F_{82}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{83}\! \left(x , y\right)\\
F_{83}\! \left(x , y\right) &= F_{84}\! \left(x , y\right)+F_{85}\! \left(x , y\right)\\
F_{84}\! \left(x , y\right) &= -\frac{y \left(F_{77}\! \left(x , 1\right)-F_{77}\! \left(x , y\right)\right)}{-1+y}\\
F_{85}\! \left(x , y\right) &= F_{86}\! \left(x , y\right)\\
F_{86}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{87}\! \left(x , y\right)\\
F_{87}\! \left(x , y\right) &= -\frac{y \left(F_{45}\! \left(x , 1\right)-F_{45}\! \left(x , y\right)\right)}{-1+y}\\
F_{89}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{88}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= F_{41}\! \left(x , y\right)+F_{89}\! \left(x , y\right)\\
F_{90}\! \left(x , y\right) &= F_{91}\! \left(x , y\right)\\
F_{91}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{69}\! \left(x , y\right)\\
F_{92}\! \left(x , y\right) &= y F_{93}\! \left(x , y\right)\\
F_{93}\! \left(x , y\right) &= F_{94}\! \left(x , y\right)\\
F_{94}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{95}\! \left(x , y\right)\\
F_{95}\! \left(x , y\right) &= F_{96}\! \left(x , 1, y\right)\\
F_{96}\! \left(x , y , z\right) &= -\frac{-F_{97}\! \left(x , y z \right) y +F_{97}\! \left(x , z\right)}{-1+y}\\
F_{97}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{41}\! \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_{4}\! \left(x \right)\\
F_{100}\! \left(x , y\right) &= F_{101}\! \left(x , y\right)+F_{39}\! \left(x , y\right)\\
F_{101}\! \left(x , y\right) &= y F_{102}\! \left(x , y\right)\\
F_{102}\! \left(x , y\right) &= F_{103}\! \left(x , y\right)\\
F_{103}\! \left(x , y\right) &= F_{104}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{104}\! \left(x , y\right) &= F_{105}\! \left(x , 1, y\right)\\
F_{105}\! \left(x , y , z\right) &= -\frac{-F_{106}\! \left(x , y z \right) y +F_{106}\! \left(x , z\right)}{-1+y}\\
F_{106}\! \left(x , y\right) &= -\frac{-y F_{97}\! \left(x , y\right)+F_{97}\! \left(x , 1\right)}{-1+y}\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 111 rules.
Finding the specification took 15744 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_{9}\! \left(x , 1\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{78}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)+F_{5}\! \left(x \right)\\
F_{11}\! \left(x , y\right) &= F_{107}\! \left(x , y\right)+F_{12}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{49}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{102}\! \left(x , y\right)+F_{15}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , 1, y\right)\\
F_{16}\! \left(x , y , z\right) &= -\frac{-F_{17}\! \left(x , y z \right) y +F_{17}\! \left(x , z\right)}{-1+y}\\
F_{17}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{18}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{49}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{21}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{22}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{23}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)+F_{82}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{26}\! \left(x , y\right)+F_{77}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)+F_{5}\! \left(x \right)\\
F_{28}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{49}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)+F_{71}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{31}\! \left(x , y\right)+F_{51}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{32}\! \left(x , y\right) F_{49}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)+F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{36}\! \left(x \right) &= \frac{F_{37}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{37}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{4}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x , 1\right)\\
F_{41}\! \left(x , y\right) &= F_{42}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\
F_{43}\! \left(x , y\right) &= F_{42}\! \left(x , y\right) F_{49}\! \left(x , y\right)\\
F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{45}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{46}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)+F_{50}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{48}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{49}\! \left(x , y\right)\\
F_{49}\! \left(x , y\right) &= y x\\
F_{50}\! \left(x , y\right) &= -\frac{y \left(F_{44}\! \left(x , 1\right)-F_{44}\! \left(x , y\right)\right)}{-1+y}\\
F_{51}\! \left(x , y\right) &= y F_{52}\! \left(x , y\right)\\
F_{52}\! \left(x , y\right) &= F_{53}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{54}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= F_{55}\! \left(x , 1, y\right)\\
F_{55}\! \left(x , y , z\right) &= -\frac{-F_{56}\! \left(x , y z \right) y +F_{56}\! \left(x , z\right)}{-1+y}\\
F_{57}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{56}\! \left(x , y\right)\\
F_{57}\! \left(x , y\right) &= F_{58}\! \left(x , y\right)\\
F_{59}\! \left(x , y\right) &= F_{49}\! \left(x , y\right) F_{58}\! \left(x , y\right)\\
F_{59}\! \left(x , y\right) &= F_{60}\! \left(x , y\right)\\
F_{60}\! \left(x , y\right) &= F_{61}\! \left(x , y\right)+F_{64}\! \left(x , y\right)\\
F_{61}\! \left(x , y\right) &= F_{62}\! \left(x , y\right)\\
F_{62}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{63}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= -\frac{y \left(F_{18}\! \left(x , 1\right)-F_{18}\! \left(x , y\right)\right)}{-1+y}\\
F_{64}\! \left(x , y\right) &= F_{65}\! \left(x , y\right)\\
F_{65}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{66}\! \left(x , y\right)\\
F_{66}\! \left(x , y\right) &= F_{67}\! \left(x , y\right)+F_{68}\! \left(x , y\right)\\
F_{67}\! \left(x , y\right) &= -\frac{y \left(F_{60}\! \left(x , 1\right)-F_{60}\! \left(x , y\right)\right)}{-1+y}\\
F_{68}\! \left(x , y\right) &= F_{69}\! \left(x , y\right)\\
F_{69}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{70}\! \left(x , y\right)\\
F_{70}\! \left(x , y\right) &= -\frac{y \left(F_{46}\! \left(x , 1\right)-F_{46}\! \left(x , y\right)\right)}{-1+y}\\
F_{72}\! \left(x , y\right) &= F_{71}\! \left(x , y\right)+F_{75}\! \left(x , y\right)\\
F_{72}\! \left(x , y\right) &= F_{31}\! \left(x , y\right)+F_{73}\! \left(x , y\right)\\
F_{73}\! \left(x , y\right) &= F_{74}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= F_{49}\! \left(x , y\right) F_{54}\! \left(x , y\right)\\
F_{76}\! \left(x , y\right) &= F_{49}\! \left(x , y\right) F_{75}\! \left(x , y\right)\\
F_{76}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)\\
F_{77}\! \left(x , y\right) &= F_{78}\! \left(x , y\right)\\
F_{78}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)+F_{79}\! \left(x , y\right)\\
F_{79}\! \left(x , y\right) &= F_{80}\! \left(x , y\right)\\
F_{80}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{81}\! \left(x , y\right)\\
F_{81}\! \left(x , y\right) &= -\frac{-F_{42}\! \left(x , y\right) y +F_{42}\! \left(x , 1\right)}{-1+y}\\
F_{82}\! \left(x , y\right) &= F_{83}\! \left(x , y\right)\\
F_{84}\! \left(x , y\right) &= F_{83}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\
F_{85}\! \left(x , y\right) &= F_{100}\! \left(x , y\right)+F_{84}\! \left(x , y\right)\\
F_{86}\! \left(x , y\right) &= F_{85}\! \left(x , y\right)+F_{98}\! \left(x , y\right)\\
F_{87}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{86}\! \left(x , y\right)\\
F_{87}\! \left(x , y\right) &= F_{88}\! \left(x , y\right)\\
F_{88}\! \left(x , y\right) &= F_{4}\! \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) &= -\frac{-F_{41}\! \left(x , y\right) y +F_{41}\! \left(x , 1\right)}{-1+y}\\
F_{91}\! \left(x , y\right) &= y 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_{4}\! \left(x \right) F_{94}\! \left(x , y\right)\\
F_{94}\! \left(x , y\right) &= F_{95}\! \left(x , 1, y\right)\\
F_{95}\! \left(x , y , z\right) &= -\frac{-F_{96}\! \left(x , y z \right) y +F_{96}\! \left(x , z\right)}{-1+y}\\
F_{96}\! \left(x , y\right) &= -\frac{-F_{97}\! \left(x , y\right) y +F_{97}\! \left(x , 1\right)}{-1+y}\\
F_{97}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)+F_{42}\! \left(x , y\right)\\
F_{98}\! \left(x , y\right) &= y F_{99}\! \left(x , y\right)\\
F_{99}\! \left(x , y\right) &= F_{53}\! \left(x , y\right)\\
F_{101}\! \left(x , y\right) &= F_{100}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{101}\! \left(x , y\right) &= F_{79}\! \left(x , y\right)\\
F_{102}\! \left(x , y\right) &= F_{103}\! \left(x , y\right)+F_{21}\! \left(x , y\right)\\
F_{103}\! \left(x , y\right) &= F_{104}\! \left(x , y\right)\\
F_{104}\! \left(x , y\right) &= F_{105}\! \left(x , y\right) F_{49}\! \left(x , y\right)\\
F_{105}\! \left(x , y\right) &= F_{106}\! \left(x , 1, y\right)\\
F_{106}\! \left(x , y , z\right) &= -\frac{-F_{42}\! \left(x , y z \right) y +F_{42}\! \left(x , z\right)}{-1+y}\\
F_{107}\! \left(x , y\right) &= F_{108}\! \left(x , y\right)\\
F_{108}\! \left(x , y\right) &= F_{109}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{109}\! \left(x , y\right) &= F_{110}\! \left(x , y\right)+F_{91}\! \left(x , y\right)\\
F_{110}\! \left(x , y\right) &= -\frac{y \left(F_{34}\! \left(x , 1\right)-F_{34}\! \left(x , y\right)\right)}{-1+y}\\
\end{align*}\)