Av(12345, 12354, 12435, 21345, 21354, 21435)
Counting Sequence
1, 1, 2, 6, 24, 114, 598, 3336, 19398, 116194, 711668, 4434970, 28024098, 179110692, 1155720558, ...
This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 45 rules.
Finding the specification took 25 seconds.
Copy 45 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_{22}\! \left(x \right) F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{22}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x , 1\right)\\
F_{6}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{35}\! \left(x , y_{0}\right)+F_{42}\! \left(x , y_{0}\right)+F_{7}\! \left(x , y_{0}\right)\\
F_{7}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{8}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= F_{9}\! \left(x , 1, y_{0}\right)\\
F_{9}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{10}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{11}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)\\
F_{11}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{14}\! \left(x , y_{0}, y_{1}\right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{41}\! \left(x , y_{0}, y_{1}\right)\\
F_{12}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}\right) F_{6}\! \left(x , y_{1}\right)\\
F_{13}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{1}\right) F_{15}\! \left(x , y_{0}, y_{1}\right)\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{9}\! \left(x , 1, y_{1}\right) y_{1}-F_{9}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x , y_{0}, y_{1}\right) F_{22}\! \left(x \right)\\
F_{17}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{18}\! \left(x , y_{0}\right) y_{0}-F_{18}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{18}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{19}\! \left(x , y_{0}\right)+F_{20}\! \left(x , y_{0}\right)+F_{23}\! \left(x , y_{0}\right)+F_{24}\! \left(x , y_{0}\right)\\
F_{19}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)\\
F_{20}\! \left(x , y_{0}\right) &= F_{21}\! \left(x , y_{0}\right) F_{22}\! \left(x \right)\\
F_{21}\! \left(x , y_{0}\right) &= -\frac{-F_{18}\! \left(x , y_{0}\right) y_{0}+F_{18}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{22}\! \left(x \right) &= x\\
F_{23}\! \left(x , y_{0}\right) &= F_{21}\! \left(x , y_{0}\right) F_{22}\! \left(x \right)\\
F_{24}\! \left(x , y_{0}\right) &= F_{22}\! \left(x \right) F_{25}\! \left(x , y_{0}\right)\\
F_{25}\! \left(x , y_{0}\right) &= F_{26}\! \left(x , y_{0}, 1\right)\\
F_{26}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{27}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{27}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{27}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{37}\! \left(x , y_{0}, y_{1}\right)+F_{39}\! \left(x , y_{0}, y_{1}\right)+F_{41}\! \left(x , y_{0}, y_{1}\right)\\
F_{28}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}\right) F_{29}\! \left(x , y_{1}\right)\\
F_{29}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{30}\! \left(x , y_{0}\right)+F_{33}\! \left(x , y_{0}\right)+F_{35}\! \left(x , y_{0}\right)\\
F_{30}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}\right)\\
F_{31}\! \left(x , y_{0}\right) &= F_{32}\! \left(x , 1, y_{0}\right)\\
F_{32}\! \left(x , y_{0}, y_{1}\right) &= F_{27}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{33}\! \left(x , y_{0}\right) &= F_{22}\! \left(x \right) F_{34}\! \left(x , y_{0}\right)\\
F_{34}\! \left(x , y_{0}\right) &= -\frac{-F_{6}\! \left(x , y_{0}\right) y_{0}+F_{6}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{35}\! \left(x , y_{0}\right) &= F_{22}\! \left(x \right) F_{36}\! \left(x , y_{0}\right)\\
F_{36}\! \left(x , y_{0}\right) &= -\frac{-F_{29}\! \left(x , y_{0}\right) y_{0}+F_{29}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{37}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{1}\right) F_{38}\! \left(x , y_{0}, y_{1}\right)\\
F_{38}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{32}\! \left(x , 1, y_{1}\right) y_{1}-F_{32}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{39}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x \right) F_{40}\! \left(x , y_{0}, y_{1}\right)\\
F_{40}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{1} F_{11}\! \left(x , y_{0}, y_{1}\right)+F_{11}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{41}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x \right) F_{26}\! \left(x , y_{0}, y_{1}\right)\\
F_{42}\! \left(x , y_{0}\right) &= F_{18}\! \left(x , y_{0}\right) F_{22}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{22}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{29}\! \left(x , 1\right)\\
\end{align*}\)
This specification was found using the strategy pack "Row Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 101 rules.
Finding the specification took 109 seconds.
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Copy 101 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_{21}\! \left(x \right) F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{99}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{21}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x \right)+F_{96}\! \left(x \right)+F_{97}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{21}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{8}\! \left(x , 1\right)\\
F_{8}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{51}\! \left(x , y\right)+F_{86}\! \left(x , y\right)+F_{9}\! \left(x , y\right)+F_{93}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{11}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= y x\\
F_{11}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{63}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{8}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{15}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)+F_{85}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)+F_{7}\! \left(x \right)\\
F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= y F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{22}\! \left(x \right)+F_{24}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{19}\! \left(x \right) &= 0\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{21}\! \left(x \right) &= x\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{18}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{18}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{21}\! \left(x \right) F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x , 1\right)\\
F_{28}\! \left(x , y\right) &= -\frac{-y F_{29}\! \left(x , y\right)+F_{29}\! \left(x , 1\right)}{-1+y}\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)+F_{37}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{31}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{32}\! \left(x , y\right)+F_{64}\! \left(x , y\right)+F_{79}\! \left(x , y\right)+F_{83}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= -\frac{-F_{35}\! \left(x , y\right) y +F_{35}\! \left(x , 1\right)}{-1+y}\\
F_{35}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{36}\! \left(x , y\right)+F_{62}\! \left(x , y\right)+F_{63}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{38}\! \left(x , y\right)+F_{39}\! \left(x , y\right)+F_{43}\! \left(x , y\right)+F_{51}\! \left(x , y\right)\\
F_{38}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{35}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{40}\! \left(x , y\right)\\
F_{40}\! \left(x , y\right) &= F_{37}\! \left(x , y\right)+F_{41}\! \left(x , y\right)\\
F_{41}\! \left(x , y\right) &= F_{42}\! \left(x , y\right)\\
F_{42}\! \left(x , y\right) &= y F_{29}\! \left(x , y\right)\\
F_{43}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{44}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{44}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{45}\! \left(x , y\right)+F_{47}\! \left(x , y\right)+F_{48}\! \left(x , y\right)+F_{49}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= -\frac{-F_{11}\! \left(x , y\right) y +F_{11}\! \left(x , 1\right)}{-1+y}\\
F_{47}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{48}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{49}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{50}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= -\frac{-F_{34}\! \left(x , y\right) y +F_{34}\! \left(x , 1\right)}{-1+y}\\
F_{51}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{52}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{52}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{49}\! \left(x , y\right)+F_{53}\! \left(x , y\right)+F_{54}\! \left(x , y\right)+F_{60}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{55}\! \left(x , y\right)\\
F_{55}\! \left(x , y\right) &= F_{56}\! \left(x \right)+F_{57}\! \left(x , y\right)\\
F_{56}\! \left(x \right) &= F_{37}\! \left(x , 1\right)\\
F_{57}\! \left(x , y\right) &= F_{58}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= y F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{29}\! \left(x , 1\right)\\
F_{60}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{61}\! \left(x , y\right)\\
F_{61}\! \left(x , y\right) &= -\frac{-F_{46}\! \left(x , y\right) y +F_{46}\! \left(x , 1\right)}{-1+y}\\
F_{62}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{46}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{34}\! \left(x , y\right)\\
F_{64}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{65}\! \left(x , y\right)\\
F_{65}\! \left(x , y\right) &= -\frac{-y F_{66}\! \left(x , y\right)+F_{66}\! \left(x , 1\right)}{-1+y}\\
F_{66}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{32}\! \left(x , y\right)+F_{67}\! \left(x , y\right)+F_{68}\! \left(x , y\right)+F_{81}\! \left(x , y\right)\\
F_{67}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{35}\! \left(x , y\right)\\
F_{68}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{69}\! \left(x , y\right)\\
F_{69}\! \left(x , y\right) &= -\frac{-F_{70}\! \left(x , y\right) y +F_{70}\! \left(x , 1\right)}{-1+y}\\
F_{70}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{71}\! \left(x , y\right)+F_{72}\! \left(x , y\right)+F_{76}\! \left(x , y\right)+F_{81}\! \left(x , y\right)\\
F_{71}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{73}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{72}\! \left(x , y\right)+F_{74}\! \left(x , y\right)+F_{76}\! \left(x , y\right)+F_{79}\! \left(x , y\right)\\
F_{73}\! \left(x , y\right) &= F_{46}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{75}\! \left(x , y\right)\\
F_{75}\! \left(x , y\right) &= -\frac{-F_{70}\! \left(x , y\right) y +F_{70}\! \left(x , 1\right)}{-1+y}\\
F_{76}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{77}\! \left(x , y\right)\\
F_{77}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)+F_{78}\! \left(x , y\right)\\
F_{78}\! \left(x , y\right) &= F_{18}\! \left(x \right)\\
F_{79}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{80}\! \left(x , y\right)\\
F_{80}\! \left(x , y\right) &= F_{50}\! \left(x , y\right)\\
F_{81}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{82}\! \left(x , y\right)\\
F_{82}\! \left(x , y\right) &= -\frac{-y F_{66}\! \left(x , y\right)+F_{66}\! \left(x , 1\right)}{-1+y}\\
F_{83}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{84}\! \left(x , y\right)\\
F_{84}\! \left(x , y\right) &= F_{61}\! \left(x , y\right)\\
F_{85}\! \left(x , y\right) &= F_{18}\! \left(x \right)\\
F_{86}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{87}\! \left(x , y\right)\\
F_{87}\! \left(x , y\right) &= F_{8}\! \left(x , y\right)+F_{88}\! \left(x , y\right)\\
F_{88}\! \left(x , y\right) &= F_{89}\! \left(x , y\right)\\
F_{89}\! \left(x , y\right) &= y F_{90}\! \left(x , y\right)\\
F_{90}\! \left(x , y\right) &= F_{91}\! \left(x , y\right)\\
F_{92}\! \left(x , y\right) &= F_{8}\! \left(x , y\right)+F_{91}\! \left(x , y\right)\\
F_{72}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{92}\! \left(x , y\right)\\
F_{93}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{94}\! \left(x , y\right)\\
F_{94}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)+F_{95}\! \left(x , y\right)\\
F_{95}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)\\
F_{96}\! \left(x \right) &= F_{21}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{21}\! \left(x \right) F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{34}\! \left(x , 1\right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{35}\! \left(x , 1\right)\\
\end{align*}\)
This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 44 rules.
Finding the specification took 21 seconds.
Copy 44 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_{21}\! \left(x \right) F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{21}\! \left(x \right) F_{5}\! \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_{34}\! \left(x , y\right)+F_{41}\! \left(x , y\right)+F_{7}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{8}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= F_{9}\! \left(x , 1, y\right)\\
F_{9}\! \left(x , y , z\right) &= F_{10}\! \left(x , y z , z\right)\\
F_{10}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x , y , z\right)+F_{13}\! \left(x , y , z\right)+F_{15}\! \left(x , y , z\right)+F_{40}\! \left(x , y , z\right)\\
F_{11}\! \left(x , y , z\right) &= F_{12}\! \left(x , y\right) F_{6}\! \left(x , z\right)\\
F_{12}\! \left(x , y\right) &= y x\\
F_{13}\! \left(x , y , z\right) &= F_{12}\! \left(x , z\right) F_{14}\! \left(x , y , z\right)\\
F_{14}\! \left(x , y , z\right) &= -\frac{F_{9}\! \left(x , 1, z\right) z -F_{9}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}\\
F_{15}\! \left(x , y , z\right) &= F_{16}\! \left(x , y , z\right) F_{21}\! \left(x \right)\\
F_{16}\! \left(x , y , z\right) &= \frac{F_{17}\! \left(x , y\right) y -F_{17}\! \left(x , z\right) z}{-z +y}\\
F_{17}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{19}\! \left(x , y\right)+F_{22}\! \left(x , y\right)+F_{23}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{20}\! \left(x , y\right) &= -\frac{-F_{17}\! \left(x , y\right) y +F_{17}\! \left(x , 1\right)}{-1+y}\\
F_{21}\! \left(x \right) &= x\\
F_{22}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{23}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{24}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , y , 1\right)\\
F_{25}\! \left(x , y , z\right) &= -\frac{-F_{26}\! \left(x , y , z\right) z +F_{26}\! \left(x , y , 1\right)}{-1+z}\\
F_{26}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{27}\! \left(x , y , z\right)+F_{36}\! \left(x , y , z\right)+F_{38}\! \left(x , y , z\right)+F_{40}\! \left(x , y , z\right)\\
F_{27}\! \left(x , y , z\right) &= F_{12}\! \left(x , y\right) F_{28}\! \left(x , z\right)\\
F_{28}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{29}\! \left(x , y\right)+F_{32}\! \left(x , y\right)+F_{34}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{30}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{31}\! \left(x , 1, y\right)\\
F_{31}\! \left(x , y , z\right) &= F_{26}\! \left(x , y z , z\right)\\
F_{32}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{33}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= -\frac{-F_{6}\! \left(x , y\right) y +F_{6}\! \left(x , 1\right)}{-1+y}\\
F_{34}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{35}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= -\frac{-F_{28}\! \left(x , y\right) y +F_{28}\! \left(x , 1\right)}{-1+y}\\
F_{36}\! \left(x , y , z\right) &= F_{12}\! \left(x , z\right) F_{37}\! \left(x , y , z\right)\\
F_{37}\! \left(x , y , z\right) &= -\frac{F_{31}\! \left(x , 1, z\right) z -F_{31}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}\\
F_{38}\! \left(x , y , z\right) &= F_{21}\! \left(x \right) F_{39}\! \left(x , y , z\right)\\
F_{39}\! \left(x , y , z\right) &= -\frac{-z F_{10}\! \left(x , y , z\right)+F_{10}\! \left(x , y , 1\right)}{-1+z}\\
F_{40}\! \left(x , y , z\right) &= F_{21}\! \left(x \right) F_{25}\! \left(x , y , z\right)\\
F_{41}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{21}\! \left(x \right) F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{28}\! \left(x , 1\right)\\
\end{align*}\)