Av(12543, 13542, 14532, 15432, 21543, 23541, 24531, 25431, 31542, 32541)
Counting Sequence
1, 1, 2, 6, 24, 110, 542, 2794, 14870, 81078, 450610, 2543572, 14543680, 84062974, 490389134, ...
This specification was found using the strategy pack "Col Placements Tracked Fusion" and has 57 rules.
Finding the specification took 18 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_{5}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{5}\! \left(x \right) &= x\\
F_{6}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{46}\! \left(x \right)+F_{48}\! \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_{5}\! \left(x \right) F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{43}\! \left(x , y\right)+F_{44}\! \left(x , y\right)+F_{45}\! \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) &= -\frac{-F_{12}\! \left(x , y\right) y +F_{12}\! \left(x , 1\right)}{-1+y}\\
F_{12}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{40}\! \left(x , y\right)+F_{41}\! \left(x , y\right)+F_{42}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{14}\! \left(x , y\right) &= -\frac{-F_{15}\! \left(x , y\right) y +F_{15}\! \left(x , 1\right)}{-1+y}\\
F_{15}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{38}\! \left(x , y\right)+F_{39}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{17}\! \left(x , y\right) &= -\frac{-F_{9}\! \left(x , y\right) y +F_{9}\! \left(x , 1\right)}{-1+y}\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{19}\! \left(x , y\right) &= -\frac{-y F_{20}\! \left(x , y\right)+F_{20}\! \left(x , 1\right)}{-1+y}\\
F_{20}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)+F_{29}\! \left(x , y\right)+F_{36}\! \left(x , y\right)+F_{37}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{22}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{22}\! \left(x , y\right) &= -\frac{-F_{23}\! \left(x , y\right) y +F_{23}\! \left(x , 1\right)}{-1+y}\\
F_{23}\! \left(x , y\right) &= -\frac{-F_{24}\! \left(x , y\right) y +F_{24}\! \left(x , 1\right)}{-1+y}\\
F_{24}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)+F_{26}\! \left(x , y\right)+F_{27}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{26}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{27}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= y x\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{30}\! \left(x , y\right) &= -\frac{-y F_{31}\! \left(x , y\right)+F_{31}\! \left(x , 1\right)}{-1+y}\\
F_{31}\! \left(x , y\right) &= -\frac{-F_{32}\! \left(x , y\right) y +F_{32}\! \left(x , 1\right)}{-1+y}\\
F_{32}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)+F_{34}\! \left(x , y\right)+F_{35}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{34}\! \left(x , y\right) &= F_{31}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{35}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{32}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{37}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\
F_{38}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{39}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{31}\! \left(x , y\right)\\
F_{40}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{41}\! \left(x , y\right) &= F_{22}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{42}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\
F_{43}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{44}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{45}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x , 1\right)\\
F_{47}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x , 1\right)\\
F_{50}\! \left(x , y\right) &= -\frac{-F_{32}\! \left(x , y\right) y +F_{32}\! \left(x , 1\right)}{-1+y}\\
F_{51}\! \left(x \right) &= F_{5}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x , 1\right)\\
F_{53}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)+F_{26}\! \left(x , y\right)+F_{54}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{55}\! \left(x , y\right)\\
F_{55}\! \left(x , y\right) &= F_{56}\! \left(x , 1, y\right)\\
F_{56}\! \left(x , y , z\right) &= -\frac{-F_{24}\! \left(x , y z \right) y +F_{24}\! \left(x , z\right)}{-1+y}\\
\end{align*}\)
This specification was found using the strategy pack "Col Placements Tracked Fusion" and has 71 rules.
Finding the specification took 47 seconds.
Copy 71 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_{5}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{5}\! \left(x \right) &= x\\
F_{6}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{60}\! \left(x \right)+F_{62}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{8}\! \left(x , 1\right)\\
F_{8}\! \left(x , y_{0}\right) &= F_{5}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}\right)+F_{55}\! \left(x , y_{0}\right)+F_{57}\! \left(x , y_{0}\right)+F_{59}\! \left(x , y_{0}\right)\\
F_{10}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , y_{0}\right) F_{5}\! \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) &= \frac{F_{13}\! \left(x , y_{0}\right) y_{0}-F_{13}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{13}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , 1, y_{0}\right)\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}, y_{1}\right)+F_{50}\! \left(x , y_{0}, y_{1}\right)+F_{51}\! \left(x , y_{0}, y_{1}\right)+F_{54}\! \left(x , y_{1}, y_{0}\right)\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= F_{16}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{17}\! \left(x , y_{0}\right) y_{0}-F_{17}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{17}\! \left(x , y_{0}\right) &= F_{18}\! \left(x , 1, y_{0}\right)\\
F_{18}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{19}\! \left(x , y_{0}, y_{1}\right)+F_{21}\! \left(x , y_{0}, y_{1}\right)+F_{46}\! \left(x , y_{0}, y_{1}\right)+F_{49}\! \left(x , y_{1}, y_{0}\right)\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)\\
F_{20}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{9}\! \left(x , y_{0}\right) y_{0}-F_{9}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{21}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)\\
F_{22}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{23}\! \left(x , y_{0}\right) y_{0}-F_{23}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{23}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{24}\! \left(x , y_{0}\right)+F_{33}\! \left(x , y_{0}\right)+F_{43}\! \left(x , y_{0}\right)+F_{45}\! \left(x , y_{0}\right)\\
F_{24}\! \left(x , y_{0}\right) &= F_{25}\! \left(x , 1, y_{0}\right)\\
F_{25}\! \left(x , y_{0}, y_{1}\right) &= F_{26}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)\\
F_{26}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{27}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{27}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{27}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{28}\! \left(x , y_{0}\right) y_{0}-y_{1} F_{28}\! \left(x , y_{1}\right)}{-y_{1}+y_{0}}\\
F_{28}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{29}\! \left(x , y_{0}\right)+F_{30}\! \left(x , y_{0}\right)+F_{31}\! \left(x , y_{0}\right)\\
F_{29}\! \left(x , y_{0}\right) &= F_{17}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)\\
F_{30}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)\\
F_{31}\! \left(x , y_{0}\right) &= F_{28}\! \left(x , y_{0}\right) F_{32}\! \left(x , y_{0}\right)\\
F_{32}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{33}\! \left(x , y_{0}\right) &= F_{34}\! \left(x , 1, y_{0}\right)\\
F_{34}\! \left(x , y_{0}, y_{1}\right) &= F_{35}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)\\
F_{35}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{36}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{36}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{36}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{37}\! \left(x , y_{0}\right) y_{0}-F_{37}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{37}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{38}\! \left(x , y_{0}\right)+F_{40}\! \left(x , y_{0}\right)+F_{42}\! \left(x , y_{0}\right)\\
F_{38}\! \left(x , y_{0}\right) &= F_{39}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)\\
F_{39}\! \left(x , y_{0}\right) &= -\frac{-F_{28}\! \left(x , y_{0}\right) y_{0}+F_{28}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{40}\! \left(x , y_{0}\right) &= F_{41}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)\\
F_{41}\! \left(x , y_{0}\right) &= -\frac{-F_{37}\! \left(x , y_{0}\right) y_{0}+F_{37}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{42}\! \left(x , y_{0}\right) &= F_{32}\! \left(x , y_{0}\right) F_{37}\! \left(x , y_{0}\right)\\
F_{43}\! \left(x , y_{0}\right) &= F_{44}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)\\
F_{44}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , 1, y_{0}\right)\\
F_{45}\! \left(x , y_{0}\right) &= F_{23}\! \left(x , y_{0}\right) F_{32}\! \left(x , y_{0}\right)\\
F_{46}\! \left(x , y_{0}, y_{1}\right) &= F_{32}\! \left(x , y_{0}\right) F_{47}\! \left(x , y_{0}, y_{1}\right)\\
F_{47}\! \left(x , y_{0}, y_{1}\right) &= F_{48}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{36}\! \left(x , y_{0} y_{1}, y_{2}\right) y_{0}+F_{36}\! \left(x , y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{49}\! \left(x , y_{0}, y_{1}\right) &= F_{32}\! \left(x , y_{0}\right) F_{36}\! \left(x , y_{1}, y_{0}\right)\\
F_{50}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}, y_{1}\right) F_{5}\! \left(x \right)\\
F_{51}\! \left(x , y_{0}, y_{1}\right) &= F_{32}\! \left(x , y_{0}\right) F_{52}\! \left(x , y_{0}, y_{1}\right)\\
F_{52}\! \left(x , y_{0}, y_{1}\right) &= F_{53}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{27}\! \left(x , y_{0} y_{1}, y_{2}\right) y_{0}+F_{27}\! \left(x , y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{54}\! \left(x , y_{0}, y_{1}\right) &= F_{27}\! \left(x , y_{1}, y_{0}\right) F_{32}\! \left(x , y_{0}\right)\\
F_{55}\! \left(x , y_{0}\right) &= F_{5}\! \left(x \right) F_{56}\! \left(x , y_{0}\right)\\
F_{56}\! \left(x , y_{0}\right) &= F_{16}\! \left(x , 1, y_{0}\right)\\
F_{57}\! \left(x , y_{0}\right) &= F_{5}\! \left(x \right) F_{58}\! \left(x , y_{0}\right)\\
F_{58}\! \left(x , y_{0}\right) &= F_{20}\! \left(x , 1, y_{0}\right)\\
F_{59}\! \left(x , y_{0}\right) &= F_{32}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{60}\! \left(x \right) &= F_{61}\! \left(x , 1\right)\\
F_{61}\! \left(x , y_{0}\right) &= F_{23}\! \left(x , y_{0}\right) F_{5}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{5}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x , 1\right)\\
F_{64}\! \left(x , y_{0}\right) &= -\frac{-F_{37}\! \left(x , y_{0}\right) y_{0}+F_{37}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{65}\! \left(x \right) &= F_{5}\! \left(x \right) F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x , 1\right)\\
F_{67}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{29}\! \left(x , y_{0}\right)+F_{30}\! \left(x , y_{0}\right)+F_{68}\! \left(x , y_{0}\right)\\
F_{68}\! \left(x , y_{0}\right) &= F_{32}\! \left(x , y_{0}\right) F_{69}\! \left(x , y_{0}\right)\\
F_{69}\! \left(x , y_{0}\right) &= F_{70}\! \left(x , 1, y_{0}\right)\\
F_{70}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{28}\! \left(x , y_{0} y_{1}\right) y_{0}+F_{28}\! \left(x , y_{1}\right)}{-1+y_{0}}\\
\end{align*}\)
This specification was found using the strategy pack "Col Placements Tracked Fusion" and has 69 rules.
Finding the specification took 30 seconds.
Copy 69 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_{5}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{5}\! \left(x \right) &= x\\
F_{6}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{58}\! \left(x \right)+F_{60}\! \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_{9}\! \left(x , 1, y\right)\\
F_{9}\! \left(x , y , z\right) &= F_{10}\! \left(x , y , z\right) F_{5}\! \left(x \right)\\
F_{10}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x , y , z\right)+F_{55}\! \left(x , y , z\right)+F_{56}\! \left(x , y , z\right)+F_{57}\! \left(x , y , z\right)\\
F_{11}\! \left(x , y , z\right) &= F_{12}\! \left(x , y , z\right) F_{5}\! \left(x \right)\\
F_{12}\! \left(x , y , z\right) &= \frac{F_{13}\! \left(x , y\right) y -F_{13}\! \left(x , z\right) z}{-z +y}\\
F_{13}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{50}\! \left(x , y\right)+F_{52}\! \left(x , y\right)+F_{53}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , 1, y\right)\\
F_{16}\! \left(x , y , z\right) &= \frac{y F_{17}\! \left(x , y\right)-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_{22}\! \left(x , y\right)+F_{38}\! \left(x , y\right)+F_{49}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , 1, y\right)\\
F_{20}\! \left(x , y , z\right) &= \frac{F_{21}\! \left(x , y , 1\right) y -F_{21}\! \left(x , y , \frac{z}{y}\right) z}{-z +y}\\
F_{21}\! \left(x , y , z\right) &= F_{10}\! \left(x , y , y z \right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{23}\! \left(x , y\right) &= -\frac{-F_{24}\! \left(x , y\right) y +F_{24}\! \left(x , 1\right)}{-1+y}\\
F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , 1, y\right)\\
F_{25}\! \left(x , y , z\right) &= -\frac{-F_{26}\! \left(x , y , z\right) y +F_{26}\! \left(x , 1, z\right)}{-1+y}\\
F_{26}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{27}\! \left(x , y , z\right)+F_{34}\! \left(x , y , z\right)+F_{37}\! \left(x , y , z\right)\\
F_{27}\! \left(x , y , z\right) &= F_{28}\! \left(x , y , z\right) F_{5}\! \left(x \right)\\
F_{28}\! \left(x , y , z\right) &= \frac{F_{29}\! \left(x , y\right) y -z F_{29}\! \left(x , z\right)}{-z +y}\\
F_{29}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{30}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{32}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{31}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{32}\! \left(x , y\right) &= F_{29}\! \left(x , y\right) F_{33}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= y x\\
F_{34}\! \left(x , y , z\right) &= F_{33}\! \left(x , y\right) F_{35}\! \left(x , y , z\right)\\
F_{35}\! \left(x , y , z\right) &= \frac{F_{36}\! \left(x , y , 1\right) y -F_{36}\! \left(x , y , \frac{z}{y}\right) z}{-z +y}\\
F_{36}\! \left(x , y , z\right) &= F_{26}\! \left(x , y , y z \right)\\
F_{37}\! \left(x , y , z\right) &= F_{26}\! \left(x , y , z\right) F_{33}\! \left(x , z\right)\\
F_{38}\! \left(x , y\right) &= F_{39}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{40}\! \left(x , y\right) &= F_{39}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{41}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{40}\! \left(x , y\right)+F_{43}\! \left(x , y\right)+F_{46}\! \left(x \right)+F_{48}\! \left(x , y\right)\\
F_{41}\! \left(x , y\right) &= -\frac{-F_{42}\! \left(x , y\right) y +F_{42}\! \left(x , 1\right)}{-1+y}\\
F_{42}\! \left(x , y\right) &= F_{26}\! \left(x , 1, y\right)\\
F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{44}\! \left(x , y\right) &= F_{45}\! \left(x , 1, y\right)\\
F_{45}\! \left(x , y , z\right) &= -\frac{-F_{28}\! \left(x , y , z\right) y +F_{28}\! \left(x , 1, z\right)}{-1+y}\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x , 1\right)\\
F_{47}\! \left(x , y\right) &= F_{33}\! \left(x , y\right) F_{42}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= F_{33}\! \left(x , y\right) F_{41}\! \left(x , y\right)\\
F_{49}\! \left(x , y\right) &= F_{33}\! \left(x , y\right) F_{41}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{51}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= F_{12}\! \left(x , 1, y\right)\\
F_{52}\! \left(x , y\right) &= F_{44}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{53}\! \left(x , y\right) &= F_{33}\! \left(x , y\right) F_{54}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= -\frac{-F_{29}\! \left(x , y\right) y +F_{29}\! \left(x , 1\right)}{-1+y}\\
F_{55}\! \left(x , y , z\right) &= F_{16}\! \left(x , y , z\right) F_{5}\! \left(x \right)\\
F_{56}\! \left(x , y , z\right) &= F_{20}\! \left(x , y , z\right) F_{33}\! \left(x , y\right)\\
F_{57}\! \left(x , y , z\right) &= F_{10}\! \left(x , y , z\right) F_{33}\! \left(x , z\right)\\
F_{58}\! \left(x \right) &= F_{59}\! \left(x , 1\right)\\
F_{59}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{5}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{62}\! \left(x , 1\right)\\
F_{62}\! \left(x , y\right) &= -\frac{-F_{42}\! \left(x , y\right) y +F_{42}\! \left(x , 1\right)}{-1+y}\\
F_{63}\! \left(x \right) &= F_{5}\! \left(x \right) F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{65}\! \left(x , 1\right)\\
F_{65}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{30}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{66}\! \left(x , y\right)\\
F_{66}\! \left(x , y\right) &= F_{33}\! \left(x , y\right) F_{67}\! \left(x , y\right)\\
F_{67}\! \left(x , y\right) &= F_{68}\! \left(x , 1, y\right)\\
F_{68}\! \left(x , y , z\right) &= -\frac{-F_{29}\! \left(x , y z \right) y +F_{29}\! \left(x , z\right)}{-1+y}\\
\end{align*}\)