Av(12543, 13542, 14532, 15432, 21543, 23541, 24531, 25431, 31542, 32541)
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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.

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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_{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.

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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_{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.

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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_{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*}\)