Av(12345, 12354, 12453, 13245, 13254, 13452, 14253, 14352)
Counting Sequence
1, 1, 2, 6, 24, 112, 568, 3034, 16783, 95121, 548544, 3203852, 18892878, 112235838, 670623291, ...
This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 107 rules.
Finding the specification took 28660 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_{25}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{100}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{25}\! \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_{29}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)+F_{96}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}, 1\right)\\
F_{10}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{0}, y_{0} y_{1}\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_{29}\! \left(x , y_{1}\right)+F_{8}\! \left(x , y_{1}\right)\\
F_{12}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{0}, y_{1}\right) F_{13}\! \left(x , y_{0}\right)\\
F_{13}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= F_{15}\! \left(x , y_{0}, y_{1}\right) F_{25}\! \left(x \right)\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{17}\! \left(x , y_{1}\right)+F_{28}\! \left(x \right)+F_{44}\! \left(x , y_{0}, y_{1}\right)+F_{46}\! \left(x , y_{0}, y_{1}\right)\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}\right) F_{15}\! \left(x , y_{0}, y_{1}\right)\\
F_{17}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{18}\! \left(x , y_{0}\right)\\
F_{18}\! \left(x , y_{0}\right) &= F_{19}\! \left(x , y_{0}, 1\right)\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{20}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{17}\! \left(x , y_{1}\right)+F_{21}\! \left(x , y_{0}, y_{1}\right)+F_{22}\! \left(x , y_{1}\right)+F_{26}\! \left(x , y_{0}, y_{1}\right)+F_{28}\! \left(x \right)\\
F_{21}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}\right) F_{20}\! \left(x , y_{0}, y_{1}\right)\\
F_{22}\! \left(x , y_{0}\right) &= F_{23}\! \left(x , y_{0}\right) F_{25}\! \left(x \right)\\
F_{23}\! \left(x , y_{0}\right) &= -\frac{-F_{24}\! \left(x , y_{0}\right) y_{0}+F_{24}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{24}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , y_{0}, 1\right)\\
F_{25}\! \left(x \right) &= x\\
F_{26}\! \left(x , y_{0}, y_{1}\right) &= F_{25}\! \left(x \right) F_{27}\! \left(x , y_{0}, y_{1}\right)\\
F_{27}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{15}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{15}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x , 1\right)\\
F_{29}\! \left(x , y_{0}\right) &= F_{25}\! \left(x \right) F_{30}\! \left(x , y_{0}\right)\\
F_{30}\! \left(x , y_{0}\right) &= F_{31}\! \left(x , y_{0}, 1\right)\\
F_{31}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{32}\! \left(x , y_{0}, y_{1}\right)+F_{33}\! \left(x , y_{1}\right)+F_{66}\! \left(x , y_{0}, y_{1}\right)+F_{71}\! \left(x , y_{0}, y_{1}\right)\\
F_{32}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}\right) F_{31}\! \left(x , y_{0}, y_{1}\right)\\
F_{33}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{34}\! \left(x , y_{0}\right)\\
F_{34}\! \left(x , y_{0}\right) &= F_{35}\! \left(x , y_{0}, 1\right)\\
F_{35}\! \left(x , y_{0}, y_{1}\right) &= F_{36}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{36}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{33}\! \left(x , y_{1}\right)+F_{37}\! \left(x , y_{0}, y_{1}\right)+F_{38}\! \left(x , y_{0}, y_{1}\right)+F_{64}\! \left(x , y_{0}, y_{1}\right)\\
F_{37}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}\right) F_{36}\! \left(x , y_{0}, y_{1}\right)\\
F_{38}\! \left(x , y_{0}, y_{1}\right) &= F_{25}\! \left(x \right) F_{39}\! \left(x , y_{0}, y_{1}\right)\\
F_{39}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{40}\! \left(x , y_{0}, y_{1}\right)+F_{41}\! \left(x , y_{1}\right)+F_{44}\! \left(x , y_{0}, y_{1}\right)+F_{46}\! \left(x , y_{0}, y_{1}\right)+F_{62}\! \left(x , y_{1}\right)\\
F_{40}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}\right) F_{39}\! \left(x , y_{0}, y_{1}\right)\\
F_{41}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{42}\! \left(x , y_{0}\right)\\
F_{42}\! \left(x , y_{0}\right) &= F_{43}\! \left(x , y_{0}, 1\right)\\
F_{43}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{10}\! \left(x , y_{0}, y_{1}\right) y_{0} y_{1}-F_{10}\! \left(x , y_{0}, \frac{1}{y_{0}}\right)}{y_{0} y_{1}-1}\\
F_{44}\! \left(x , y_{0}, y_{1}\right) &= F_{25}\! \left(x \right) F_{45}\! \left(x , y_{0}, y_{1}\right)\\
F_{45}\! \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_{46}\! \left(x , y_{0}, y_{1}\right) &= F_{47}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{47}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{25}\! \left(x \right) F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{28}\! \left(x \right)+F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{50}\! \left(x , y_{1}, y_{2}\right)+F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{13}\! \left(x , y_{0}\right) F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{50}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{0}, y_{1}\right)\\
F_{51}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{19}\! \left(x , y_{0}, 1\right) y_{0}-F_{19}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{13}\! \left(x , y_{2}\right) F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{54}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{54}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{54}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{55}\! \left(x , 1, y_{1}\right) y_{1}-F_{55}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{55}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{25}\! \left(x \right) F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{59}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{59}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}\\
F_{59}\! \left(x , y_{0}, y_{1}\right) &= F_{45}\! \left(x , y_{0}, y_{1}\right)\\
F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{25}\! \left(x \right) F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{48}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{62}\! \left(x , y_{0}\right) &= F_{25}\! \left(x \right) F_{63}\! \left(x , y_{0}\right)\\
F_{63}\! \left(x , y_{0}\right) &= -\frac{-F_{30}\! \left(x , y_{0}\right) y_{0}+F_{30}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{64}\! \left(x , y_{0}, y_{1}\right) &= F_{25}\! \left(x \right) F_{65}\! \left(x , y_{0}, y_{1}\right)\\
F_{65}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{31}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{31}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{66}\! \left(x , y_{0}, y_{1}\right) &= F_{25}\! \left(x \right) F_{67}\! \left(x , y_{0}, y_{1}\right)\\
F_{67}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{41}\! \left(x , y_{1}\right)+F_{44}\! \left(x , y_{0}, y_{1}\right)+F_{46}\! \left(x , y_{0}, y_{1}\right)+F_{68}\! \left(x , y_{0}, y_{1}\right)+F_{69}\! \left(x , y_{0}, y_{1}\right)\\
F_{68}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}\right) F_{67}\! \left(x , y_{0}, y_{1}\right)\\
F_{69}\! \left(x , y_{0}, y_{1}\right) &= F_{25}\! \left(x \right) F_{70}\! \left(x , y_{0}, y_{1}\right)\\
F_{70}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{63}\! \left(x , y_{0}\right) y_{0}-F_{63}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{71}\! \left(x , y_{0}, y_{1}\right) &= F_{25}\! \left(x \right) F_{72}\! \left(x , y_{0}, y_{1}\right)\\
F_{72}\! \left(x , y_{0}, y_{1}\right) &= F_{73}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{73}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{74}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{75}\! \left(x , y_{1}, y_{2}\right)+F_{77}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{81}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{94}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{74}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{13}\! \left(x , y_{0}\right) F_{73}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{75}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}\right) F_{76}\! \left(x , y_{0}, y_{1}\right)\\
F_{76}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{35}\! \left(x , y_{0}, 1\right) y_{0}-F_{35}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{77}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{13}\! \left(x , y_{2}\right) F_{78}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{78}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{79}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{79}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{79}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{80}\! \left(x , 1, y_{1}\right) y_{1}-F_{80}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{80}\! \left(x , y_{0}, y_{1}\right) &= F_{36}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{81}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{25}\! \left(x \right) F_{82}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{82}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{83}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{83}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{83}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{47}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{84}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{85}\! \left(x , y_{1}, y_{2}\right)+F_{87}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{91}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{84}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{13}\! \left(x , y_{0}\right) F_{83}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{85}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}\right) F_{86}\! \left(x , y_{0}, y_{1}\right)\\
F_{86}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{10}\! \left(x , y_{0}, 1\right) y_{0}-F_{10}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{87}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{13}\! \left(x , y_{2}\right) F_{88}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{88}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{89}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{89}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{89}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{90}\! \left(x , 1, y_{1}\right) y_{1}-F_{90}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{90}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{91}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{25}\! \left(x \right) F_{92}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{92}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{93}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{93}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{93}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{30}\! \left(x , y_{0}\right) y_{0}-F_{30}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{94}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{25}\! \left(x \right) F_{95}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{95}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{73}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{73}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{96}\! \left(x , y_{0}\right) &= F_{25}\! \left(x \right) F_{97}\! \left(x , y_{0}\right)\\
F_{97}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{17}\! \left(x , y_{0}\right)+F_{22}\! \left(x , y_{0}\right)+F_{28}\! \left(x \right)+F_{98}\! \left(x , y_{0}\right)\\
F_{98}\! \left(x , y_{0}\right) &= F_{25}\! \left(x \right) F_{99}\! \left(x , y_{0}\right)\\
F_{99}\! \left(x , y_{0}\right) &= -\frac{-F_{97}\! \left(x , y_{0}\right) y_{0}+F_{97}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{102}\! \left(x , 1\right)\\
F_{102}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{103}\! \left(x , y_{0}\right)+F_{105}\! \left(x , y_{0}\right)+F_{33}\! \left(x , y_{0}\right)\\
F_{103}\! \left(x , y_{0}\right) &= F_{104}\! \left(x , y_{0}\right) F_{25}\! \left(x \right)\\
F_{104}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{7}\! \left(x , y_{0}\right)+F_{7}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{105}\! \left(x , y_{0}\right) &= F_{106}\! \left(x , y_{0}\right) F_{25}\! \left(x \right)\\
F_{106}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{102}\! \left(x , y_{0}\right)+F_{102}\! \left(x , 1\right)}{-1+y_{0}}\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 193 rules.
Finding the specification took 111224 seconds.
This tree is too big to show here. Click to view tree on new page.
Copy 193 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_{48}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{6}\! \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_{9}\! \left(x , y_{0}\right) &= F_{39}\! \left(x , y_{0}\right) F_{8}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right)\\
F_{10}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , y_{0}\right) F_{39}\! \left(x , y_{0}\right)\\
F_{11}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right)+F_{176}\! \left(x , y_{0}\right)\\
F_{12}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right)+F_{4}\! \left(x \right)\\
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_{15}\! \left(x , y_{0}, y_{1}\right)\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= F_{16}\! \left(x , y_{0}, y_{1}\right) F_{39}\! \left(x , y_{1}\right)\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x , y_{0}, y_{1}\right)+F_{53}\! \left(x , y_{0}, y_{1}\right)\\
F_{17}\! \left(x , y_{0}, y_{1}\right) &= F_{140}\! \left(x , y_{0}, y_{1}\right)+F_{18}\! \left(x , y_{0}\right)\\
F_{18}\! \left(x , y_{0}\right) &= F_{19}\! \left(x , y_{0}\right)+F_{4}\! \left(x \right)\\
F_{19}\! \left(x , y_{0}\right) &= F_{20}\! \left(x , y_{0}\right)\\
F_{20}\! \left(x , y_{0}\right) &= F_{21}\! \left(x , y_{0}\right) F_{39}\! \left(x , y_{0}\right)\\
F_{21}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}, 1\right)\\
F_{22}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{23}\! \left(x , y_{0}, y_{1}\right) &= F_{24}\! \left(x , y_{0}, y_{1}\right)+F_{52}\! \left(x , y_{1}\right)\\
F_{24}\! \left(x , y_{0}, y_{1}\right) &= F_{25}\! \left(x , y_{1}\right)+F_{26}\! \left(x , y_{0}, y_{1}\right)\\
F_{25}\! \left(x , y_{0}\right) &= F_{17}\! \left(x , y_{0}, 1\right)\\
F_{26}\! \left(x , y_{0}, y_{1}\right) &= F_{27}\! \left(x , y_{0}, y_{1}\right)+F_{49}\! \left(x , y_{0}, y_{1}\right)\\
F_{27}\! \left(x , y_{0}, y_{1}\right) &= F_{28}\! \left(x , y_{0}, y_{1}\right)\\
F_{28}\! \left(x , y_{0}, y_{1}\right) &= F_{29}\! \left(x , y_{0}, y_{1}\right) F_{44}\! \left(x , y_{0}\right)\\
F_{29}\! \left(x , y_{0}, y_{1}\right) &= F_{30}\! \left(x , y_{0}, y_{1}\right)\\
F_{30}\! \left(x , y_{0}, y_{1}\right) &= F_{31}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{33}\! \left(x , y_{1}, y_{2}\right)+F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{33}\! \left(x , y_{0}, y_{1}\right) &= F_{34}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{35}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)\\
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{17}\! \left(x , y_{0}, y_{1}\right)+F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{37}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{39}\! \left(x , y_{2}\right)\\
F_{39}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{44}\! \left(x , y_{0}\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_{2}+F_{43}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{44}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{46}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}\\
F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{47}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{47}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= x\\
F_{49}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{50}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{50}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{50}\! \left(x , y_{0}, y_{1}\right) &= F_{51}\! \left(x , y_{0}, y_{1}\right)\\
F_{51}\! \left(x , y_{0}, y_{1}\right) &= F_{26}\! \left(x , y_{0}, y_{1}\right) F_{48}\! \left(x \right)\\
F_{52}\! \left(x , y_{0}\right) &= F_{53}\! \left(x , y_{0}, 1\right)\\
F_{53}\! \left(x , y_{0}, y_{1}\right) &= y_{1} F_{54}\! \left(x , y_{0}, y_{1}\right)\\
F_{54}\! \left(x , y_{0}, y_{1}\right) &= F_{55}\! \left(x , y_{0}, y_{1}\right)\\
F_{55}\! \left(x , y_{0}, y_{1}\right) &= F_{48}\! \left(x \right) F_{56}\! \left(x , y_{0}, y_{1}\right)\\
F_{56}\! \left(x , y_{0}, y_{1}\right) &= F_{57}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{58}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)\\
F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{173}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{59}\! \left(x , y_{1}, y_{2}\right)\\
F_{59}\! \left(x , y_{0}, y_{1}\right) &= F_{60}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{133}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{61}\! \left(x , y_{0}, y_{1}\right)\\
F_{61}\! \left(x , y_{0}, y_{1}\right) &= F_{140}\! \left(x , y_{0}, y_{1}\right)+F_{62}\! \left(x , y_{0}\right)\\
F_{62}\! \left(x , y_{0}\right) &= F_{4}\! \left(x \right)+F_{63}\! \left(x , y_{0}\right)\\
F_{63}\! \left(x , y_{0}\right) &= F_{64}\! \left(x , y_{0}\right)\\
F_{64}\! \left(x , y_{0}\right) &= F_{39}\! \left(x , y_{0}\right) F_{65}\! \left(x , y_{0}\right)\\
F_{65}\! \left(x , y_{0}\right) &= F_{66}\! \left(x , y_{0}, 1\right)\\
F_{66}\! \left(x , y_{0}, y_{1}\right) &= F_{67}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{67}\! \left(x , y_{0}, y_{1}\right) &= F_{68}\! \left(x , y_{1}\right)+F_{96}\! \left(x , y_{0}, y_{1}\right)\\
F_{68}\! \left(x , y_{0}\right) &= F_{69}\! \left(x , y_{0}, 1\right)\\
F_{69}\! \left(x , y_{0}, y_{1}\right) &= F_{61}\! \left(x , y_{0}, y_{1}\right)+F_{70}\! \left(x , y_{0}, y_{1}\right)\\
F_{71}\! \left(x , y_{0}, y_{1}\right) &= F_{164}\! \left(x , y_{0}, y_{1}\right)+F_{70}\! \left(x , y_{0}, y_{1}\right)\\
F_{71}\! \left(x , y_{0}, y_{1}\right) &= F_{72}\! \left(x , y_{1}\right)+F_{76}\! \left(x , y_{0}, y_{1}\right)\\
F_{72}\! \left(x , y_{0}\right) &= F_{73}\! \left(x , 1, y_{0}\right)\\
F_{73}\! \left(x , y_{0}, y_{1}\right) &= F_{74}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{74}\! \left(x , y_{0}, y_{1}\right) &= F_{75}\! \left(x , y_{0}, y_{1}\right)+F_{8}\! \left(x , y_{0}\right)\\
F_{75}\! \left(x , y_{0}, y_{1}\right) &= F_{37}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{76}\! \left(x , y_{0}, y_{1}\right) &= F_{77}\! \left(x , y_{0}, y_{1}\right)\\
F_{77}\! \left(x , y_{0}, y_{1}\right) &= F_{39}\! \left(x , y_{0}\right) F_{78}\! \left(x , y_{0}, y_{1}\right)\\
F_{78}\! \left(x , y_{0}, y_{1}\right) &= F_{79}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{79}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{F_{80}\! \left(x , y_{0}, 1, y_{2}\right) y_{2}-F_{80}\! \left(x , y_{0}, \frac{y_{1}}{y_{2}}, y_{2}\right) y_{1}}{-y_{2}+y_{1}}\\
F_{80}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{81}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)\\
F_{81}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{157}\! \left(x , y_{0}, y_{1}\right)+F_{82}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{82}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{83}\! \left(x , y_{0}, y_{1}\right)\\
F_{83}\! \left(x , y_{0}, y_{1}\right) &= F_{84}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{84}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{152}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{85}\! \left(x , y_{0}, y_{1}\right)\\
F_{85}\! \left(x , y_{0}, y_{1}\right) &= F_{86}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{87}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{151}\! \left(x , y_{1}, y_{2}\right)+F_{86}\! \left(x , y_{0}, y_{1}\right)\\
F_{88}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{137}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{87}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{88}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{132}\! \left(x , y_{1}, y_{2}\right)+F_{89}\! \left(x , y_{0}, y_{1}\right)\\
F_{67}\! \left(x , y_{0}, y_{1}\right) &= F_{89}\! \left(x , y_{0}, y_{1}\right)+F_{90}\! \left(x , y_{0}, y_{1}\right)\\
F_{90}\! \left(x , y_{0}, y_{1}\right) &= F_{91}\! \left(x , y_{0}, y_{1}\right)\\
F_{91}\! \left(x , y_{0}, y_{1}\right) &= F_{48}\! \left(x \right) F_{92}\! \left(x , y_{0}, y_{1}\right)\\
F_{92}\! \left(x , y_{0}, y_{1}\right) &= F_{127}\! \left(x , y_{1}\right)+F_{93}\! \left(x , y_{0}, y_{1}\right)\\
F_{93}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{94}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{94}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{94}\! \left(x , y_{0}, y_{1}\right) &= F_{95}\! \left(x , y_{1}\right)+F_{96}\! \left(x , y_{0}, y_{1}\right)\\
F_{95}\! \left(x , y_{0}\right) &= F_{71}\! \left(x , y_{0}, 1\right)\\
F_{96}\! \left(x , y_{0}, y_{1}\right) &= F_{97}\! \left(x , y_{0}, y_{1}\right)\\
F_{97}\! \left(x , y_{0}, y_{1}\right) &= F_{39}\! \left(x , y_{0}\right) F_{98}\! \left(x , y_{0}, y_{1}\right)\\
F_{98}\! \left(x , y_{0}, y_{1}\right) &= F_{99}\! \left(x , y_{0}, y_{1}\right)\\
F_{99}\! \left(x , y_{0}, y_{1}\right) &= F_{100}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{100}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{101}\! \left(x , y_{1}, y_{2}\right)+F_{124}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{102}\! \left(x , y_{0}, y_{1}\right) &= F_{101}\! \left(x , y_{0}, y_{1}\right)+F_{123}\! \left(x , y_{0}, y_{1}\right)\\
F_{102}\! \left(x , y_{0}, y_{1}\right) &= F_{103}\! \left(x , y_{0}, y_{1}\right)+F_{119}\! \left(x , y_{0}, y_{1}\right)\\
F_{103}\! \left(x , y_{0}, y_{1}\right) &= F_{104}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{104}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{105}\! \left(x , y_{0}, y_{1}\right)+F_{114}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{106}\! \left(x , y_{0}, y_{1}\right) &= F_{105}\! \left(x , y_{0}, y_{1}\right) F_{48}\! \left(x \right)\\
F_{106}\! \left(x , y_{0}, y_{1}\right) &= F_{107}\! \left(x , y_{0}, y_{1}\right)\\
F_{107}\! \left(x , y_{0}, y_{1}\right) &= F_{108}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{108}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{109}\! \left(x , y_{1}, y_{2}\right)+F_{111}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{109}\! \left(x , y_{0}, y_{1}\right) &= F_{110}\! \left(x , y_{0}, y_{1}\right)\\
F_{110}\! \left(x , y_{0}, y_{1}\right) &= F_{48}\! \left(x \right) F_{69}\! \left(x , y_{0}, y_{1}\right)\\
F_{111}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{112}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{112}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{113}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{39}\! \left(x , y_{0}\right)\\
F_{113}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{108}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{108}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{114}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{115}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{115}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{115}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{116}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{116}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{117}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{39}\! \left(x , y_{2}\right)\\
F_{117}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{114}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{118}\! \left(x , y_{0}, y_{1}\right)\\
F_{118}\! \left(x , y_{0}, y_{1}\right) &= F_{31}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{119}\! \left(x , y_{0}, y_{1}\right) &= F_{120}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{120}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{121}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{121}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{122}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{48}\! \left(x \right)\\
F_{122}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{100}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{100}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}\\
F_{123}\! \left(x , y_{0}, y_{1}\right) &= F_{124}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{124}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{125}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{125}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{126}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{44}\! \left(x , y_{0}\right)\\
F_{126}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{100}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{100}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{127}\! \left(x , y_{0}\right) &= F_{128}\! \left(x , y_{0}, 1\right)\\
F_{129}\! \left(x , y_{0}, y_{1}\right) &= F_{128}\! \left(x , y_{0}, y_{1}\right)+F_{131}\! \left(x , y_{0}, y_{1}\right)\\
F_{130}\! \left(x , y_{0}, y_{1}\right) &= F_{129}\! \left(x , y_{0}, y_{1}\right) F_{39}\! \left(x , y_{1}\right)\\
F_{130}\! \left(x , y_{0}, y_{1}\right) &= F_{70}\! \left(x , y_{0}, y_{1}\right)\\
F_{131}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{71}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{71}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{132}\! \left(x , y_{0}, y_{1}\right) &= F_{133}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{133}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{134}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{75}\! \left(x , y_{1}, y_{2}\right)\\
F_{134}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{135}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{135}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{136}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{39}\! \left(x , y_{0}\right)\\
F_{136}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{133}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{133}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}\\
F_{137}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{138}\! \left(x , y_{1}, y_{2}\right)+F_{49}\! \left(x , y_{0}, y_{1}\right)\\
F_{138}\! \left(x , y_{0}, y_{1}\right) &= F_{139}\! \left(x , y_{0}\right)+F_{141}\! \left(x , y_{0}, y_{1}\right)\\
F_{139}\! \left(x , y_{0}\right) &= F_{140}\! \left(x , y_{0}, 1\right)\\
F_{140}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{14}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{14}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{132}\! \left(x , y_{0}, y_{1}\right) &= F_{141}\! \left(x , y_{0}, y_{1}\right)+F_{142}\! \left(x , y_{0}, y_{1}\right)\\
F_{142}\! \left(x , y_{0}, y_{1}\right) &= F_{143}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{143}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{144}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{144}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{145}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{39}\! \left(x , y_{2}\right)\\
F_{145}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{146}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{146}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{147}\! \left(x , y_{0}, y_{1}\right)+F_{149}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{147}\! \left(x , y_{0}, y_{1}\right) &= F_{148}\! \left(x , y_{0}, y_{1}\right)\\
F_{148}\! \left(x , y_{0}, y_{1}\right) &= F_{18}\! \left(x , y_{1}\right)+F_{27}\! \left(x , y_{0}, y_{1}\right)\\
F_{149}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{150}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{150}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}\\
F_{150}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{143}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{151}\! \left(x , y_{0}, y_{1}\right) &= F_{142}\! \left(x , y_{0}, y_{1}\right)+F_{62}\! \left(x , y_{0}\right)\\
F_{152}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{153}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)\\
F_{153}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{154}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{154}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}\\
F_{154}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{155}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{155}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{156}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{39}\! \left(x , y_{2}\right)\\
F_{156}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{153}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{27}\! \left(x , y_{0}, y_{1}\right)\\
F_{157}\! \left(x , y_{0}, y_{1}\right) &= F_{158}\! \left(x , y_{0}, y_{1}\right)\\
F_{158}\! \left(x , y_{0}, y_{1}\right) &= F_{159}\! \left(x , y_{0}, y_{1}\right) F_{39}\! \left(x , y_{1}\right)\\
F_{159}\! \left(x , y_{0}, y_{1}\right) &= F_{128}\! \left(x , y_{0}, y_{1}\right)+F_{160}\! \left(x , y_{0}, y_{1}\right)\\
F_{160}\! \left(x , y_{0}, y_{1}\right) &= F_{161}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{161}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{162}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0} y_{1}-F_{162}\! \left(x , y_{0}, \frac{1}{y_{0}}, y_{2}\right)}{y_{0} y_{1}-1}\\
F_{162}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{163}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{170}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{163}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{164}\! \left(x , y_{0} y_{1}, y_{2}\right)+F_{84}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{164}\! \left(x , y_{0}, y_{1}\right) &= F_{165}\! \left(x , y_{0}, y_{1}\right)+F_{61}\! \left(x , y_{0}, y_{1}\right)\\
F_{165}\! \left(x , y_{0}, y_{1}\right) &= F_{166}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{166}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{167}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{167}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{168}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{39}\! \left(x , y_{2}\right)\\
F_{168}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{169}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{169}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{166}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{166}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}\\
F_{170}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{171}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{171}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{172}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{39}\! \left(x , y_{2}\right)\\
F_{172}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{128}\! \left(x , y_{0} y_{1}, y_{2}\right)+F_{161}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{173}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{174}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{174}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{175}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{39}\! \left(x , y_{0}\right)\\
F_{175}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-y_{1} F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{58}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}\\
F_{176}\! \left(x , y_{0}\right) &= F_{177}\! \left(x , y_{0}\right)\\
F_{177}\! \left(x , y_{0}\right) &= F_{178}\! \left(x , y_{0}\right) F_{39}\! \left(x , y_{0}\right)\\
F_{178}\! \left(x , y_{0}\right) &= F_{179}\! \left(x , y_{0}\right)+F_{180}\! \left(x , y_{0}\right)\\
F_{179}\! \left(x , y_{0}\right) &= F_{71}\! \left(x , 1, y_{0}\right)\\
F_{180}\! \left(x , y_{0}\right) &= y_{0} F_{181}\! \left(x , y_{0}\right)\\
F_{181}\! \left(x , y_{0}\right) &= F_{182}\! \left(x , 1, y_{0}\right)\\
F_{182}\! \left(x , y_{0}, y_{1}\right) &= F_{107}\! \left(x , y_{0}, y_{1}\right)+F_{183}\! \left(x , y_{0}, y_{1}\right)\\
F_{183}\! \left(x , y_{0}, y_{1}\right) &= F_{184}\! \left(x , y_{0}, y_{1}\right)\\
F_{184}\! \left(x , y_{0}, y_{1}\right) &= F_{185}\! \left(x , y_{0}, y_{1}\right) F_{39}\! \left(x , y_{1}\right)\\
F_{185}\! \left(x , y_{0}, y_{1}\right) &= F_{186}\! \left(x , y_{0}, y_{1}\right)+F_{192}\! \left(x , y_{0}, y_{1}\right)\\
F_{186}\! \left(x , y_{0}, y_{1}\right) &= F_{187}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{187}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{188}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{188}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{189}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{48}\! \left(x \right)\\
F_{189}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{190}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{190}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{191}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{191}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}\\
F_{191}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{168}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{192}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{182}\! \left(x , y_{0}, y_{1}\right)+F_{182}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
\end{align*}\)