Av(12345, 12435, 13245, 13425, 13452, 14235, 14325, 14352)
Counting Sequence
1, 1, 2, 6, 24, 112, 568, 3040, 16933, 97295, 572976, 3441666, 21009275, 129977901, 813245131, ...
This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 47 rules.
Finding the specification took 122 seconds.
Copy 47 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_{30}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x , 1\right)\\
F_{5}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{45}\! \left(x , y_{0}\right)+F_{6}\! \left(x , y_{0}\right)\\
F_{6}\! \left(x , y_{0}\right) &= F_{15}\! \left(x , y_{0}\right) F_{7}\! \left(x , y_{0}\right)\\
F_{7}\! \left(x , y_{0}\right) &= F_{8}\! \left(x , y_{0}, 1\right)\\
F_{8}\! \left(x , y_{0}, y_{1}\right) &= F_{9}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{9}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}, y_{1}\right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{18}\! \left(x , y_{0}, y_{1}\right)\\
F_{10}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{0}, y_{1}\right)\\
F_{11}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}\right) F_{15}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}, y_{1}\right)\\
F_{12}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}\right)\\
F_{13}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right)\\
F_{14}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right) F_{15}\! \left(x , y_{0}\right)\\
F_{15}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x , y_{0}, y_{1}\right)\\
F_{17}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}\right) F_{15}\! \left(x , y_{1}\right) F_{7}\! \left(x , y_{1}\right)\\
F_{18}\! \left(x , y_{0}, y_{1}\right) &= F_{19}\! \left(x , y_{0}, y_{1}\right) F_{30}\! \left(x \right)\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{20}\! \left(x , y_{0}, y_{1}\right)+F_{22}\! \left(x , y_{0}, y_{1}\right)+F_{26}\! \left(x , y_{0}, y_{1}\right)+F_{31}\! \left(x , y_{0}, y_{1}\right)\\
F_{20}\! \left(x , y_{0}, y_{1}\right) &= F_{21}\! \left(x , y_{0}, y_{1}\right)\\
F_{21}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}\right) F_{15}\! \left(x , y_{0}\right) F_{19}\! \left(x , y_{0}, y_{1}\right)\\
F_{22}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , y_{0}, y_{1}\right)\\
F_{23}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}\right) F_{15}\! \left(x , y_{1}\right) F_{24}\! \left(x , y_{1}\right)\\
F_{24}\! \left(x , y_{0}\right) &= F_{25}\! \left(x , y_{0}, 1\right)\\
F_{25}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{8}\! \left(x , y_{0}, y_{1}\right) y_{0} y_{1}-F_{8}\! \left(x , y_{0}, \frac{1}{y_{0}}\right)}{y_{0} y_{1}-1}\\
F_{26}\! \left(x , y_{0}, y_{1}\right) &= F_{27}\! \left(x , y_{0}, y_{1}\right) F_{30}\! \left(x \right)\\
F_{27}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{28}\! \left(x , y_{0}\right) y_{0}-F_{28}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{28}\! \left(x , y_{0}\right) &= -\frac{-F_{29}\! \left(x , y_{0}\right) y_{0}+F_{29}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{29}\! \left(x , y_{0}\right) &= F_{9}\! \left(x , y_{0}, 1\right)\\
F_{30}\! \left(x \right) &= x\\
F_{31}\! \left(x , y_{0}, y_{1}\right) &= F_{30}\! \left(x \right) F_{32}\! \left(x , y_{0}, y_{1}\right)\\
F_{32}\! \left(x , y_{0}, y_{1}\right) &= F_{33}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{34}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{12}\! \left(x , y_{0}\right) F_{15}\! \left(x , y_{0}\right) F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
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_{12}\! \left(x , y_{0}\right) F_{15}\! \left(x , y_{1}\right) F_{39}\! \left(x , y_{1}, y_{2}\right)\\
F_{39}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{8}\! \left(x , y_{0}, 1\right) y_{0}-y_{1} F_{8}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}\\
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{15}\! \left(x , 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) &= \frac{y_{0} F_{42}\! \left(x , y_{0}, y_{2}\right)-F_{42}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{42}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{43}\! \left(x , 1, y_{1}\right) y_{1}-F_{43}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{43}\! \left(x , y_{0}, y_{1}\right) &= F_{9}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{30}\! \left(x \right) F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{45}\! \left(x , y_{0}\right) &= F_{30}\! \left(x \right) F_{46}\! \left(x , y_{0}\right)\\
F_{46}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{5}\! \left(x , y_{0}\right)+F_{5}\! \left(x , 1\right)}{-1+y_{0}}\\
\end{align*}\)
This specification was found using the strategy pack "All The Strategies 2 Tracked Fusion Tracked Component Fusion Symmetries" and has 37 rules.
Finding the specification took 31982 seconds.
Copy 37 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 , 1\right)\\
F_{4}\! \left(x , y_{0}\right) &= F_{35}\! \left(x \right) F_{5}\! \left(x , y_{0}\right)\\
F_{5}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{36}\! \left(x , y_{0}\right)+F_{6}\! \left(x , y_{0}\right)\\
F_{6}\! \left(x , y_{0}\right) &= F_{15}\! \left(x , y_{0}\right) F_{7}\! \left(x , y_{0}\right)\\
F_{7}\! \left(x , y_{0}\right) &= F_{8}\! \left(x , 1, y_{0}\right)\\
F_{8}\! \left(x , y_{0}, y_{1}\right) &= F_{9}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{9}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y_{0}, y_{1}\right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{18}\! \left(x , y_{0}, y_{1}\right)\\
F_{10}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{0}, y_{1}\right)\\
F_{11}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}\right) F_{15}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}, y_{1}\right)\\
F_{12}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}\right)\\
F_{13}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right)\\
F_{14}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right) F_{15}\! \left(x , y_{0}\right)\\
F_{15}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x , y_{0}, y_{1}\right)\\
F_{17}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}\right) F_{15}\! \left(x , y_{1}\right) F_{7}\! \left(x , y_{1}\right)\\
F_{18}\! \left(x , y_{0}, y_{1}\right) &= F_{19}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{35}\! \left(x \right)\\
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{12}\! \left(x , y_{0}\right) F_{15}\! \left(x , y_{0}\right) F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{25}\! \left(x , y_{0}, y_{1}, 1\right) y_{1}-F_{25}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right) y_{2}}{-y_{2}+y_{1}}\\
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{15}\! \left(x , y_{1}\right) F_{26}\! \left(x , y_{0}\right) F_{30}\! \left(x , y_{1}, y_{2}\right)\\
F_{26}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{27}\! \left(x , y_{0}\right)\\
F_{27}\! \left(x , y_{0}\right) &= F_{28}\! \left(x , y_{0}\right)\\
F_{28}\! \left(x , y_{0}\right) &= F_{26}\! \left(x , y_{0}\right) F_{29}\! \left(x , y_{0}\right)\\
F_{29}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{30}\! \left(x , y_{0}, y_{1}\right) &= F_{9}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{32}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{32}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{32}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{33}\! \left(x , 1, y_{1}\right) y_{1}-F_{33}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{33}\! \left(x , y_{0}, y_{1}\right) &= F_{15}\! \left(x , y_{1}\right) F_{8}\! \left(x , y_{0}, y_{1}\right)\\
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-y_{2} F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{19}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{35}\! \left(x \right) &= x\\
F_{36}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{4}\! \left(x , y_{0}\right)+F_{4}\! \left(x , 1\right)}{-1+y_{0}}\\
\end{align*}\)
This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 46 rules.
Finding the specification took 176 seconds.
Copy 46 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_{29}\! \left(x \right) F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x , 1\right)\\
F_{4}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{44}\! \left(x , y_{0}\right)+F_{5}\! \left(x , y_{0}\right)\\
F_{5}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{6}\! \left(x , y_{0}\right)\\
F_{6}\! \left(x , y_{0}\right) &= F_{7}\! \left(x , y_{0}, 1\right)\\
F_{7}\! \left(x , y_{0}, y_{1}\right) &= F_{8}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{8}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}, y_{1}\right)+F_{17}\! \left(x , y_{0}, y_{1}\right)+F_{9}\! \left(x , y_{0}, y_{1}\right)\\
F_{9}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}, y_{1}\right)\\
F_{10}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right) F_{8}\! \left(x , y_{0}, y_{1}\right)\\
F_{11}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}\right)\\
F_{12}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right)\\
F_{13}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right)\\
F_{14}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= F_{16}\! \left(x , y_{0}, y_{1}\right)\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{1}\right) F_{6}\! \left(x , y_{1}\right)\\
F_{17}\! \left(x , y_{0}, y_{1}\right) &= F_{18}\! \left(x , y_{0}, y_{1}\right) F_{29}\! \left(x \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_{25}\! \left(x , y_{0}, y_{1}\right)+F_{30}\! \left(x , y_{0}, y_{1}\right)\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{0}, y_{1}\right)\\
F_{20}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right) F_{18}\! \left(x , y_{0}, y_{1}\right)\\
F_{21}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{0}, y_{1}\right)\\
F_{22}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{1}\right) F_{23}\! \left(x , y_{1}\right)\\
F_{23}\! \left(x , y_{0}\right) &= F_{24}\! \left(x , y_{0}, 1\right)\\
F_{24}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{7}\! \left(x , y_{0}, y_{1}\right) y_{0} y_{1}-F_{7}\! \left(x , y_{0}, \frac{1}{y_{0}}\right)}{y_{0} y_{1}-1}\\
F_{25}\! \left(x , y_{0}, y_{1}\right) &= F_{26}\! \left(x , y_{0}, y_{1}\right) F_{29}\! \left(x \right)\\
F_{26}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{27}\! \left(x , y_{0}\right) y_{0}-F_{27}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{27}\! \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_{28}\! \left(x , y_{0}\right) &= F_{8}\! \left(x , y_{0}, 1\right)\\
F_{29}\! \left(x \right) &= x\\
F_{30}\! \left(x , y_{0}, y_{1}\right) &= F_{29}\! \left(x \right) F_{31}\! \left(x , y_{0}, y_{1}\right)\\
F_{31}\! \left(x , y_{0}, y_{1}\right) &= F_{32}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{33}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{11}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{0}\right) F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{11}\! \left(x , y_{0}\right) F_{14}\! \left(x , y_{1}\right) F_{38}\! \left(x , y_{1}, y_{2}\right)\\
F_{38}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{7}\! \left(x , y_{0}, 1\right) y_{0}-y_{1} F_{7}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}\\
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{14}\! \left(x , y_{2}\right) F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{0} F_{41}\! \left(x , y_{0}, y_{2}\right)-F_{41}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{41}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{42}\! \left(x , 1, y_{1}\right) y_{1}-F_{42}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{42}\! \left(x , y_{0}, y_{1}\right) &= F_{8}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{29}\! \left(x \right) F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{44}\! \left(x , y_{0}\right) &= F_{29}\! \left(x \right) F_{45}\! \left(x , y_{0}\right)\\
F_{45}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{4}\! \left(x , y_{0}\right)+F_{4}\! \left(x , 1\right)}{-1+y_{0}}\\
\end{align*}\)