Av(21453, 24153, 24513, 42153, 42513, 45213)
Counting Sequence
1, 1, 2, 6, 24, 114, 596, 3302, 19044, 113292, 691320, 4310192, 27374264, 176669540, 1156339560, ...
This specification was found using the strategy pack "Row And Col Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 35 rules.
Finding the specification took 240 seconds.
Copy 35 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_{4}\! \left(x \right)\\
F_{3}\! \left(x \right) &= x\\
F_{4}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{34}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{3}\! \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_{10}\! \left(x , y_{0}\right)+F_{30}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= F_{3}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= -\frac{-F_{7}\! \left(x , y_{0}\right) y_{0}+F_{7}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{10}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , y_{0}\right) F_{3}\! \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) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{26}\! \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_{13}\! \left(x , y_{0}, y_{1}\right) &= y_{0} F_{14}\! \left(x , y_{0}, y_{1}\right)\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= F_{15}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= F_{16}\! \left(x , y_{1}, y_{0}\right)\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{18}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{19}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{20}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{20}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}\\
F_{20}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x , y_{0}, y_{1}\right)+F_{25}\! \left(x , y_{0}, y_{1}\right)\\
F_{21}\! \left(x , y_{0}, y_{1}\right) &= y_{0} F_{22}\! \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_{3}\! \left(x \right)\\
F_{23}\! \left(x , y_{0}, y_{1}\right) &= F_{24}\! \left(x , y_{1}, y_{0}\right)\\
F_{24}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{20}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{20}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{25}\! \left(x , y_{0}, y_{1}\right) &= F_{21}\! \left(x , y_{1}, y_{0}\right)\\
F_{26}\! \left(x , y_{0}, y_{1}\right) &= F_{27}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)\\
F_{27}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{12}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{12}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{28}\! \left(x , y_{0}, y_{1}\right) &= F_{26}\! \left(x , y_{1}, y_{0}\right)\\
F_{29}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{1}, y_{0}\right)\\
F_{30}\! \left(x , y_{0}\right) &= y_{0} F_{31}\! \left(x , y_{0}\right)\\
F_{31}\! \left(x , y_{0}\right) &= F_{3}\! \left(x \right) F_{32}\! \left(x , y_{0}\right)\\
F_{32}\! \left(x , y_{0}\right) &= F_{33}\! \left(x , 1, y_{0}\right)\\
F_{33}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{24}\! \left(x , y_{0}, y_{1}\right)+F_{24}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{34}\! \left(x \right) &= F_{5}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "All The Strategies 2 Tracked Fusion Tracked Component Fusion Symmetries" and has 31 rules.
Finding the specification took 3287 seconds.
Copy 31 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_{5}\! \left(x \right)\\
F_{4}\! \left(x \right) &= x\\
F_{5}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{30}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{4}\! \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_{11}\! \left(x , y\right)+F_{28}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{10}\! \left(x , y\right) &= -\frac{-F_{8}\! \left(x , y\right) y +F_{8}\! \left(x , 1\right)}{-1+y}\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , 1, y\right)\\
F_{13}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y , z\right)+F_{24}\! \left(x , y , z\right)+F_{26}\! \left(x , y , z\right)+F_{27}\! \left(x , y , z\right)\\
F_{14}\! \left(x , y , z\right) &= y F_{15}\! \left(x , y , z\right)\\
F_{15}\! \left(x , y , z\right) &= F_{16}\! \left(x , y , z\right) F_{4}\! \left(x \right)\\
F_{16}\! \left(x , y , z\right) &= F_{17}\! \left(x , z , y\right)\\
F_{17}\! \left(x , y , z\right) &= -\frac{-y F_{18}\! \left(x , y , z\right)+F_{18}\! \left(x , 1, z\right)}{-1+y}\\
F_{18}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{19}\! \left(x , y , z\right)+F_{21}\! \left(x , y , z\right)+F_{22}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)\\
F_{19}\! \left(x , y , z\right) &= y F_{20}\! \left(x , y , z\right)\\
F_{20}\! \left(x , y , z\right) &= F_{18}\! \left(x , y , z\right) F_{4}\! \left(x \right)\\
F_{21}\! \left(x , y , z\right) &= F_{17}\! \left(x , y , z\right) F_{4}\! \left(x \right)\\
F_{22}\! \left(x , y , z\right) &= F_{21}\! \left(x , z , y\right)\\
F_{23}\! \left(x , y , z\right) &= F_{19}\! \left(x , z , y\right)\\
F_{24}\! \left(x , y , z\right) &= F_{25}\! \left(x , y , z\right) F_{4}\! \left(x \right)\\
F_{25}\! \left(x , y , z\right) &= -\frac{-z F_{13}\! \left(x , y , z\right)+F_{13}\! \left(x , y , 1\right)}{-1+z}\\
F_{26}\! \left(x , y , z\right) &= F_{24}\! \left(x , z , y\right)\\
F_{27}\! \left(x , y , z\right) &= F_{14}\! \left(x , z , y\right)\\
F_{28}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{19}\! \left(x , y , 1\right)\\
F_{30}\! \left(x \right) &= F_{6}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Col Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 32 rules.
Finding the specification took 60 seconds.
Copy 32 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_{4}\! \left(x \right)\\
F_{3}\! \left(x \right) &= x\\
F_{4}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{31}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{3}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x , 1\right)\\
F_{7}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{28}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= -\frac{-F_{7}\! \left(x , y\right) y +F_{7}\! \left(x , 1\right)}{-1+y}\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{3}\! \left(x \right)\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , 1, y\right)\\
F_{12}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y , z\right)+F_{24}\! \left(x , y , z\right)+F_{26}\! \left(x , y , z\right)+F_{27}\! \left(x , y , z\right)\\
F_{13}\! \left(x , y , z\right) &= y F_{14}\! \left(x , y , z\right)\\
F_{14}\! \left(x , y , z\right) &= F_{15}\! \left(x , y , z\right) F_{3}\! \left(x \right)\\
F_{15}\! \left(x , y , z\right) &= F_{16}\! \left(x , z , y\right)\\
F_{16}\! \left(x , y , z\right) &= -\frac{-F_{17}\! \left(x , y , z\right) y +F_{17}\! \left(x , 1, z\right)}{-1+y}\\
F_{17}\! \left(x , y , z\right) &= -\frac{-y F_{18}\! \left(x , y , z\right)+F_{18}\! \left(x , 1, z\right)}{-1+y}\\
F_{18}\! \left(x , y , z\right) &= -\frac{-F_{19}\! \left(x , y , z\right) z +F_{19}\! \left(x , y , 1\right)}{-1+z}\\
F_{19}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{20}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)\\
F_{20}\! \left(x , y , z\right) &= y F_{21}\! \left(x , y , z\right)\\
F_{21}\! \left(x , y , z\right) &= F_{22}\! \left(x , y , z\right) F_{3}\! \left(x \right)\\
F_{22}\! \left(x , y , z\right) &= F_{18}\! \left(x , z , y\right)\\
F_{23}\! \left(x , y , z\right) &= F_{20}\! \left(x , z , y\right)\\
F_{24}\! \left(x , y , z\right) &= F_{25}\! \left(x , y , z\right) F_{3}\! \left(x \right)\\
F_{25}\! \left(x , y , z\right) &= -\frac{-z F_{12}\! \left(x , y , z\right)+F_{12}\! \left(x , y , 1\right)}{-1+z}\\
F_{26}\! \left(x , y , z\right) &= F_{24}\! \left(x , z , y\right)\\
F_{27}\! \left(x , y , z\right) &= F_{13}\! \left(x , z , y\right)\\
F_{28}\! \left(x , y\right) &= y F_{29}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{30}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{17}\! \left(x , 1, y\right)\\
F_{31}\! \left(x \right) &= F_{5}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point And Row And Col Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 36 rules.
Finding the specification took 320 seconds.
Copy 36 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_{5}\! \left(x \right)\\
F_{4}\! \left(x \right) &= x\\
F_{5}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{35}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{4}\! \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_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}\right)+F_{31}\! \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}\right) F_{4}\! \left(x \right)\\
F_{10}\! \left(x , y_{0}\right) &= -\frac{-F_{8}\! \left(x , y_{0}\right) y_{0}+F_{8}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{11}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)\\
F_{12}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , 1, y_{0}\right)\\
F_{13}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y_{0}, y_{1}\right)+F_{27}\! \left(x , y_{0}, y_{1}\right)+F_{29}\! \left(x , y_{0}, y_{1}\right)+F_{30}\! \left(x , y_{0}, y_{1}\right)\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= y_{0} 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_{4}\! \left(x \right)\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x , y_{1}, y_{0}\right)\\
F_{17}\! \left(x , y_{0}, y_{1}\right) &= F_{18}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{19}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{20}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{21}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{21}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}\\
F_{21}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{22}\! \left(x , y_{0}, y_{1}\right)+F_{26}\! \left(x , y_{0}, y_{1}\right)\\
F_{22}\! \left(x , y_{0}, y_{1}\right) &= y_{0} F_{23}\! \left(x , y_{0}, y_{1}\right)\\
F_{23}\! \left(x , y_{0}, y_{1}\right) &= F_{24}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)\\
F_{24}\! \left(x , y_{0}, y_{1}\right) &= F_{25}\! \left(x , y_{1}, y_{0}\right)\\
F_{25}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{21}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{21}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{26}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{1}, y_{0}\right)\\
F_{27}\! \left(x , y_{0}, y_{1}\right) &= F_{28}\! \left(x , y_{0}, y_{1}\right) F_{4}\! \left(x \right)\\
F_{28}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{13}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{13}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{29}\! \left(x , y_{0}, y_{1}\right) &= F_{27}\! \left(x , y_{1}, y_{0}\right)\\
F_{30}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}, y_{0}\right)\\
F_{31}\! \left(x , y_{0}\right) &= y_{0} F_{32}\! \left(x , y_{0}\right)\\
F_{32}\! \left(x , y_{0}\right) &= F_{33}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)\\
F_{33}\! \left(x , y_{0}\right) &= F_{34}\! \left(x , 1, y_{0}\right)\\
F_{34}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{25}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{35}\! \left(x \right) &= F_{6}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Col Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 34 rules.
Finding the specification took 52 seconds.
Copy 34 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_{4}\! \left(x \right)\\
F_{3}\! \left(x \right) &= x\\
F_{4}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{33}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{3}\! \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_{10}\! \left(x , y_{0}\right)+F_{29}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= F_{3}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= -\frac{-F_{7}\! \left(x , y_{0}\right) y_{0}+F_{7}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{10}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , y_{0}\right) F_{3}\! \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) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{25}\! \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_{13}\! \left(x , y_{0}, y_{1}\right) &= y_{0} F_{14}\! \left(x , y_{0}, y_{1}\right)\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= F_{15}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{16}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{16}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{1}+F_{18}\! \left(x , y_{0}, 1, y_{2}\right)}{-1+y_{1}}\\
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{19}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{19}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{20}\! \left(x , y_{0}, y_{1}\right)+F_{24}\! \left(x , y_{0}, y_{1}\right)\\
F_{20}\! \left(x , y_{0}, y_{1}\right) &= y_{0} F_{21}\! \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_{3}\! \left(x \right)\\
F_{22}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , y_{1}, y_{0}\right)\\
F_{23}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{19}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{19}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{24}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{1}, y_{0}\right)\\
F_{25}\! \left(x , y_{0}, y_{1}\right) &= F_{26}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)\\
F_{26}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{12}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{12}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{27}\! \left(x , y_{0}, y_{1}\right) &= F_{25}\! \left(x , y_{1}, y_{0}\right)\\
F_{28}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{1}, y_{0}\right)\\
F_{29}\! \left(x , y_{0}\right) &= y_{0} F_{30}\! \left(x , y_{0}\right)\\
F_{30}\! \left(x , y_{0}\right) &= F_{3}\! \left(x \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) &= -\frac{-y_{0} F_{23}\! \left(x , y_{0}, y_{1}\right)+F_{23}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{33}\! \left(x \right) &= F_{5}\! \left(x \right)\\
\end{align*}\)