Av(12453, 13452, 14352, 15342, 23451, 24351, 25341, 34251, 35241)
Counting Sequence
1, 1, 2, 6, 24, 111, 546, 2758, 14110, 72687, 375998, 1950212, 10134024, 52730484, 274647566, ...
This specification was found using the strategy pack "Point And Col Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 30 rules.
Finding the specification took 102 seconds.
Copy 30 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_{6}\! \left(x , 1\right)\\
F_{6}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{7}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{8}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= -\frac{-F_{6}\! \left(x , y\right) y +F_{6}\! \left(x , 1\right)}{-1+y}\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{11}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= y x\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , 1, y\right)\\
F_{12}\! \left(x , y , z\right) &= -\frac{-F_{13}\! \left(x , y z \right) y +F_{13}\! \left(x , z\right)}{-1+y}\\
F_{13}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{14}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{16}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{21}\! \left(x , y\right)+F_{28}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{18}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)^{2} F_{10}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{22}\! \left(x , y\right) F_{25}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{23}\! \left(x , y\right) &= F_{22}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{23}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)+F_{24}\! \left(x , y\right)\\
F_{25}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{26}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{25} \left(x \right)^{2} F_{4}\! \left(x \right)\\
F_{28}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{16}\! \left(x , y\right) F_{18}\! \left(x , y\right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion" and has 30 rules.
Finding the specification took 1745 seconds.
Copy 30 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_{6}\! \left(x , 1\right)\\
F_{6}\! \left(x , y\right) &= F_{7}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= y^{2} x^{2}+4 x F_{7}\! \left(x , y\right)^{2} y -8 x F_{7}\! \left(x , y\right) y +4 y x -F_{7}\! \left(x , y\right)^{2}+3 F_{7}\! \left(x , y\right)-1\\
F_{8}\! \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) &= F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= -\frac{-F_{6}\! \left(x , y\right) y +F_{6}\! \left(x , 1\right)}{-1+y}\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{15}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= y x\\
F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y , 1\right)\\
F_{16}\! \left(x , y , z\right) &= F_{17}\! \left(x , y , y z \right)\\
F_{18}\! \left(x , y , z\right) &= F_{17}\! \left(x , y , z\right) F_{4}\! \left(x \right)\\
F_{18}\! \left(x , y , z\right) &= F_{19}\! \left(x , z , y\right)\\
F_{19}\! \left(x , y , z\right) &= \frac{y F_{20}\! \left(x , y\right)-F_{20}\! \left(x , z\right) z}{-z +y}\\
F_{21}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)+F_{27}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{22}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{24}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)+F_{25}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{26}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= -\frac{-y F_{27}\! \left(x , y\right)+F_{27}\! \left(x , 1\right)}{-1+y}\\
F_{27}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{28}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)^{2} F_{14}\! \left(x , y\right)\\
\end{align*}\)