Av(12453, 14253, 14523, 41253, 41523, 45123)
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 Placements Tracked Fusion" and has 25 rules.
Found on January 22, 2022.Finding the specification took 8 seconds.
Copy 25 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_{7}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x , 1\right)\\
F_{4}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{5}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\
F_{5}\! \left(x , y\right) &= F_{6}\! \left(x , y\right) F_{7}\! \left(x \right)\\
F_{6}\! \left(x , y\right) &= \frac{y F_{4}\! \left(x , y\right)-F_{4}\! \left(x , 1\right)}{-1+y}\\
F_{7}\! \left(x \right) &= x\\
F_{8}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , 1, y\right)\\
F_{10}\! \left(x , y , z\right) &= F_{11}\! \left(x , y z , z\right)\\
F_{11}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{14}\! \left(x , y , z\right)+F_{18}\! \left(x , y , z\right)\\
F_{12}\! \left(x , y , z\right) &= F_{13}\! \left(x , y , z\right) F_{7}\! \left(x \right)\\
F_{13}\! \left(x , y , z\right) &= \frac{y F_{11}\! \left(x , y , z\right)-F_{11}\! \left(x , 1, z\right)}{-1+y}\\
F_{14}\! \left(x , y , z\right) &= F_{15}\! \left(x , y , z\right) F_{17}\! \left(x , y\right)\\
F_{15}\! \left(x , y , z\right) &= \frac{y F_{16}\! \left(x , y , 1\right)-z F_{16}\! \left(x , y , \frac{z}{y}\right)}{-z +y}\\
F_{16}\! \left(x , y , z\right) &= F_{11}\! \left(x , y , y z \right)\\
F_{17}\! \left(x , y\right) &= y x\\
F_{18}\! \left(x , y , z\right) &= F_{17}\! \left(x , z\right) F_{19}\! \left(x , y , z\right)\\
F_{19}\! \left(x , y , z\right) &= \frac{y F_{20}\! \left(x , y , z\right)-F_{20}\! \left(x , 1, z\right)}{-1+y}\\
F_{20}\! \left(x , y , z\right) &= \frac{-z F_{21}\! \left(x , 1, z\right)+y F_{21}\! \left(x , \frac{y}{z}, z\right)}{-z +y}\\
F_{21}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{22}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)\\
F_{22}\! \left(x , y , z\right) &= F_{17}\! \left(x , z\right) F_{21}\! \left(x , y , z\right)\\
F_{23}\! \left(x , y , z\right) &= F_{17}\! \left(x , z\right) F_{24}\! \left(x , y , z\right)\\
F_{24}\! \left(x , y , z\right) &= F_{20}\! \left(x , y z , z\right)\\
\end{align*}\)