Av(12345, 12435, 12453, 14235, 14253, 14523)
Counting Sequence
1, 1, 2, 6, 24, 114, 596, 3297, 18926, 111597, 672010, 4117475, 25603898, 161273099, 1027367194, ...
This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 36 rules.
Found on January 22, 2022.Finding the specification took 196 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_{28}\! \left(x \right) F_{3}\! \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_{34}\! \left(x , y\right)+F_{5}\! \left(x , y\right)\\
F_{5}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{6}\! \left(x , y\right)\\
F_{6}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{29}\! \left(x , y\right)+F_{32}\! \left(x , y\right)+F_{7}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{8}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= F_{9}\! \left(x , 1, y\right)\\
F_{9}\! \left(x , y , z\right) &= F_{10}\! \left(x , y z , z\right)\\
F_{10}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x , y , z\right)+F_{14}\! \left(x , y , z\right)+F_{16}\! \left(x , y , z\right)+F_{21}\! \left(x , y , z\right)\\
F_{12}\! \left(x , y , z\right) &= F_{11}\! \left(x , y z , z\right)\\
F_{12}\! \left(x , y , z\right) &= F_{13}\! \left(x , z\right) F_{9}\! \left(x , y , z\right)\\
F_{13}\! \left(x , y\right) &= y x\\
F_{14}\! \left(x , y , z\right) &= F_{13}\! \left(x , z\right) F_{15}\! \left(x , y , z\right)\\
F_{15}\! \left(x , y , z\right) &= \frac{-z F_{9}\! \left(x , 1, z\right)+y F_{9}\! \left(x , \frac{y}{z}, z\right)}{-z +y}\\
F_{16}\! \left(x , y , z\right) &= F_{13}\! \left(x , z\right) F_{17}\! \left(x , y , z\right)\\
F_{17}\! \left(x , y , z\right) &= \frac{-z F_{18}\! \left(x , 1, z\right)+y F_{18}\! \left(x , \frac{y}{z}, z\right)}{-z +y}\\
F_{18}\! \left(x , y , z\right) &= F_{19}\! \left(x , y z , z\right)\\
F_{19}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y , z\right)+F_{20}\! \left(x , y , z\right)+F_{21}\! \left(x , y , z\right)+F_{7}\! \left(x , z\right)\\
F_{20}\! \left(x , y , z\right) &= F_{13}\! \left(x , y\right) F_{19}\! \left(x , y , z\right)\\
F_{21}\! \left(x , y , z\right) &= F_{22}\! \left(x , y , z\right) F_{28}\! \left(x \right)\\
F_{22}\! \left(x , y , z\right) &= \frac{-z F_{23}\! \left(x , 1, z\right)+y F_{23}\! \left(x , \frac{y}{z}, z\right)}{-z +y}\\
F_{23}\! \left(x , y , z\right) &= F_{24}\! \left(x , y z , z\right)\\
F_{24}\! \left(x , y , z\right) &= \frac{z F_{25}\! \left(x , y , z\right)-F_{25}\! \left(x , y , 1\right)}{-1+z}\\
F_{25}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{26}\! \left(x , y , z\right)+F_{27}\! \left(x , y , z\right)+F_{5}\! \left(x , z\right)\\
F_{26}\! \left(x , y , z\right) &= F_{13}\! \left(x , y\right) F_{25}\! \left(x , y , z\right)\\
F_{27}\! \left(x , y , z\right) &= F_{24}\! \left(x , y , z\right) F_{28}\! \left(x \right)\\
F_{28}\! \left(x \right) &= x\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y , 1\right)\\
F_{30}\! \left(x , y , z\right) &= F_{31}\! \left(x , y , y z \right)\\
F_{31}\! \left(x , y , z\right) &= F_{13}\! \left(x , z\right) F_{19}\! \left(x , y , z\right)\\
F_{32}\! \left(x , y\right) &= F_{33}\! \left(x , y , 1\right)\\
F_{33}\! \left(x , y , z\right) &= F_{27}\! \left(x , y , y z \right)\\
F_{34}\! \left(x , y\right) &= F_{28}\! \left(x \right) F_{35}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= \frac{y F_{4}\! \left(x , y\right)-F_{4}\! \left(x , 1\right)}{-1+y}\\
\end{align*}\)