Av(12354, 12453, 13452, 21354, 21453, 23451, 31254, 31452, 32451, 41253, 41352, 42351)
Counting Sequence
1, 1, 2, 6, 24, 108, 512, 2498, 12410, 62410, 316576, 1615962, 8287620, 42657584, 220184686, ...
This specification was found using the strategy pack "Col Placements Tracked Fusion" and has 25 rules.
Found on January 22, 2022.Finding the specification took 7 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_{4}\! \left(x \right)\\
F_{3}\! \left(x \right) &= x\\
F_{4}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{24}\! \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_{22}\! \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{-y F_{7}\! \left(x , y\right)+F_{7}\! \left(x , 1\right)}{-1+y}\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{19}\! \left(x , y\right) F_{3}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x , 1\right)\\
F_{13}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{16}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{3}\! \left(x \right)\\
F_{15}\! \left(x , y\right) &= -\frac{-y F_{13}\! \left(x , y\right)+F_{13}\! \left(x , 1\right)}{-1+y}\\
F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{18}\! \left(x , y\right) F_{19}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= y x\\
F_{19}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{20}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{19}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{19}\! \left(x , y\right) F_{7}\! \left(x , y\right)\\
F_{24}\! \left(x \right) &= F_{12}\! \left(x \right) F_{3}\! \left(x \right)\\
\end{align*}\)