Av(13452, 23451)
Counting Sequence
1, 1, 2, 6, 24, 118, 672, 4256, 29176, 212586, 1625704, 12930160, 106242392, 897210996, 7756325952, ...
This specification was found using the strategy pack "Row Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 31 rules.
Finding the specification took 52 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_{9}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{30}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x , 1\right)\\
F_{6}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{28}\! \left(x , y\right)+F_{7}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= F_{8}\! \left(x , y\right) F_{9}\! \left(x \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 \right) &= x\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{22}\! \left(x , y\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_{15}\! \left(x , y , z\right)+F_{25}\! \left(x , y , z\right)+F_{26}\! \left(x , y , z\right)\\
F_{13}\! \left(x , y , z\right) &= F_{14}\! \left(x , y , z\right) F_{9}\! \left(x \right)\\
F_{14}\! \left(x , y , z\right) &= \frac{F_{12}\! \left(x , y , z\right) y z -F_{12}\! \left(x , \frac{1}{z}, z\right)}{y z -1}\\
F_{15}\! \left(x , y , z\right) &= F_{16}\! \left(x , y z , z\right)\\
F_{17}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y , z\right)+F_{18}\! \left(x , y , z\right)+F_{20}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)\\
F_{17}\! \left(x , y , z\right) &= \frac{F_{6}\! \left(x , y\right) y -F_{6}\! \left(x , z\right) z}{-z +y}\\
F_{18}\! \left(x , y , z\right) &= F_{19}\! \left(x , y , z\right) F_{9}\! \left(x \right)\\
F_{19}\! \left(x , y , z\right) &= -\frac{-F_{17}\! \left(x , y , z\right) y +F_{17}\! \left(x , 1, z\right)}{-1+y}\\
F_{20}\! \left(x , y , z\right) &= F_{21}\! \left(x , y , z\right) F_{22}\! \left(x , z\right)\\
F_{21}\! \left(x , y , z\right) &= -\frac{z F_{12}\! \left(x , 1, z\right)-y F_{12}\! \left(x , \frac{y}{z}, z\right)}{-z +y}\\
F_{22}\! \left(x , y\right) &= y x\\
F_{23}\! \left(x , y , z\right) &= F_{24}\! \left(x , y , z\right) F_{9}\! \left(x \right)\\
F_{24}\! \left(x , y , z\right) &= F_{19}\! \left(x , y , z\right)\\
F_{25}\! \left(x , y , z\right) &= F_{12}\! \left(x , y , z\right) F_{22}\! \left(x , z\right)\\
F_{26}\! \left(x , y , z\right) &= F_{27}\! \left(x , y , z\right) F_{9}\! \left(x \right)\\
F_{27}\! \left(x , y , z\right) &= F_{14}\! \left(x , y , z\right)\\
F_{28}\! \left(x , y\right) &= F_{29}\! \left(x , y\right) F_{9}\! \left(x \right)\\
F_{29}\! \left(x , y\right) &= F_{8}\! \left(x , y\right)\\
F_{30}\! \left(x \right) &= F_{5}\! \left(x \right) F_{9}\! \left(x \right)\\
\end{align*}\)