Av(13254, 13524, 13542, 31254, 31524, 31542, 32154, 32514, 35124, 35142, 35214)
Counting Sequence
1, 1, 2, 6, 24, 109, 522, 2568, 12846, 65017, 331980, 1706894, 8825656, 45848634, 239134024, ...
This specification was found using the strategy pack "Row And Col Placements Tracked Fusion" and has 41 rules.
Found on January 23, 2022.Finding the specification took 38 seconds.
Copy 41 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_{12}\! \left(x \right) F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{39}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{12}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x \right)+F_{38}\! \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_{12}\! \left(x \right) F_{8}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= F_{5}\! \left(x \right)+F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{11}\! \left(x , y\right) F_{8}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= y x\\
F_{12}\! \left(x \right) &= x\\
F_{13}\! \left(x \right) &= F_{12}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x , 1\right)\\
F_{15}\! \left(x , y\right) &= \frac{F_{16}\! \left(x , y\right) y -F_{16}\! \left(x , 1\right)}{-1+y}\\
F_{16}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)+F_{22}\! \left(x , y\right)+F_{31}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{18}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= \frac{F_{19}\! \left(x , y\right) y -F_{19}\! \left(x , 1\right)}{-1+y}\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)+F_{3}\! \left(x \right)\\
F_{20}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{11}\! \left(x , y\right) F_{19}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , 1, y\right)\\
F_{23}\! \left(x , y , z\right) &= F_{11}\! \left(x , y\right) F_{24}\! \left(x , y , z\right)\\
F_{24}\! \left(x , y , z\right) &= \frac{F_{25}\! \left(x , y , 1\right) y -F_{25}\! \left(x , y , \frac{z}{y}\right) z}{-z +y}\\
F_{25}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{26}\! \left(x , y , z\right)+F_{29}\! \left(x , y , z\right)+F_{30}\! \left(x , y , z\right)\\
F_{26}\! \left(x , y , z\right) &= F_{27}\! \left(x , y , y z \right)\\
F_{27}\! \left(x , y , z\right) &= F_{12}\! \left(x \right) F_{28}\! \left(x , y , z\right)\\
F_{28}\! \left(x , y , z\right) &= \frac{F_{19}\! \left(x , y\right) y -F_{19}\! \left(x , z\right) z}{-z +y}\\
F_{29}\! \left(x , y , z\right) &= F_{23}\! \left(x , y , y z \right)\\
F_{30}\! \left(x , y , z\right) &= F_{11}\! \left(x , z\right) F_{25}\! \left(x , y , z\right)\\
F_{31}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{32}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= \frac{F_{33}\! \left(x , 1, y\right) y -F_{33}\! \left(x , \frac{1}{y}, y\right)}{-1+y}\\
F_{33}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{34}\! \left(x , y , z\right)+F_{35}\! \left(x , y , z\right)+F_{36}\! \left(x , y , z\right)\\
F_{34}\! \left(x , y , z\right) &= F_{27}\! \left(x , y z , z\right)\\
F_{35}\! \left(x , y , z\right) &= F_{23}\! \left(x , y z , z\right)\\
F_{36}\! \left(x , y , z\right) &= F_{11}\! \left(x , z\right) F_{37}\! \left(x , y , z\right)\\
F_{37}\! \left(x , y , z\right) &= \frac{F_{33}\! \left(x , y , z\right) y -F_{33}\! \left(x , 1, z\right)}{-1+y}\\
F_{38}\! \left(x \right) &= F_{31}\! \left(x , 1\right)\\
F_{39}\! \left(x \right) &= F_{12}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{16}\! \left(x , 1\right)\\
\end{align*}\)