Av(13524, 13542, 15324, 15342, 51324, 51342)
Counting Sequence
1, 1, 2, 6, 24, 114, 596, 3294, 18852, 110488, 658864, 3981542, 24317396, 149821368, 929862640, ...
This specification was found using the strategy pack "Point And Col Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 49 rules.
Finding the specification took 334 seconds.
Copy 49 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_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{4}\! \left(x \right) &= x\\
F_{5}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{48}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{4}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{8}\! \left(x , 1\right)\\
F_{8}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{14}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= y F_{10}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{11}\! \left(x , y\right) &= -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{13}\! \left(x , y\right) &= -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{15}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{19}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{39}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= y F_{17}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{18}\! \left(x , y\right) &= -\frac{-F_{15}\! \left(x , y\right) y +F_{15}\! \left(x , 1\right)}{-1+y}\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{20}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)+F_{21}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= \frac{F_{23}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{23}\! \left(x \right) &= -F_{31}\! \left(x \right)-F_{32}\! \left(x \right)-F_{33}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{26}\! \left(x \right)+F_{28}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{15}\! \left(x , 1\right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{25}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{29}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{32}\! \left(x \right) &= 0\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{24}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{35}\! \left(x , y\right) &= F_{36}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{36}\! \left(x , y\right) &= F_{29}\! \left(x \right)+F_{37}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= F_{38}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{25}\! \left(x \right)+F_{38}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{40}\! \left(x , y\right)\\
F_{40}\! \left(x , y\right) &= 2 F_{39}\! \left(x , y\right)+F_{1}\! \left(x \right)+F_{41}\! \left(x , y\right)+F_{44}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{41}\! \left(x , y\right) &= y F_{42}\! \left(x , y\right)\\
F_{42}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{43}\! \left(x , y\right)\\
F_{43}\! \left(x , y\right) &= -\frac{-y F_{40}\! \left(x , y\right)+F_{40}\! \left(x , 1\right)}{-1+y}\\
F_{44}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{45}\! \left(x \right)-2 F_{31}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{4}\! \left(x \right) F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{25}\! \left(x \right) F_{4}\! \left(x \right)\\
\end{align*}\)