Av(12354, 13254, 13524, 13542, 21354, 23154, 31254, 31524, 31542, 32154)
Counting Sequence
1, 1, 2, 6, 24, 110, 540, 2762, 14544, 78342, 429852, 2394858, 13514320, 77090282, 443819364, ...
This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 40 rules.
Found on January 23, 2022.Finding the specification took 18 seconds.
Copy 40 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_{11}\! \left(x \right) F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{32}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{11}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{29}\! \left(x \right)+F_{31}\! \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_{11}\! \left(x \right) F_{8}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{28}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{11}\! \left(x \right)\\
F_{10}\! \left(x , y\right) &= -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}\\
F_{11}\! \left(x \right) &= x\\
F_{12}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{13}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= -\frac{-y F_{14}\! \left(x , y\right)+F_{14}\! \left(x , 1\right)}{-1+y}\\
F_{14}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{26}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{28}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{16}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= -\frac{-y F_{17}\! \left(x , y\right)+F_{17}\! \left(x , 1\right)}{-1+y}\\
F_{17}\! \left(x , y\right) &= -\frac{-y F_{18}\! \left(x , y\right)+F_{18}\! \left(x , 1\right)}{-1+y}\\
F_{18}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)+F_{20}\! \left(x , y\right)+F_{7}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{14}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{20}\! \left(x , y\right)+F_{22}\! \left(x , y\right)+F_{23}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{17}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{24}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= -\frac{-y F_{21}\! \left(x , y\right)+F_{21}\! \left(x , 1\right)}{-1+y}\\
F_{25}\! \left(x , y\right) &= y x\\
F_{24}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{20}\! \left(x , y\right)+F_{23}\! \left(x , y\right)+F_{26}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{13}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{29}\! \left(x \right) &= F_{11}\! \left(x \right) F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{14}\! \left(x , 1\right)\\
F_{31}\! \left(x \right) &= F_{11}\! \left(x \right) F_{30}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{11}\! \left(x \right) F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{31}\! \left(x \right)+F_{34}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{11}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x , 1\right)\\
F_{36}\! \left(x , y\right) &= -\frac{-y F_{18}\! \left(x , y\right)+F_{18}\! \left(x , 1\right)}{-1+y}\\
F_{37}\! \left(x \right) &= F_{11}\! \left(x \right) F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x , 1\right)\\
F_{39}\! \left(x , y\right) &= -\frac{-y F_{21}\! \left(x , y\right)+F_{21}\! \left(x , 1\right)}{-1+y}\\
\end{align*}\)