Av(12453, 14253, 14523, 14532, 21453, 24153, 41253, 41523, 41532, 42153)
Counting Sequence
1, 1, 2, 6, 24, 110, 540, 2762, 14542, 78288, 429076, 2386508, 13437952, 76458612, 438927358, ...
This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 36 rules.
Found on January 22, 2022.Finding the specification took 31 seconds.
Copy 36 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_{34}\! \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_{26}\! \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_{9}\! \left(x \right)\\
F_{11}\! \left(x , y\right) &= \frac{F_{12}\! \left(x , y\right) y -F_{12}\! \left(x , 1\right)}{-1+y}\\
F_{12}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{24}\! \left(x , y\right)+F_{7}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{9}\! \left(x \right)\\
F_{14}\! \left(x , y\right) &= \frac{F_{15}\! \left(x , y\right) y -F_{15}\! \left(x , 1\right)}{-1+y}\\
F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , 1, y\right)\\
F_{16}\! \left(x , y , z\right) &= F_{17}\! \left(x , y , y z \right)\\
F_{17}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x , z\right)+F_{19}\! \left(x , y , z\right)+F_{21}\! \left(x , y , z\right)\\
F_{18}\! \left(x , y\right) &= F_{6}\! \left(x , y\right) F_{9}\! \left(x \right)\\
F_{19}\! \left(x , y , z\right) &= F_{17}\! \left(x , y , z\right) F_{20}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= y x\\
F_{21}\! \left(x , y , z\right) &= F_{20}\! \left(x , z\right) F_{22}\! \left(x , y , z\right)\\
F_{22}\! \left(x , y , z\right) &= \frac{-F_{23}\! \left(x , 1, z\right) z +F_{23}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}\\
F_{23}\! \left(x , y , z\right) &= F_{17}\! \left(x , y z , z\right)\\
F_{24}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= \frac{F_{23}\! \left(x , 1, y\right) y -F_{23}\! \left(x , \frac{1}{y}, y\right)}{-1+y}\\
F_{26}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y , 1\right)\\
F_{28}\! \left(x , y , z\right) &= F_{29}\! \left(x , y , y z \right)\\
F_{29}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , z\right)+F_{30}\! \left(x , y , z\right)+F_{32}\! \left(x , y , z\right)+F_{7}\! \left(x , z\right)\\
F_{30}\! \left(x , y , z\right) &= F_{20}\! \left(x , y\right) F_{31}\! \left(x , y , z\right)\\
F_{31}\! \left(x , y , z\right) &= \frac{F_{17}\! \left(x , y , z\right) y -F_{17}\! \left(x , 1, z\right)}{-1+y}\\
F_{31}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x , z\right)+F_{30}\! \left(x , y , z\right)+F_{32}\! \left(x , y , z\right)+F_{33}\! \left(x , z\right)\\
F_{33}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{9}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{12}\! \left(x , 1\right)\\
\end{align*}\)