Av(14523, 14532, 41523, 41532, 45123, 45132, 45312)
Counting Sequence
1, 1, 2, 6, 24, 113, 580, 3129, 17442, 99574, 579108, 3419056, 20440024, 123494294, 752913720, ...
This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 38 rules.
Found on January 22, 2022.Finding the specification took 50 seconds.
Copy 38 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_{7}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x , 1\right)\\
F_{4}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{5}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\
F_{5}\! \left(x , y\right) &= F_{6}\! \left(x , y\right) F_{7}\! \left(x \right)\\
F_{6}\! \left(x , y\right) &= \frac{y F_{4}\! \left(x , y\right)-F_{4}\! \left(x , 1\right)}{-1+y}\\
F_{7}\! \left(x \right) &= x\\
F_{8}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{37}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{7}\! \left(x \right)\\
F_{12}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{19}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{32}\! \left(x , y\right)+F_{34}\! \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_{30}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{7}\! \left(x \right)\\
F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , 1, y\right)\\
F_{17}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x , y , z\right)+F_{20}\! \left(x , y , z\right)+F_{22}\! \left(x , y , z\right)\\
F_{18}\! \left(x , y , z\right) &= F_{17}\! \left(x , y , z\right) F_{19}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= y x\\
F_{20}\! \left(x , y , z\right) &= F_{21}\! \left(x , y , z\right) F_{7}\! \left(x \right)\\
F_{21}\! \left(x , y , z\right) &= \frac{y F_{17}\! \left(x , y , z\right)-F_{17}\! \left(x , 1, z\right)}{-1+y}\\
F_{22}\! \left(x , y , z\right) &= F_{19}\! \left(x , z\right) F_{23}\! \left(x , y , z\right)\\
F_{23}\! \left(x , y , z\right) &= \frac{y F_{24}\! \left(x , y , z\right)-F_{24}\! \left(x , 1, z\right)}{-1+y}\\
F_{24}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x , y , z\right)+F_{26}\! \left(x , y , z\right)+F_{29}\! \left(x , y , z\right)\\
F_{25}\! \left(x , y , z\right) &= F_{19}\! \left(x , y\right) F_{24}\! \left(x , y , z\right)\\
F_{26}\! \left(x , y , z\right) &= F_{19}\! \left(x , z\right) F_{27}\! \left(x , y , z\right)\\
F_{27}\! \left(x , y , z\right) &= \frac{-z F_{28}\! \left(x , 1, z\right)+y F_{28}\! \left(x , \frac{y}{z}, z\right)}{-z +y}\\
F_{28}\! \left(x , y , z\right) &= F_{24}\! \left(x , y z , z\right)\\
F_{29}\! \left(x , y , z\right) &= F_{19}\! \left(x , z\right) F_{27}\! \left(x , y , z\right)\\
F_{30}\! \left(x , y\right) &= F_{31}\! \left(x , 1, y\right)\\
F_{31}\! \left(x , y , z\right) &= F_{19}\! \left(x , z\right) F_{24}\! \left(x , y , z\right)\\
F_{32}\! \left(x , y\right) &= F_{33}\! \left(x , y\right) F_{7}\! \left(x \right)\\
F_{33}\! \left(x , y\right) &= \frac{y F_{16}\! \left(x , y\right)-F_{16}\! \left(x , 1\right)}{-1+y}\\
F_{34}\! \left(x , y\right) &= F_{33}\! \left(x , y\right) F_{7}\! \left(x \right)\\
F_{35}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= \frac{y F_{28}\! \left(x , 1, y\right)-F_{28}\! \left(x , \frac{1}{y}, y\right)}{-1+y}\\
F_{37}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{36}\! \left(x , y\right)\\
\end{align*}\)