Av(14352, 14523, 14532, 41352, 41523, 41532, 43152, 43512, 45123, 45132, 45312)
Counting Sequence
1, 1, 2, 6, 24, 109, 522, 2574, 12964, 66426, 345300, 1816976, 9660732, 51825093, 280168474, ...
This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 40 rules.
Found on January 22, 2022.Finding the specification took 127 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_{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{F_{4}\! \left(x , y\right) y -F_{4}\! \left(x , 1\right)}{-1+y}\\
F_{7}\! \left(x \right) &= x\\
F_{8}\! \left(x , y\right) &= F_{22}\! \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_{36}\! \left(x , y\right)+F_{38}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{7}\! \left(x \right)\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , 1, y\right)\\
F_{12}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y , z\right)+F_{30}\! \left(x , y , z\right)+F_{32}\! \left(x , y , z\right)+F_{34}\! \left(x , y , z\right)\\
F_{14}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)+F_{25}\! \left(x , y , z\right)\\
F_{15}\! \left(x , y , z\right) &= F_{14}\! \left(x , y z , z\right)\\
F_{15}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y , z\right)+F_{28}\! \left(x , y , z\right)+F_{29}\! \left(x , y , z\right)\\
F_{16}\! \left(x , y , z\right) &= F_{17}\! \left(x , y , z\right) F_{22}\! \left(x , z\right)\\
F_{17}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y , z\right)+F_{18}\! \left(x , y , z\right)\\
F_{18}\! \left(x , y , z\right) &= F_{19}\! \left(x , y z , z\right)\\
F_{19}\! \left(x , y , z\right) &= F_{20}\! \left(x , y , z\right) F_{22}\! \left(x , z\right)\\
F_{20}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)+F_{25}\! \left(x , y , z\right)\\
F_{21}\! \left(x , y , z\right) &= F_{14}\! \left(x , y , z\right) F_{22}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= y x\\
F_{23}\! \left(x , y , z\right) &= F_{22}\! \left(x , z\right) F_{24}\! \left(x , y , z\right)\\
F_{24}\! \left(x , y , z\right) &= \frac{-F_{15}\! \left(x , 1, z\right) z +F_{15}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}\\
F_{25}\! \left(x , y , z\right) &= F_{22}\! \left(x , z\right) F_{26}\! \left(x , y , z\right)\\
F_{26}\! \left(x , y , z\right) &= \frac{-F_{27}\! \left(x , 1, z\right) z +F_{27}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}\\
F_{27}\! \left(x , y , z\right) &= F_{20}\! \left(x , y z , z\right)\\
F_{28}\! \left(x , y , z\right) &= F_{23}\! \left(x , y z , z\right)\\
F_{29}\! \left(x , y , z\right) &= F_{25}\! \left(x , y z , z\right)\\
F_{30}\! \left(x , y , z\right) &= F_{31}\! \left(x , y , z\right) F_{7}\! \left(x \right)\\
F_{31}\! \left(x , y , z\right) &= \frac{F_{12}\! \left(x , y , z\right) y -F_{12}\! \left(x , 1, z\right)}{-1+y}\\
F_{32}\! \left(x , y , z\right) &= F_{22}\! \left(x , z\right) F_{33}\! \left(x , y , z\right)\\
F_{33}\! \left(x , y , z\right) &= \frac{F_{24}\! \left(x , y , z\right) y -F_{24}\! \left(x , 1, z\right)}{-1+y}\\
F_{34}\! \left(x , y , z\right) &= F_{22}\! \left(x , z\right) F_{35}\! \left(x , y , z\right)\\
F_{35}\! \left(x , y , z\right) &= \frac{F_{26}\! \left(x , y , z\right) y -F_{26}\! \left(x , 1, z\right)}{-1+y}\\
F_{36}\! \left(x , y\right) &= F_{22}\! \left(x , y\right) F_{37}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= \frac{F_{15}\! \left(x , 1, y\right) y -F_{15}\! \left(x , \frac{1}{y}, y\right)}{-1+y}\\
F_{38}\! \left(x , y\right) &= F_{22}\! \left(x , y\right) F_{39}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= \frac{F_{27}\! \left(x , 1, y\right) y -F_{27}\! \left(x , \frac{1}{y}, y\right)}{-1+y}\\
\end{align*}\)