Av(13254, 13524, 13542, 15324, 15342, 15432, 51324, 51342, 51432)
Counting Sequence
1, 1, 2, 6, 24, 111, 546, 2758, 14110, 72687, 375998, 1950212, 10134024, 52730484, 274647566, ...
This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 28 rules.
Found on January 22, 2022.Finding the specification took 17 seconds.
Copy 28 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_{17}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= \frac{y F_{10}\! \left(x , 1, y\right)-F_{10}\! \left(x , \frac{1}{y}, y\right)}{-1+y}\\
F_{10}\! \left(x , y , z\right) &= F_{11}\! \left(x , y z , z\right)\\
F_{11}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{18}\! \left(x , y , z\right)\\
F_{12}\! \left(x , y , z\right) &= F_{13}\! \left(x , y , z\right)\\
F_{13}\! \left(x , y , z\right) &= F_{11}\! \left(x , y , z\right) F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)^{2} F_{17}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= y x\\
F_{18}\! \left(x , y , z\right) &= F_{17}\! \left(x , z\right) F_{19}\! \left(x , y , z\right)\\
F_{19}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{20}\! \left(x , y , z\right)+F_{22}\! \left(x , y , z\right)+F_{26}\! \left(x , z\right)\\
F_{20}\! \left(x , y , z\right) &= F_{21}\! \left(x , y , z\right)\\
F_{21}\! \left(x , y , z\right) &= F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right) F_{19}\! \left(x , y , z\right)\\
F_{22}\! \left(x , y , z\right) &= F_{23}\! \left(x , y , z\right)\\
F_{23}\! \left(x , y , z\right) &= F_{17}\! \left(x , z\right) F_{24}\! \left(x , y , z\right) F_{25}\! \left(x , z\right)\\
F_{24}\! \left(x , y , z\right) &= \frac{y F_{14}\! \left(x , y\right)-z F_{14}\! \left(x , z\right)}{-z +y}\\
F_{25}\! \left(x , y\right) &= F_{10}\! \left(x , 1, y\right)\\
F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , 1, y\right)\\
F_{27}\! \left(x , y , z\right) &= F_{18}\! \left(x , y z , z\right)\\
\end{align*}\)