Av(12543, 13542, 23541)
Counting Sequence
1, 1, 2, 6, 24, 117, 652, 3988, 26112, 180126, 1295090, 9631656, 73676572, 577180996, 4615090192, ...
This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 32 rules.
Found on January 22, 2022.Finding the specification took 10 seconds.
Copy 32 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_{30}\! \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_{23}\! \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{y F_{6}\! \left(x , y\right)-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_{19}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y , 1\right)\\
F_{12}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y , z\right)+F_{17}\! \left(x , y , z\right)+F_{20}\! \left(x , y , z\right)+F_{21}\! \left(x , y , z\right)\\
F_{13}\! \left(x , y , z\right) &= F_{14}\! \left(x , y , y z \right)\\
F_{14}\! \left(x , y , z\right) &= F_{15}\! \left(x , y , z\right) F_{9}\! \left(x \right)\\
F_{15}\! \left(x , y , z\right) &= \frac{y F_{16}\! \left(x , y , z\right)-F_{16}\! \left(x , 1, z\right)}{-1+y}\\
F_{12}\! \left(x , y , z\right) &= F_{16}\! \left(x , y , y z \right)\\
F_{17}\! \left(x , y , z\right) &= F_{18}\! \left(x , y , z\right) F_{19}\! \left(x , y\right)\\
F_{18}\! \left(x , y , z\right) &= \frac{z F_{12}\! \left(x , y , z\right)-F_{12}\! \left(x , y , 1\right)}{-1+z}\\
F_{19}\! \left(x , y\right) &= y x\\
F_{20}\! \left(x , y , z\right) &= F_{12}\! \left(x , y , z\right) F_{19}\! \left(x , z\right)\\
F_{21}\! \left(x , y , z\right) &= F_{22}\! \left(x , y , z\right) F_{9}\! \left(x \right)\\
F_{22}\! \left(x , y , z\right) &= \frac{y z F_{12}\! \left(x , y , z\right)-F_{12}\! \left(x , y , \frac{1}{y}\right)}{y z -1}\\
F_{23}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{9}\! \left(x \right)\\
F_{24}\! \left(x , y\right) &= \frac{y F_{25}\! \left(x , y\right)-F_{25}\! \left(x , 1\right)}{-1+y}\\
F_{25}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{26}\! \left(x , y\right)+F_{28}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right) F_{9}\! \left(x \right)\\
F_{27}\! \left(x , y\right) &= \frac{y F_{25}\! \left(x , y\right)-F_{25}\! \left(x , 1\right)}{-1+y}\\
F_{28}\! \left(x , y\right) &= F_{29}\! \left(x , y\right) F_{9}\! \left(x \right)\\
F_{29}\! \left(x , y\right) &= F_{16}\! \left(x , y , 1\right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{25}\! \left(x , 1\right)\\
\end{align*}\)