Av(12435, 12453, 12543, 14235, 14253, 14325, 41235, 41253, 41325, 43125)
Counting Sequence
1, 1, 2, 6, 24, 110, 530, 2605, 12996, 65830, 338372, 1761778, 9272894, 49253461, 263655194, ...
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 29 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_{30}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , 1, y\right)\\
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_{15}\! \left(x , y , z\right)+F_{38}\! \left(x , y , z\right)\\
F_{12}\! \left(x , y , z\right) &= F_{13}\! \left(x , y , z\right) F_{7}\! \left(x \right)\\
F_{13}\! \left(x , y , z\right) &= \frac{F_{14}\! \left(x , y , z\right) y -F_{14}\! \left(x , 1, z\right)}{-1+y}\\
F_{14}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x , y , z\right)+F_{38}\! \left(x , y , z\right)+F_{5}\! \left(x , y\right)\\
F_{15}\! \left(x , y , z\right) &= F_{16}\! \left(x , y , z\right) F_{30}\! \left(x , y\right)\\
F_{16}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)+F_{19}\! \left(x , y\right)+F_{21}\! \left(x , y , z\right)+F_{32}\! \left(x , y , z\right)\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , 1, y\right)\\
F_{18}\! \left(x , y , z\right) &= F_{12}\! \left(x , y z , z\right)\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , 1, y\right)\\
F_{20}\! \left(x , y , z\right) &= F_{15}\! \left(x , y z , z\right)\\
F_{21}\! \left(x , y , z\right) &= F_{22}\! \left(x , y , z\right)\\
F_{22}\! \left(x , y , z\right) &= F_{23}\! \left(x , y , z\right) F_{30}\! \left(x , y\right) F_{4}\! \left(x , y\right)\\
F_{23}\! \left(x , y , z\right) &= \frac{F_{24}\! \left(x , y , 1\right) y -F_{24}\! \left(x , y , \frac{z}{y}\right) z}{-z +y}\\
F_{24}\! \left(x , y , z\right) &= F_{25}\! \left(x , y z \right)+F_{31}\! \left(x , y , z\right)\\
F_{25}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{26}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)^{2} F_{30}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{29}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{30}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= y x\\
F_{31}\! \left(x , y , z\right) &= F_{28}\! \left(x , z\right) F_{30}\! \left(x , y\right)\\
F_{32}\! \left(x , y , z\right) &= F_{33}\! \left(x , y , z\right)\\
F_{33}\! \left(x , y , z\right) &= F_{30}\! \left(x , z\right) F_{34}\! \left(x , y , z\right) F_{4}\! \left(x , y\right)\\
F_{34}\! \left(x , y , z\right) &= F_{35}\! \left(x , z\right)+F_{37}\! \left(x , y , z\right)\\
F_{35}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)+F_{36}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{30}\! \left(x , y\right)\\
F_{37}\! \left(x , y , z\right) &= F_{28}\! \left(x , z\right) F_{30}\! \left(x , y\right)\\
F_{38}\! \left(x , y , z\right) &= F_{39}\! \left(x , y , z\right)\\
F_{39}\! \left(x , y , z\right) &= F_{30}\! \left(x , z\right) F_{35}\! \left(x , z\right) F_{4}\! \left(x , y\right)\\
\end{align*}\)