Av(12435, 13425, 14325, 23415, 24315, 34215)
Counting Sequence
1, 1, 2, 6, 24, 114, 596, 3299, 18945, 111577, 669245, 4069941, 25020310, 155169018, 969357579, ...
This specification was found using the strategy pack "Col Placements Tracked Fusion" and has 33 rules.
Found on January 22, 2022.Finding the specification took 42 seconds.
Copy 33 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_{4}\! \left(x \right)\\
F_{3}\! \left(x \right) &= x\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x , 1\right)\\
F_{5}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\
F_{6}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{7}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= \frac{F_{5}\! \left(x , y\right) y -F_{5}\! \left(x , 1\right)}{-1+y}\\
F_{8}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= y x\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , 1, y\right)\\
F_{11}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{20}\! \left(x , y , z\right)+F_{31}\! \left(x , z , y\right)\\
F_{12}\! \left(x , y , z\right) &= F_{13}\! \left(x , y z , z\right)\\
F_{13}\! \left(x , y , z\right) &= F_{14}\! \left(x , y , z\right) F_{3}\! \left(x \right)\\
F_{14}\! \left(x , y , z\right) &= \frac{F_{15}\! \left(x , y , z\right) y -F_{15}\! \left(x , 1, z\right)}{-1+y}\\
F_{15}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y , z\right)+F_{29}\! \left(x , z , y\right)+F_{6}\! \left(x , y\right)\\
F_{16}\! \left(x , y , z\right) &= F_{17}\! \left(x , y , z\right) F_{9}\! \left(x , y\right)\\
F_{17}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{19}\! \left(x , y\right)+F_{21}\! \left(x , y , z\right)+F_{27}\! \left(x , z , y\right)\\
F_{18}\! \left(x , y\right) &= F_{12}\! \left(x , 1, y\right)\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , 1, y\right)\\
F_{20}\! \left(x , y , z\right) &= F_{16}\! \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_{10}\! \left(x , y\right) F_{23}\! \left(x , y , z\right) F_{9}\! \left(x , y\right)\\
F_{23}\! \left(x , y , z\right) &= \frac{F_{24}\! \left(x , y\right) y -F_{24}\! \left(x , z\right) z}{-z +y}\\
F_{24}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{26}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)^{2} F_{9}\! \left(x , y\right)\\
F_{27}\! \left(x , y , z\right) &= F_{28}\! \left(x , y , z\right)\\
F_{28}\! \left(x , y , z\right) &= F_{17}\! \left(x , z , y\right) F_{24}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
F_{29}\! \left(x , y , z\right) &= F_{30}\! \left(x , y , z\right)\\
F_{30}\! \left(x , y , z\right) &= F_{15}\! \left(x , z , y\right) F_{24}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
F_{31}\! \left(x , y , z\right) &= F_{32}\! \left(x , y , z\right)\\
F_{32}\! \left(x , y , z\right) &= F_{11}\! \left(x , z , y\right) F_{24}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
\end{align*}\)