Av(12345, 12354, 12435, 12453, 12534, 12543, 13452, 13542)
Counting Sequence
1, 1, 2, 6, 24, 112, 568, 3026, 16640, 93510, 533720, 3081626, 17950264, 105280232, 620863656, ...
This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 43 rules.
Finding the specification took 2038 seconds.
Copy 43 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_{3}\! \left(x \right) &= F_{14}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{42}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{14}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{40}\! \left(x \right)+F_{41}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{14}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{9}\! \left(x , 1\right)\\
F_{9}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{40}\! \left(x \right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= y x\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{14}\! \left(x \right)\\
F_{13}\! \left(x , y\right) &= -\frac{-F_{9}\! \left(x , y\right) y +F_{9}\! \left(x , 1\right)}{-1+y}\\
F_{14}\! \left(x \right) &= x\\
F_{15}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{16}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)+F_{18}\! \left(x \right)+F_{29}\! \left(x \right)+F_{30}\! \left(x , y\right)+F_{32}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{16}\! \left(x , y\right)\\
F_{18}\! \left(x \right) &= F_{14}\! \left(x \right) F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x \right)+F_{20}\! \left(x \right)+F_{22}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{14}\! \left(x \right) F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{13}\! \left(x , 1\right)\\
F_{22}\! \left(x \right) &= F_{14}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x , 1\right)\\
F_{24}\! \left(x , y\right) &= -\frac{-F_{25}\! \left(x , y\right) y +F_{25}\! \left(x , 1\right)}{-1+y}\\
F_{25}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{26}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{28}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{24}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{24}\! \left(x , y\right)\\
F_{29}\! \left(x \right) &= F_{14}\! \left(x \right) F_{23}\! \left(x \right)\\
F_{30}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{31}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= -\frac{-y F_{13}\! \left(x , y\right)+F_{13}\! \left(x , 1\right)}{-1+y}\\
F_{32}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{33}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{34}\! \left(x , y , 1\right)\\
F_{34}\! \left(x , y , z\right) &= -\frac{-F_{35}\! \left(x , y , z\right) z +F_{35}\! \left(x , y , 1\right)}{-1+z}\\
F_{35}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{26}\! \left(x , z\right)+F_{28}\! \left(x , z\right)+F_{36}\! \left(x , y , z\right)+F_{37}\! \left(x , y , z\right)+F_{39}\! \left(x , y , z\right)\\
F_{36}\! \left(x , y , z\right) &= F_{11}\! \left(x , y\right) F_{35}\! \left(x , y , z\right)\\
F_{37}\! \left(x , y , z\right) &= F_{14}\! \left(x \right) F_{38}\! \left(x , y , z\right)\\
F_{38}\! \left(x , y , z\right) &= \frac{y F_{13}\! \left(x , y\right)-z F_{13}\! \left(x , z\right)}{-z +y}\\
F_{39}\! \left(x , y , z\right) &= F_{14}\! \left(x \right) F_{34}\! \left(x , y , z\right)\\
F_{40}\! \left(x \right) &= F_{14}\! \left(x \right) F_{19}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{14}\! \left(x \right) F_{19}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{14}\! \left(x \right) F_{6}\! \left(x \right)\\
\end{align*}\)