Av(12354, 12453, 12543, 13452, 13542, 14532, 23451, 23541, 24531, 34521)
Counting Sequence
1, 1, 2, 6, 24, 110, 530, 2597, 12796, 63156, 311826, 1539461, 7598492, 37496186, 184997956, ...
This specification was found using the strategy pack "Col Placements Tracked Fusion" and has 23 rules.
Finding the specification took 1 seconds.
Copy 23 equations to clipboard:
\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x , 1\right)\\
F_{4}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{5}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\
F_{5}\! \left(x , y\right) &= F_{6}\! \left(x , y\right) F_{7}\! \left(x \right)\\
F_{6}\! \left(x , y\right) &= -\frac{-y F_{4}\! \left(x , y\right)+F_{4}\! \left(x , 1\right)}{-1+y}\\
F_{7}\! \left(x \right) &= x\\
F_{8}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , 1, y\right)\\
F_{10}\! \left(x , y , z\right) &= -\frac{-F_{11}\! \left(x , y z \right) y +F_{11}\! \left(x , z\right)}{-1+y}\\
F_{11}\! \left(x , y\right) &= -\frac{-F_{12}\! \left(x , y\right) y +F_{12}\! \left(x , 1\right)}{-1+y}\\
F_{12}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{16}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{17}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{16}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= y x\\
F_{17}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{18}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , 1, y\right)\\
F_{19}\! \left(x , y , z\right) &= -\frac{-y F_{20}\! \left(x , y , z\right)+F_{20}\! \left(x , 1, z\right)}{-1+y}\\
F_{20}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x , y , z\right)+F_{22}\! \left(x , y , z\right)\\
F_{21}\! \left(x , y , z\right) &= F_{16}\! \left(x , z\right) F_{20}\! \left(x , y , z\right)\\
F_{22}\! \left(x , y , z\right) &= F_{16}\! \left(x , z\right) F_{19}\! \left(x , y , z\right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion" and has 29 rules.
Finding the specification took 498 seconds.
Copy 29 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_{28}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x , 1\right)\\
F_{5}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{6}\! \left(x , y\right)\\
F_{6}\! \left(x , y\right) &= F_{7}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{8}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= F_{23}\! \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) &= -\frac{F_{11}\! \left(x , 1, z\right) z -y F_{11}\! \left(x , \frac{y}{z}, z\right)}{-z +y}\\
F_{11}\! \left(x , y , z\right) &= -\frac{-F_{12}\! \left(x , y z \right) y +F_{12}\! \left(x , z\right)}{-1+y}\\
F_{12}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{16}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{17}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{16}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= y x\\
F_{17}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{18}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , 1, y\right)\\
F_{19}\! \left(x , y , z\right) &= -\frac{-y F_{20}\! \left(x , y , z\right)+F_{20}\! \left(x , 1, z\right)}{-1+y}\\
F_{20}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x , y , z\right)+F_{22}\! \left(x , y , z\right)\\
F_{21}\! \left(x , y , z\right) &= F_{16}\! \left(x , z\right) F_{20}\! \left(x , y , z\right)\\
F_{22}\! \left(x , y , z\right) &= F_{16}\! \left(x , z\right) F_{19}\! \left(x , y , z\right)\\
F_{23}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , y\right) F_{28}\! \left(x \right)\\
F_{26}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}\\
F_{28}\! \left(x \right) &= x\\
\end{align*}\)