Av(12345, 12354, 12435, 13245, 13254, 13425, 13452, 13524, 13542, 14235, 14325, 14352, 21345, 21354, 21435)
Counting Sequence
1, 1, 2, 6, 24, 105, 485, 2324, 11448, 57585, 294483, 1526201, 7997663, 42301336, 225524751, ...
This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 30 rules.
Found on January 23, 2022.Finding the specification took 5 seconds.
Copy 30 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_{28}\! \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_{1}\! \left(x \right)+F_{10}\! \left(x \right)+F_{12}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{5}\! \left(x \right) F_{8}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= x\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{5}\! \left(x \right) F_{8}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x , 1\right)\\
F_{14}\! \left(x , y\right) &= -\frac{-y F_{15}\! \left(x , y\right)+F_{15}\! \left(x , 1\right)}{-1+y}\\
F_{15}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{20}\! \left(x , y\right)+F_{27}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{18}\! \left(x , y\right) F_{19}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= y x\\
F_{20}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{9}\! \left(x \right)\\
F_{21}\! \left(x , y\right) &= -\frac{-y F_{22}\! \left(x , y\right)+F_{22}\! \left(x , 1\right)}{-1+y}\\
F_{22}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x , y\right)+F_{25}\! \left(x , y\right)+F_{27}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{19}\! \left(x , y\right) F_{22}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{26}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{5}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{27}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{9}\! \left(x \right)\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right) F_{9}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{15}\! \left(x , 1\right)\\
\end{align*}\)