Av(13425, 13452, 14325, 14352, 14532, 31425, 31452)
Counting Sequence
1, 1, 2, 6, 24, 113, 580, 3130, 17464, 99856, 581916, 3443309, 20631962, 124929658, 763247534, ...
This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 41 rules.
Found on January 23, 2022.Finding the specification took 239 seconds.
Copy 41 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_{40}\! \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_{38}\! \left(x , y\right)+F_{5}\! \left(x , y\right)\\
F_{5}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{6}\! \left(x , y\right)\\
F_{6}\! \left(x , y\right) &= F_{7}\! \left(x , y , 1\right)\\
F_{7}\! \left(x , y , z\right) &= F_{8}\! \left(x , y , y z \right)\\
F_{8}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x , y , z\right)+F_{35}\! \left(x , y , z\right)+F_{9}\! \left(x , y , z\right)\\
F_{9}\! \left(x , y , z\right) &= F_{10}\! \left(x , y , z\right)\\
F_{10}\! \left(x , y , z\right) &= F_{11}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{4}\! \left(x , z\right)\\
F_{11}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{17}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{15}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= y x\\
F_{15}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{14}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y , 1\right)\\
F_{18}\! \left(x , y , z\right) &= F_{19}\! \left(x , y , y z \right)\\
F_{19}\! \left(x , y , z\right) &= F_{14}\! \left(x , z\right) F_{20}\! \left(x , y , z\right)\\
F_{20}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{17}\! \left(x , z\right)+F_{21}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)\\
F_{21}\! \left(x , y , z\right) &= F_{22}\! \left(x , y , z\right)\\
F_{22}\! \left(x , y , z\right) &= F_{15}\! \left(x , z\right)^{2} F_{11}\! \left(x , y\right) F_{14}\! \left(x , y\right)\\
F_{23}\! \left(x , y , z\right) &= F_{24}\! \left(x , y , z\right)\\
F_{24}\! \left(x , y , z\right) &= F_{14}\! \left(x , z\right) F_{15}\! \left(x , z\right) F_{20}\! \left(x , y , z\right)\\
F_{25}\! \left(x , y , z\right) &= F_{14}\! \left(x , z\right) F_{26}\! \left(x , y , z\right)\\
F_{26}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{27}\! \left(x , y , z\right)+F_{29}\! \left(x , y , z\right)+F_{31}\! \left(x , z\right)+F_{33}\! \left(x , z\right)\\
F_{27}\! \left(x , y , z\right) &= F_{28}\! \left(x , y , z\right)\\
F_{28}\! \left(x , y , z\right) &= F_{11}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{15}\! \left(x , z\right) F_{4}\! \left(x , z\right)\\
F_{29}\! \left(x , y , z\right) &= F_{30}\! \left(x , y , z\right)\\
F_{30}\! \left(x , y , z\right) &= F_{14}\! \left(x , z\right) F_{20}\! \left(x , y , z\right) F_{4}\! \left(x , z\right)\\
F_{31}\! \left(x , y\right) &= F_{32}\! \left(x , y , 1\right)\\
F_{32}\! \left(x , y , z\right) &= F_{25}\! \left(x , y , y z \right)\\
F_{33}\! \left(x , y\right) &= F_{34}\! \left(x , y , 1\right)\\
F_{34}\! \left(x , y , z\right) &= F_{35}\! \left(x , y , y z \right)\\
F_{35}\! \left(x , y , z\right) &= F_{36}\! \left(x , y , z\right) F_{40}\! \left(x \right)\\
F_{36}\! \left(x , y , z\right) &= \frac{F_{37}\! \left(x , y , z\right) z -F_{37}\! \left(x , y , 1\right)}{-1+z}\\
F_{37}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x , y , z\right)+F_{38}\! \left(x , z\right)+F_{9}\! \left(x , y , z\right)\\
F_{38}\! \left(x , y\right) &= F_{39}\! \left(x , y\right) F_{40}\! \left(x \right)\\
F_{39}\! \left(x , y\right) &= \frac{F_{4}\! \left(x , y\right) y -F_{4}\! \left(x , 1\right)}{-1+y}\\
F_{40}\! \left(x \right) &= x\\
\end{align*}\)