Av(13254, 13524, 15324, 31254, 31524, 35124, 51324, 53124)
Counting Sequence
1, 1, 2, 6, 24, 112, 568, 3032, 16768, 95200, 551616, 3248704, 19389824, 117021824, 712934784, ...
This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 60 rules.
Found on January 23, 2022.Finding the specification took 41 seconds.
Copy 60 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_{15}\! \left(x \right) F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{15}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x , 1\right)\\
F_{6}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{45}\! \left(x , y\right)+F_{57}\! \left(x , y\right)+F_{7}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= F_{15}\! \left(x \right) F_{8}\! \left(x , y\right)\\
F_{8}\! \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_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{15}\! \left(x \right)\\
F_{10}\! \left(x , y\right) &= -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}\\
F_{11}\! \left(x , y\right) &= -\frac{-y F_{12}\! \left(x , y\right)+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_{16}\! \left(x , y\right)+F_{17}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{15}\! \left(x \right)\\
F_{14}\! \left(x , y\right) &= -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}\\
F_{15}\! \left(x \right) &= x\\
F_{16}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{15}\! \left(x \right)\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{19}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= y x\\
F_{20}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{22}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)^{2} F_{19}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{15}\! \left(x \right) F_{24}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= -\frac{-y F_{14}\! \left(x , y\right)+F_{14}\! \left(x , 1\right)}{-1+y}\\
F_{25}\! \left(x , y\right) &= F_{15}\! \left(x \right) F_{26}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}\\
F_{14}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{28}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{15}\! \left(x \right) F_{29}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= -\frac{-y F_{30}\! \left(x , y\right)+F_{30}\! \left(x , 1\right)}{-1+y}\\
F_{30}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)+F_{31}\! \left(x , y\right)+F_{40}\! \left(x , y\right)+F_{44}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{31}\! \left(x , y\right)+F_{40}\! \left(x , y\right)+F_{41}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)+F_{34}\! \left(x , y\right)+F_{38}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{15}\! \left(x \right) F_{30}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{15}\! \left(x \right) F_{35}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{34}\! \left(x , y\right)+F_{36}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{37}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{20}\! \left(x , y\right) F_{35}\! \left(x , y\right)\\
F_{38}\! \left(x , y\right) &= F_{39}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{20}\! \left(x , y\right) F_{32}\! \left(x , y\right)\\
F_{40}\! \left(x , y\right) &= F_{15}\! \left(x \right) F_{32}\! \left(x , y\right)\\
F_{6}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{41}\! \left(x , y\right)+F_{42}\! \left(x , y\right)+F_{43}\! \left(x , y\right)\\
F_{42}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{15}\! \left(x \right)\\
F_{43}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{15}\! \left(x \right)\\
F_{44}\! \left(x , y\right) &= F_{15}\! \left(x \right) F_{30}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{15}\! \left(x \right) F_{46}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{47}\! \left(x , y\right)+F_{51}\! \left(x , y\right)+F_{53}\! \left(x , y\right)+F_{55}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{48}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= F_{15}\! \left(x \right) F_{49}\! \left(x \right) F_{50}\! \left(x , y\right)\\
F_{49}\! \left(x \right) &= F_{12}\! \left(x , 1\right)\\
F_{50}\! \left(x , y\right) &= -\frac{-y F_{20}\! \left(x , y\right)+F_{20}\! \left(x , 1\right)}{-1+y}\\
F_{51}\! \left(x , y\right) &= F_{52}\! \left(x , y\right)\\
F_{52}\! \left(x , y\right) &= F_{15}\! \left(x \right) F_{5}\! \left(x \right) F_{50}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{15}\! \left(x \right) F_{54}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= -\frac{-y F_{46}\! \left(x , y\right)+F_{46}\! \left(x , 1\right)}{-1+y}\\
F_{35}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{55}\! \left(x , y\right)+F_{56}\! \left(x , y\right)\\
F_{56}\! \left(x , y\right) &= F_{15}\! \left(x \right) F_{35}\! \left(x , y\right)\\
F_{57}\! \left(x , y\right) &= F_{58}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{20}\! \left(x , y\right) F_{6}\! \left(x , y\right)\\
F_{59}\! \left(x \right) &= F_{15}\! \left(x \right) F_{49}\! \left(x \right)\\
\end{align*}\)