Av(13254, 13524, 15324, 31254, 31524, 32154, 32514, 35124, 35214, 51324, 53124, 53214)
Counting Sequence
1, 1, 2, 6, 24, 108, 512, 2498, 12410, 62410, 316576, 1615962, 8287620, 42657584, 220184686, ...
This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 69 rules.
Found on January 23, 2022.Finding the specification took 15 seconds.
Copy 69 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_{19}\! \left(x \right) F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{19}\! \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_{57}\! \left(x , y\right)+F_{59}\! \left(x , y\right)+F_{7}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= F_{19}\! \left(x \right) F_{8}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}\\
F_{9}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{47}\! \left(x , y\right)+F_{55}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{19}\! \left(x \right)\\
F_{11}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x \right)+F_{42}\! \left(x , y\right)+F_{43}\! \left(x , y\right)+F_{45}\! \left(x , y\right)\\
F_{12}\! \left(x \right) &= -F_{1}\! \left(x \right)-F_{13}\! \left(x \right)-F_{37}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x , 1\right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{19}\! \left(x \right)\\
F_{15}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{28}\! \left(x , y\right)+F_{30}\! \left(x , y\right)+F_{32}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x \right) F_{19}\! \left(x \right) F_{20}\! \left(x , y\right)\\
F_{18}\! \left(x \right) &= F_{9}\! \left(x , 1\right)\\
F_{19}\! \left(x \right) &= x\\
F_{20}\! \left(x , y\right) &= -\frac{-y F_{21}\! \left(x , y\right)+F_{21}\! \left(x , 1\right)}{-1+y}\\
F_{21}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{22}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{24}\! \left(x , y\right)+F_{26}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= y x\\
F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{23}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{19}\! \left(x \right) F_{20}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{30}\! \left(x , y\right) &= F_{19}\! \left(x \right) F_{31}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= -\frac{-y F_{15}\! \left(x , y\right)+F_{15}\! \left(x , 1\right)}{-1+y}\\
F_{32}\! \left(x , y\right) &= F_{25}\! \left(x , y\right) F_{33}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{24}\! \left(x , y\right)+F_{34}\! \left(x , y\right)+F_{35}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{19}\! \left(x \right) F_{33}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= F_{36}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{25}\! \left(x , y\right) F_{33}\! \left(x , y\right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{19}\! \left(x \right) F_{39}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{39} \left(x \right)^{2} F_{19}\! \left(x \right)\\
F_{42}\! \left(x , y\right) &= F_{19}\! \left(x \right) F_{31}\! \left(x , y\right)\\
F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{19}\! \left(x \right) F_{20}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{45}\! \left(x , y\right) &= F_{46}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{21}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{19}\! \left(x \right) F_{48}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{49}\! \left(x \right)+F_{50}\! \left(x \right)+F_{51}\! \left(x , y\right)+F_{53}\! \left(x , y\right)\\
F_{49}\! \left(x \right) &= F_{10}\! \left(x , 1\right)\\
F_{50}\! \left(x \right) &= F_{47}\! \left(x , 1\right)\\
F_{51}\! \left(x , y\right) &= F_{52}\! \left(x , y\right)\\
F_{52}\! \left(x , y\right) &= F_{18}\! \left(x \right) F_{19}\! \left(x \right) F_{20}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{54}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{25}\! \left(x , y\right) F_{48}\! \left(x , y\right)\\
F_{55}\! \left(x , y\right) &= F_{56}\! \left(x , y\right)\\
F_{56}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{25}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
F_{57}\! \left(x , y\right) &= F_{19}\! \left(x \right) F_{58}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}\\
F_{60}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{59}\! \left(x , y\right)+F_{64}\! \left(x , y\right)+F_{67}\! \left(x , y\right)\\
F_{60}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{61}\! \left(x , y\right)+F_{62}\! \left(x , y\right)+F_{65}\! \left(x , y\right)\\
F_{61}\! \left(x , y\right) &= F_{19}\! \left(x \right) F_{60}\! \left(x , y\right)\\
F_{62}\! \left(x , y\right) &= F_{19}\! \left(x \right) F_{63}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{32}\! \left(x , y\right)+F_{64}\! \left(x , y\right)\\
F_{64}\! \left(x , y\right) &= F_{19}\! \left(x \right) F_{63}\! \left(x , y\right)\\
F_{65}\! \left(x , y\right) &= F_{66}\! \left(x , y\right)\\
F_{66}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{25}\! \left(x , y\right) F_{60}\! \left(x , y\right)\\
F_{67}\! \left(x , y\right) &= F_{19}\! \left(x \right) F_{60}\! \left(x , y\right)\\
F_{68}\! \left(x \right) &= F_{18}\! \left(x \right) F_{19}\! \left(x \right)\\
\end{align*}\)