Av(13452, 14253, 14352, 15243, 15342, 23451, 24351, 25341, 32451)
Counting Sequence
1, 1, 2, 6, 24, 111, 547, 2767, 14186, 73435, 383322, 2015808, 10670239, 56802614, 303879311, ...
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 72 rules.
Finding the specification took 10617 seconds.
Copy 72 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_{4}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{42}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{8}\! \left(x , 1\right)\\
F_{8}\! \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_{4}\! \left(x \right)\\
F_{10}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)+F_{18}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= y x\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)+F_{22}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{21}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x \right)+F_{24}\! \left(x , y\right)+F_{26}\! \left(x , y\right)\\
F_{23}\! \left(x \right) &= 0\\
F_{24}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)+F_{22}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{18}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)+F_{43}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)+F_{36}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{2}\! \left(x \right)+F_{30}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{31}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{32}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)+F_{33}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)+F_{34}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{35}\! \left(x , y\right)+F_{36}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{2}\! \left(x \right)\\
F_{36}\! \left(x , y\right) &= F_{37}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= F_{38}\! \left(x , y\right) F_{42}\! \left(x \right)\\
F_{38}\! \left(x , y\right) &= F_{39}\! \left(x , y\right)+F_{41}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{40}\! \left(x , y\right)\\
F_{40}\! \left(x , y\right) &= -\frac{-F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}\\
F_{41}\! \left(x , y\right) &= -\frac{-F_{27}\! \left(x , y\right) y +F_{27}\! \left(x , 1\right)}{-1+y}\\
F_{42}\! \left(x \right) &= x\\
F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{42}\! \left(x \right) F_{45}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{46}\! \left(x , y\right)+F_{55}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{40}\! \left(x , y\right) F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{2}\! \left(x \right) F_{51}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{53}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{42}\! \left(x \right) F_{51}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{55}\! \left(x , y\right) &= F_{56}\! \left(x , y\right)\\
F_{56}\! \left(x , y\right) &= F_{42}\! \left(x \right) F_{57}\! \left(x , y\right)\\
F_{57}\! \left(x , y\right) &= -\frac{-y F_{58}\! \left(x , y\right)+F_{58}\! \left(x , 1\right)}{-1+y}\\
F_{59}\! \left(x , y\right) &= F_{42}\! \left(x \right) F_{58}\! \left(x , y\right)\\
F_{59}\! \left(x , y\right) &= F_{60}\! \left(x , y\right)\\
F_{60}\! \left(x , y\right) &= F_{42}\! \left(x \right) F_{61}\! \left(x , y\right)\\
F_{61}\! \left(x , y\right) &= F_{62}\! \left(x , y\right)+F_{64}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= F_{42}\! \left(x \right) F_{62}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)\\
F_{64}\! \left(x , y\right) &= F_{65}\! \left(x , y\right)\\
F_{65}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{66}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{2}\! \left(x \right) F_{53}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{42}\! \left(x \right) F_{68}\! \left(x \right)\\
\end{align*}\)