Av(12345, 12354, 12453, 13452, 21345, 21354, 21453, 31245, 31254, 41235)
Counting Sequence
1, 1, 2, 6, 24, 110, 536, 2690, 13711, 70494, 364281, 1888200, 9805703, 50982966, 265278047, ...
This specification was found using the strategy pack "Point And Col Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 81 rules.
Finding the specification took 2325 seconds.
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\(\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_{19}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{19}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x , 1\right)\\
F_{7}\! \left(x , y\right) &= F_{4}\! \left(x \right)+F_{8}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{63}\! \left(x , y\right)+F_{79}\! \left(x , y\right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= 0\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{39}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right)+F_{7}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= y F_{13}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\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_{16}\! \left(x \right)+F_{37}\! \left(x , y\right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{18}\! \left(x \right)+F_{76}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{19}\! \left(x \right) &= x\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x , 1\right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x \right)+F_{45}\! \left(x , y\right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{4}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{19}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x , 1\right)\\
F_{26}\! \left(x , y\right) &= F_{23}\! \left(x \right)+F_{27}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= -\frac{y \left(F_{28}\! \left(x , 1\right)-F_{28}\! \left(x , y\right)\right)}{-1+y}\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)+F_{36}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{19}\! \left(x \right) F_{31}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{33}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{33}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{35}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= -\frac{y \left(F_{8}\! \left(x , 1\right)-F_{8}\! \left(x , y\right)\right)}{-1+y}\\
F_{36}\! \left(x , y\right) &= -\frac{y \left(F_{37}\! \left(x , 1\right)-F_{37}\! \left(x , y\right)\right)}{-1+y}\\
F_{37}\! \left(x , y\right) &= F_{38}\! \left(x , y\right)+F_{40}\! \left(x , y\right)+F_{42}\! \left(x , y\right)+F_{9}\! \left(x \right)\\
F_{38}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{39}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= y x\\
F_{40}\! \left(x , y\right) &= F_{19}\! \left(x \right) F_{41}\! \left(x , y\right)\\
F_{41}\! \left(x , y\right) &= F_{36}\! \left(x , y\right)\\
F_{42}\! \left(x , y\right) &= F_{19}\! \left(x \right) F_{43}\! \left(x , y\right)\\
F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= -\frac{y \left(F_{45}\! \left(x , 1\right)-F_{45}\! \left(x , y\right)\right)}{-1+y}\\
F_{45}\! \left(x , y\right) &= 2 F_{9}\! \left(x \right)+F_{42}\! \left(x , y\right)+F_{46}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{22}\! \left(x , y\right) F_{39}\! \left(x , y\right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{19}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{51}\! \left(x \right)+F_{65}\! \left(x \right)+F_{66}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x , 1\right)\\
F_{52}\! \left(x , y\right) &= F_{4}\! \left(x \right)+F_{53}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{54}\! \left(x , y\right)+F_{59}\! \left(x , y\right)+F_{63}\! \left(x , y\right)+F_{9}\! \left(x \right)\\
F_{54}\! \left(x , y\right) &= F_{39}\! \left(x , y\right) F_{55}\! \left(x , y\right)\\
F_{55}\! \left(x , y\right) &= F_{52}\! \left(x , y\right)+F_{56}\! \left(x , y\right)\\
F_{56}\! \left(x , y\right) &= y F_{57}\! \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 \right) F_{22}\! \left(x , y\right)\\
F_{59}\! \left(x , y\right) &= F_{19}\! \left(x \right) F_{60}\! \left(x , y\right)\\
F_{60}\! \left(x , y\right) &= y F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{19}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{63}\! \left(x , y\right) &= F_{19}\! \left(x \right) F_{64}\! \left(x , y\right)\\
F_{64}\! \left(x , y\right) &= -\frac{y \left(F_{53}\! \left(x , 1\right)-F_{53}\! \left(x , y\right)\right)}{-1+y}\\
F_{65}\! \left(x \right) &= F_{46}\! \left(x , 1\right)\\
F_{66}\! \left(x \right) &= F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{19}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{75}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x , 1\right)\\
F_{70}\! \left(x , y\right) &= -\frac{-y F_{71}\! \left(x , y\right)+F_{71}\! \left(x , 1\right)}{-1+y}\\
F_{71}\! \left(x , y\right) &= F_{24}\! \left(x \right)+F_{52}\! \left(x , y\right)+F_{65}\! \left(x \right)+F_{72}\! \left(x , y\right)\\
F_{72}\! \left(x , y\right) &= F_{73}\! \left(x , y\right)\\
F_{73}\! \left(x , y\right) &= F_{19}\! \left(x \right) F_{74}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= F_{70}\! \left(x , y\right)+F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{44}\! \left(x , 1\right)\\
F_{76}\! \left(x \right) &= F_{19}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= F_{15}\! \left(x , 1\right)\\
F_{79}\! \left(x , y\right) &= F_{19}\! \left(x \right) F_{35}\! \left(x , y\right)\\
F_{80}\! \left(x \right) &= F_{19}\! \left(x \right) F_{51}\! \left(x \right)\\
\end{align*}\)