Av(12453, 12543, 13452, 13542, 14532, 23451, 23541, 24531)
Counting Sequence
1, 1, 2, 6, 24, 112, 562, 2924, 15536, 83720, 455910, 2503448, 13840904, 76964144, 430083692, ...
This specification was found using the strategy pack "Row And Col Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 91 rules.
Finding the specification took 1598 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_{4}\! \left(x \right)\\
F_{3}\! \left(x \right) &= x\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{3}\! \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_{11}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{7}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= y x\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{3}\! \left(x \right)\\
F_{12}\! \left(x , y\right) &= -\frac{-F_{7}\! \left(x , y\right) y +F_{7}\! \left(x , 1\right)}{-1+y}\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{59}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)+F_{89}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{81}\! \left(x \right)\\
F_{18}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{64}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{3}\! \left(x \right)\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{22}\! \left(x \right)+F_{74}\! \left(x , y\right)\\
F_{22}\! \left(x \right) &= -F_{73}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right) F_{3}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{27}\! \left(x \right)+F_{63}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x , 1\right)\\
F_{28}\! \left(x , y\right) &= F_{29}\! \left(x \right) F_{52}\! \left(x , y\right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{32}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{3}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{3}\! \left(x \right) F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{29}\! \left(x \right)+F_{34}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{3}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= \frac{F_{37}\! \left(x \right)}{F_{3}\! \left(x \right)}\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= -F_{41}\! \left(x \right)-F_{6}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x , 1\right)\\
F_{40}\! \left(x , y\right) &= -\frac{-F_{7}\! \left(x , y\right) y +F_{7}\! \left(x , 1\right)}{-1+y}\\
F_{41}\! \left(x \right) &= F_{3}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x , 1\right)\\
F_{43}\! \left(x , y\right) &= -\frac{-y F_{44}\! \left(x , y\right)+F_{44}\! \left(x , 1\right)}{-1+y}\\
F_{45}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{44}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= F_{30}\! \left(x \right)+F_{45}\! \left(x , y\right)+F_{46}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{30}\! \left(x \right)+F_{47}\! \left(x , y\right)+F_{48}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{16}\! \left(x , y\right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{14}\! \left(x , 1\right)\\
F_{51}\! \left(x \right) &= F_{29}\! \left(x \right) F_{3}\! \left(x \right)\\
F_{52}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{53}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{54}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= F_{10}\! \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) &= F_{57}\! \left(x , y\right)+F_{60}\! \left(x , y\right)\\
F_{57}\! \left(x , y\right) &= F_{58}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{59}\! \left(x , y\right)\\
F_{59}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{57}\! \left(x , y\right)\\
F_{60}\! \left(x , y\right) &= F_{61}\! \left(x , y\right)\\
F_{61}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{62}\! \left(x , y\right)\\
F_{62}\! \left(x , y\right) &= F_{53}\! \left(x , y\right)+F_{60}\! \left(x , y\right)\\
F_{63}\! \left(x \right) &= F_{64}\! \left(x , 1\right)\\
F_{64}\! \left(x , y\right) &= F_{65}\! \left(x \right)+F_{66}\! \left(x , y\right)+F_{71}\! \left(x , y\right)\\
F_{65}\! \left(x \right) &= 0\\
F_{66}\! \left(x , y\right) &= F_{67}\! \left(x , y\right)\\
F_{67}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{3}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{3}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{71}\! \left(x , y\right) &= F_{72}\! \left(x , y\right)\\
F_{72}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{64}\! \left(x , y\right) F_{68}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x , 1\right)\\
F_{74}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{75}\! \left(x , y\right)\\
F_{75}\! \left(x , y\right) &= F_{64}\! \left(x , y\right)+F_{76}\! \left(x , y\right)\\
F_{76}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)+F_{77}\! \left(x , y\right)+F_{79}\! \left(x , y\right)\\
F_{77}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{78}\! \left(x , y\right)\\
F_{78}\! \left(x , y\right) &= -\frac{-y F_{76}\! \left(x , y\right)+F_{76}\! \left(x , 1\right)}{-1+y}\\
F_{79}\! \left(x , y\right) &= F_{80}\! \left(x , y\right)\\
F_{80}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{59}\! \left(x , y\right) F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= F_{3}\! \left(x \right) F_{84}\! \left(x \right)\\
F_{84}\! \left(x \right) &= F_{81}\! \left(x \right)+F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{3}\! \left(x \right) F_{88}\! \left(x \right)\\
F_{88}\! \left(x \right) &= F_{82}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{89}\! \left(x , y\right) &= F_{90}\! \left(x , y\right)\\
F_{90}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{59}\! \left(x , y\right)\\
\end{align*}\)