Av(13425, 13452, 31425, 31452, 34125, 34152)
Counting Sequence
1, 1, 2, 6, 24, 114, 596, 3292, 18806, 109850, 651902, 3915492, 23744870, 145156886, 893509416, ...
This specification was found using the strategy pack "Row And Col Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 81 rules.
Finding the specification took 14776 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_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{80}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{3}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{4}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{3}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{9}\! \left(x , 1\right)\\
F_{10}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{4}\! \left(x \right)+F_{63}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{79}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{13}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{14}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= y x\\
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) &= F_{18}\! \left(x , y\right)+F_{73}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)+F_{72}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)+F_{21}\! \left(x , y\right)+F_{4}\! \left(x \right)\\
F_{20}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{19}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{22}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)+F_{23}\! \left(x , y\right)+F_{64}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{25}\! \left(x , y\right) F_{31}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{26}\! \left(x , y\right)+F_{29}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)+F_{28}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{26}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{25}\! \left(x , y\right) F_{26}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= F_{32}\! \left(x \right)+F_{36}\! \left(x , y\right)+F_{37}\! \left(x , y\right)\\
F_{32}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{3}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{31}\! \left(x , 1\right)\\
F_{36}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{31}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{37}\! \left(x , y\right)+F_{38}\! \left(x \right)+F_{42}\! \left(x , y\right)+F_{43}\! \left(x , y\right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{3}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{22}\! \left(x , 1\right)\\
F_{42}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{22}\! \left(x , y\right)\\
F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)+F_{45}\! \left(x , y\right)+F_{6}\! \left(x \right)+F_{63}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{46}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)+F_{61}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{48}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{49}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{49}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)+F_{50}\! \left(x , y\right)+F_{56}\! \left(x , y\right)+F_{60}\! \left(x , y\right)\\
F_{52}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{51}\! \left(x , y\right)\\
F_{52}\! \left(x , y\right) &= F_{53}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)+F_{53}\! \left(x , y\right)+F_{54}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{55}\! \left(x , y\right)\\
F_{55}\! \left(x , y\right) &= -\frac{-F_{9}\! \left(x , y\right) y +F_{9}\! \left(x , 1\right)}{-1+y}\\
F_{56}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{31}\! \left(x , y\right) F_{57}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{57}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{28}\! \left(x , y\right)+F_{58}\! \left(x , y\right)+F_{59}\! \left(x , y\right)\\
F_{59}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{60}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{25}\! \left(x , y\right) F_{31}\! \left(x , y\right)\\
F_{61}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{62}\! \left(x , y\right)\\
F_{62}\! \left(x , y\right) &= -\frac{-F_{46}\! \left(x , y\right) y +F_{46}\! \left(x , 1\right)}{-1+y}\\
F_{63}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)\\
F_{64}\! \left(x , y\right) &= F_{65}\! \left(x , y\right)\\
F_{65}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{66}\! \left(x , y\right)\\
F_{67}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{66}\! \left(x , y\right)\\
F_{67}\! \left(x , y\right) &= F_{68}\! \left(x , y\right)\\
F_{69}\! \left(x , y\right) &= F_{68}\! \left(x , y\right)+F_{70}\! \left(x \right)+F_{71}\! \left(x , y\right)\\
F_{69}\! \left(x , y\right) &= -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}\\
F_{70}\! \left(x \right) &= F_{11}\! \left(x , 1\right)\\
F_{71}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{55}\! \left(x , y\right)\\
F_{72}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{73}\! \left(x , y\right) &= F_{74}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{26}\! \left(x , y\right) F_{31}\! \left(x , y\right) F_{75}\! \left(x , y\right)\\
F_{75}\! \left(x , y\right) &= F_{76}\! \left(x , y\right)+F_{77}\! \left(x , y\right)\\
F_{76}\! \left(x , y\right) &= x^{2} F_{76}\! \left(x , y\right)^{2} y^{2}-2 y x F_{76}\! \left(x , y\right)^{2}+x F_{76}\! \left(x , y\right) y +2 F_{76}\! \left(x , y\right)-1\\
F_{77}\! \left(x , y\right) &= F_{78}\! \left(x , y\right)\\
F_{78}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{26}\! \left(x , y\right) F_{75}\! \left(x , y\right)\\
F_{79}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{69}\! \left(x , y\right)\\
F_{80}\! \left(x \right) &= F_{3}\! \left(x \right) F_{38}\! \left(x \right)\\
\end{align*}\)