Av(13425, 13452, 14235, 14325, 14352, 31425, 31452)
Counting Sequence
1, 1, 2, 6, 24, 113, 581, 3149, 17688, 101992, 600062, 3587117, 21721993, 132948119, 821012904, ...
This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 74 rules.
Finding the specification took 766 seconds.
Copy 74 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_{5}\! \left(x \right)\\
F_{4}\! \left(x \right) &= x\\
F_{5}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{4}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{9}\! \left(x , 1\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{14}\! \left(x , y\right)+F_{72}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{0}\! \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_{9}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= y x\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{16}\! \left(x , y\right) F_{31}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{16}\! \left(x , y\right) F_{30}\! \left(x \right)\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{19}\! \left(x , y\right) F_{30}\! \left(x \right)\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(y x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{21}\! \left(x \right) &= x^{2} F_{21} \left(x \right)^{3}-x^{2} F_{21} \left(x \right)^{2}+x F_{21} \left(x \right)^{2}+1\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x , 1\right)\\
F_{23}\! \left(x , y\right) &= F_{24}\! \left(x \right)+F_{25}\! \left(x , y\right)+F_{27}\! \left(x , y\right)\\
F_{24}\! \left(x \right) &= 0\\
F_{25}\! \left(x , y\right) &= F_{26}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{19}\! \left(x , y\right) F_{21}\! \left(x \right)\\
F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{21} \left(x \right)^{2} F_{29}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{29}\! \left(x , y\right) &= x^{2} F_{29}\! \left(x , y\right)^{3} y^{2}+2 x^{2} F_{29}\! \left(x , y\right)^{2} y^{2}+x^{2} F_{29}\! \left(x , y\right) y^{2}+x F_{29}\! \left(x , y\right)^{2} y +2 x F_{29}\! \left(x , y\right) y +y x\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x , 1\right)\\
F_{31}\! \left(x , y\right) &= F_{32}\! \left(x , y\right)+F_{69}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{33}\! \left(x , y\right)+F_{5}\! \left(x \right)\\
F_{33}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)+F_{34}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{35}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{35}\! \left(x , y\right) &= F_{24}\! \left(x \right)+F_{36}\! \left(x , y\right)+F_{38}\! \left(x , y\right)+F_{62}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{37}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= -\frac{y \left(F_{11}\! \left(x , 1\right)-F_{11}\! \left(x , y\right)\right)}{-1+y}\\
F_{38}\! \left(x , y\right) &= F_{39}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{39}\! \left(x , y\right) &= -\frac{y \left(F_{40}\! \left(x , 1\right)-F_{40}\! \left(x , y\right)\right)}{-1+y}\\
F_{40}\! \left(x , y\right) &= F_{24}\! \left(x \right)+F_{41}\! \left(x , y\right)+F_{43}\! \left(x , y\right)+F_{45}\! \left(x , y\right)\\
F_{41}\! \left(x , y\right) &= F_{42}\! \left(x , y\right)\\
F_{42}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{19}\! \left(x , y\right) F_{8}\! \left(x \right)\\
F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{29}\! \left(x , y\right) F_{4}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{46}\! \left(x , y\right) &= F_{24}\! \left(x \right)+F_{45}\! \left(x , y\right)+F_{57}\! \left(x , y\right)+F_{60}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{19}\! \left(x , y\right) F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= \frac{F_{49}\! \left(x \right)}{F_{4}\! \left(x \right) F_{56}\! \left(x \right)}\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x , 1\right)\\
F_{52}\! \left(x , y\right) &= F_{33}\! \left(x , y\right)+F_{51}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= -\frac{y \left(F_{52}\! \left(x , 1\right)-F_{52}\! \left(x , y\right)\right)}{-1+y}\\
F_{54}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{53}\! \left(x , y\right)\\
F_{55}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)+F_{54}\! \left(x , y\right)\\
F_{55}\! \left(x , y\right) &= F_{37}\! \left(x , y\right)\\
F_{56}\! \left(x \right) &= F_{16}\! \left(x , 1\right)\\
F_{57}\! \left(x , y\right) &= F_{58}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{19}\! \left(x , y\right) F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{32}\! \left(x , 1\right)\\
F_{60}\! \left(x , y\right) &= F_{61}\! \left(x , y\right)\\
F_{61}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{29}\! \left(x , y\right) F_{4}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{62}\! \left(x , y\right) &= F_{63}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{64}\! \left(x , y\right)\\
F_{64}\! \left(x , y\right) &= -\frac{y \left(F_{65}\! \left(x , 1\right)-F_{65}\! \left(x , y\right)\right)}{-1+y}\\
F_{66}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{65}\! \left(x , y\right)\\
F_{66}\! \left(x , y\right) &= F_{67}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{24}\! \left(x \right)+F_{67}\! \left(x , y\right)+F_{68}\! \left(x , y\right)\\
F_{68}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)\\
F_{69}\! \left(x , y\right) &= F_{70}\! \left(x , y\right)\\
F_{70}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{32}\! \left(x , y\right) F_{71}\! \left(x , y\right)\\
F_{71}\! \left(x , y\right) &= y^{2} x^{2} F_{71}\! \left(x , y\right)^{3}-x^{2} F_{71}\! \left(x , y\right)^{2} y^{2}+y x F_{71}\! \left(x , y\right)^{2}+1\\
F_{72}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{73}\! \left(x , y\right)\\
F_{73}\! \left(x , y\right) &= -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}\\
\end{align*}\)