Av(13452, 13542, 14352, 23451, 23541, 24351)
Counting Sequence
1, 1, 2, 6, 24, 114, 598, 3336, 19400, 116252, 712618, 4446792, 28149686, 180318532, 1166591178, ...
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 58 rules.
Finding the specification took 2445 seconds.
Copy 58 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 , 1\right)\\
F_{7}\! \left(x , y\right) &= F_{8}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= x F_{8}\! \left(x , y\right)^{3} y +2 x F_{8}\! \left(x , y\right)^{2} y +2 x F_{8}\! \left(x , y\right) y +y x\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right)+F_{13}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= -\frac{y \left(F_{7}\! \left(x , 1\right)-F_{7}\! \left(x , y\right)\right)}{-1+y}\\
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_{16}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= y x\\
F_{17}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)+F_{20}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= F_{2}\! \left(x \right)+F_{9}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{48}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)+F_{25}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{24}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= x F_{24}\! \left(x , y\right)^{3} y -x F_{24}\! \left(x , y\right)^{2} y +x F_{24}\! \left(x , y\right) y +1\\
F_{26}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)+F_{57}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)+F_{28}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{7}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{30}\! \left(x , y\right) &= -\frac{-y F_{31}\! \left(x , y\right)+F_{31}\! \left(x , 1\right)}{-1+y}\\
F_{31}\! \left(x , y\right) &= F_{26}\! \left(x , y\right)+F_{32}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{33}\! \left(x \right)+F_{46}\! \left(x , y\right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{34}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= \frac{F_{36}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{36}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{37}\! \left(x \right) &= -F_{56}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= -F_{42}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= \frac{F_{40}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{43}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{43}\! \left(x \right) &= -F_{35}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{26}\! \left(x , 1\right)\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x , 1\right)\\
F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{33}\! \left(x \right) F_{48}\! \left(x , y\right)\\
F_{49}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{48}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{49}\! \left(x , y\right)+F_{52}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{50}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= F_{7}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{52}\! \left(x , y\right)+F_{55}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{53}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= F_{9}\! \left(x , y\right)\\
F_{55}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{48}\! \left(x , y\right)\\
F_{56}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{57}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{24}\! \left(x , y\right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion" and has 49 rules.
Finding the specification took 1806 seconds.
Copy 49 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_{6}\! \left(x , 1\right)\\
F_{6}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{7}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= F_{8}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= x F_{8}\! \left(x , y\right)^{3} y +2 x F_{8}\! \left(x , y\right)^{2} y +2 x F_{8}\! \left(x , y\right) y +y x\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right)+F_{13}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= -\frac{y \left(F_{7}\! \left(x , 1\right)-F_{7}\! \left(x , y\right)\right)}{-1+y}\\
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_{16}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= y x\\
F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y , 1\right)\\
F_{17}\! \left(x , y , z\right) &= F_{18}\! \left(x , y , y z \right)\\
F_{19}\! \left(x , y , z\right) &= F_{18}\! \left(x , y , z\right) F_{4}\! \left(x \right)\\
F_{19}\! \left(x , y , z\right) &= F_{20}\! \left(x , z , y\right)\\
F_{21}\! \left(x , y , z\right) &= F_{20}\! \left(x , y , z\right)+F_{46}\! \left(x , y , z\right)\\
F_{21}\! \left(x , y , z\right) &= F_{22}\! \left(x , y , z\right)+F_{6}\! \left(x , y\right)\\
F_{22}\! \left(x , y , z\right) &= F_{23}\! \left(x , y , z\right)\\
F_{23}\! \left(x , y , z\right) &= F_{15}\! \left(x , z\right) F_{24}\! \left(x , y\right) F_{44}\! \left(x , z\right)\\
F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)+F_{43}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{26}\! \left(x , y\right)+F_{6}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{28}\! \left(x , y\right) &= -\frac{-y F_{29}\! \left(x , y\right)+F_{29}\! \left(x , 1\right)}{-1+y}\\
F_{29}\! \left(x , y\right) &= F_{25}\! \left(x , y\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_{32}\! \left(x \right) F_{4}\! \left(x \right) F_{42}\! \left(x , y\right)\\
F_{32}\! \left(x \right) &= \frac{F_{33}\! \left(x \right)}{F_{4}\! \left(x \right) F_{41}\! \left(x \right)}\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= -F_{40}\! \left(x \right)+F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= \frac{F_{36}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{36}\! \left(x \right) &= F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= \frac{F_{39}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{39}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{25}\! \left(x , 1\right)\\
F_{41}\! \left(x \right) &= x F_{41} \left(x \right)^{3}-x F_{41} \left(x \right)^{2}+x F_{41}\! \left(x \right)+1\\
F_{42}\! \left(x , y\right) &= y x F_{42}\! \left(x , y\right)^{3}-y x F_{42}\! \left(x , y\right)^{2}+y x F_{42}\! \left(x , y\right)+1\\
F_{43}\! \left(x , y\right) &= F_{42}\! \left(x , y\right) F_{7}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{45}\! \left(x , 1, y\right)\\
F_{45}\! \left(x , y , z\right) &= F_{46}\! \left(x , y z , z\right)\\
F_{46}\! \left(x , y , z\right) &= F_{42}\! \left(x , y\right)+F_{47}\! \left(x , y , z\right)\\
F_{47}\! \left(x , y , z\right) &= F_{48}\! \left(x , y , z\right)\\
F_{48}\! \left(x , y , z\right) &= F_{42}\! \left(x , y\right)^{2} F_{15}\! \left(x , z\right) F_{44}\! \left(x , z\right)\\
\end{align*}\)