Av(12453, 12534, 12543, 13524, 21453, 21534, 21543, 31452, 31542)
Counting Sequence
1, 1, 2, 6, 24, 111, 549, 2817, 14809, 79256, 430166, 2361629, 13090327, 73155326, 411743737, ...
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 50 rules.
Finding the specification took 2366 seconds.
Copy 50 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_{22}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{22}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{2}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{0}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{0}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= x^{2} F_{18} \left(x \right)^{3}-x^{2} F_{18} \left(x \right)^{2}+x F_{18} \left(x \right)^{2}+1\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{15}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= x\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{22}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{28}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{15}\! \left(x \right) F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= x^{2} F_{27} \left(x \right)^{3}+2 x^{2} F_{27} \left(x \right)^{2}+x^{2} F_{27}\! \left(x \right)+x F_{27} \left(x \right)^{2}+2 x F_{27}\! \left(x \right)+x\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{18}\! \left(x \right) F_{27}\! \left(x \right) F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{18}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{18}\! \left(x \right) F_{30}\! \left(x \right) F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= \frac{F_{37}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{37}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{22}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{41}\! \left(x \right) &= F_{2}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= \frac{F_{43}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{43}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{35}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= \frac{F_{46}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{11}\! \left(x \right) F_{22}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 49 rules.
Finding the specification took 2605 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_{22}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{22}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{2}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)+F_{32}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{0}\! \left(x \right) F_{15}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)+F_{31}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{19}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{0}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= x^{2} F_{18} \left(x \right)^{3}-x^{2} F_{18} \left(x \right)^{2}+x F_{18} \left(x \right)^{2}+1\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\
F_{21}\! \left(x \right) &= F_{15}\! \left(x \right) F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= x\\
F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{22}\! \left(x \right) F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{28}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{15}\! \left(x \right) F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= x^{2} F_{27} \left(x \right)^{3}+2 x^{2} F_{27} \left(x \right)^{2}+x^{2} F_{27}\! \left(x \right)+x F_{27} \left(x \right)^{2}+2 x F_{27}\! \left(x \right)+x\\
F_{28}\! \left(x \right) &= F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{18}\! \left(x \right) F_{27}\! \left(x \right) F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{18}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{18}\! \left(x \right) F_{30}\! \left(x \right) F_{34}\! \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_{22}\! \left(x \right)}\\
F_{36}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{22}\! \left(x \right) F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)+F_{43}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{2}\! \left(x \right) F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= \frac{F_{42}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{42}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{34}\! \left(x \right) F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= \frac{F_{45}\! \left(x \right)}{F_{22}\! \left(x \right)}\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{11}\! \left(x \right) F_{22}\! \left(x \right)\\
\end{align*}\)