Av(12354, 12453, 13254, 13452, 14253, 14352, 15243, 15342, 21354, 21453)
Counting Sequence
1, 1, 2, 6, 24, 110, 542, 2800, 14966, 82074, 459208, 2610938, 15042218, 87621664, 515190026, ...
This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 97 rules.
Finding the specification took 57034 seconds.
This tree is too big to show here. Click to view tree on new page.
Copy 97 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_{33}\! \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_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{33}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{8}\! \left(x \right)+F_{93}\! \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_{84}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)+F_{22}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)+F_{18}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)+F_{17}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= y x\\
F_{17}\! \left(x , y\right) &= y \,x^{2}\\
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_{12}\! \left(x , y\right) F_{15}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{33}\! \left(x \right)\\
F_{24}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{25}\! \left(x , y\right)+F_{92}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{26}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)+F_{90}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)+F_{29}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{24}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= y F_{30}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{31}\! \left(x , y\right) F_{33}\! \left(x \right)\\
F_{31}\! \left(x , y\right) &= F_{32}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{34}\! \left(x , y\right)\\
F_{33}\! \left(x \right) &= x\\
F_{34}\! \left(x , y\right) &= F_{35}\! \left(x , y\right)+F_{89}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{36}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{37}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{38}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{38}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= F_{40}\! \left(x , y\right)\\
F_{40}\! \left(x , y\right) &= F_{41}\! \left(x , y\right)+F_{45}\! \left(x , y\right)\\
F_{41}\! \left(x , y\right) &= 2 F_{42}\! \left(x \right)+F_{43}\! \left(x , y\right)+F_{44}\! \left(x , y\right)\\
F_{42}\! \left(x \right) &= 0\\
F_{43}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{33}\! \left(x \right)\\
F_{44}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{40}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{46}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{47}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{48}\! \left(x , y\right)+F_{51}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= F_{49}\! \left(x , y\right)\\
F_{49}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{50}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= -\frac{-F_{34}\! \left(x , y\right) y +F_{34}\! \left(x , 1\right)}{-1+y}\\
F_{52}\! \left(x , y\right) &= F_{51}\! \left(x , y\right)+F_{81}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{52}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{54}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{55}\! \left(x , y\right)\\
F_{55}\! \left(x , y\right) &= F_{56}\! \left(x , y\right)+F_{78}\! \left(x , y\right)\\
F_{56}\! \left(x , y\right) &= F_{57}\! \left(x , y\right)+F_{70}\! \left(x , y\right)\\
F_{57}\! \left(x , y\right) &= F_{58}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= F_{59}\! \left(x \right) F_{60}\! \left(x , y\right)\\
F_{59}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{60}\! \left(x , y\right) &= F_{61}\! \left(x , y\right)+F_{62}\! \left(x , y\right)\\
F_{61}\! \left(x , y\right) &= -\frac{-F_{9}\! \left(x , y\right) y +F_{9}\! \left(x , 1\right)}{-1+y}\\
F_{62}\! \left(x , y\right) &= F_{63}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{64}\! \left(x , y\right)\\
F_{64}\! \left(x , y\right) &= F_{65}\! \left(x , y\right)+F_{69}\! \left(x , y\right)\\
F_{65}\! \left(x , y\right) &= y F_{66}\! \left(x , y\right)\\
F_{66}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{67}\! \left(x , y\right)\\
F_{67}\! \left(x , y\right) &= -\frac{-F_{68}\! \left(x , y\right) y +F_{68}\! \left(x , 1\right)}{-1+y}\\
F_{68}\! \left(x , y\right) &= F_{40}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\
F_{69}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{61}\! \left(x , y\right)\\
F_{70}\! \left(x , y\right) &= F_{71}\! \left(x , y\right)\\
F_{71}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{72}\! \left(x , y\right) F_{77}\! \left(x \right)\\
F_{72}\! \left(x , y\right) &= F_{73}\! \left(x , y\right)+F_{74}\! \left(x , y\right)\\
F_{73}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)+F_{31}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= 2 F_{42}\! \left(x \right)+F_{75}\! \left(x , y\right)+F_{76}\! \left(x , y\right)\\
F_{75}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{33}\! \left(x \right)\\
F_{76}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{51}\! \left(x , y\right)\\
F_{77}\! \left(x \right) &= F_{68}\! \left(x , 1\right)\\
F_{78}\! \left(x , y\right) &= F_{79}\! \left(x , y\right)\\
F_{79}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{80}\! \left(x , y\right)\\
F_{80}\! \left(x , y\right) &= -\frac{-y F_{38}\! \left(x , y\right)+F_{38}\! \left(x , 1\right)}{-1+y}\\
F_{81}\! \left(x , y\right) &= F_{48}\! \left(x , y\right)+F_{82}\! \left(x , y\right)\\
F_{83}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{82}\! \left(x , y\right)\\
F_{83}\! \left(x , y\right) &= F_{84}\! \left(x , y\right)\\
F_{84}\! \left(x , y\right) &= F_{85}\! \left(x , y\right)\\
F_{85}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{86}\! \left(x , y\right)\\
F_{86}\! \left(x , y\right) &= F_{60}\! \left(x , y\right)+F_{87}\! \left(x , y\right)\\
F_{87}\! \left(x , y\right) &= F_{88}\! \left(x , y\right)\\
F_{88}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{33}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{89}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{50}\! \left(x , y\right)\\
F_{90}\! \left(x , y\right) &= y F_{91}\! \left(x , y\right)\\
F_{91}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{74}\! \left(x , y\right)\\
F_{92}\! \left(x , y\right) &= F_{33}\! \left(x \right) F_{82}\! \left(x , y\right)\\
F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{33}\! \left(x \right) F_{77}\! \left(x \right) F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= \frac{F_{96}\! \left(x \right)}{F_{33}\! \left(x \right)}\\
F_{96}\! \left(x \right) &= F_{2}\! \left(x \right)\\
\end{align*}\)