Av(13452, 13542, 14352, 23451, 23541, 24351, 34251)
Counting Sequence
1, 1, 2, 6, 24, 113, 582, 3168, 17906, 104016, 616950, 3719871, 22728729, 140408972, 875454265, ...
This specification was found using the strategy pack "Point Placements Tracked Fusion Req Corrob Symmetries" and has 36 rules.
Finding the specification took 2713 seconds.
Copy 36 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_{28}\! \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) &= y 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)+1\\
F_{25}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)+F_{26}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{27}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= -\frac{-F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}\\
F_{29}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{28}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)+F_{32}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{30}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= F_{7}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{32}\! \left(x , y\right)+F_{35}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{33}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{9}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{28}\! \left(x , y\right)\\
\end{align*}\)
This specification was found using the strategy pack "Point And Col Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 27 rules.
Finding the specification took 2222 seconds.
Copy 27 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_{1}\! \left(x \right)+F_{7}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{8}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{11}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= y x\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right)+F_{6}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{23}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)+F_{26}\! \left(x , y\right)+F_{6}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{17}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{22}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= -\frac{-y F_{19}\! \left(x , y\right)+F_{19}\! \left(x , 1\right)}{-1+y}\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{22}\! \left(x \right) F_{4}\! \left(x \right) F_{6}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= x F_{21}\! \left(x , y\right)^{3} y -x F_{21}\! \left(x , y\right)^{2} y +x F_{21}\! \left(x , y\right) y +1\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x , 1\right)\\
F_{23}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)+F_{24}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)^{2} F_{10}\! \left(x , y\right) F_{23}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{11}\! \left(x , y\right) F_{21}\! \left(x , y\right)\\
\end{align*}\)