Av(12435, 12453, 14235, 14253, 14523, 21435, 21453)
Counting Sequence
1, 1, 2, 6, 24, 113, 580, 3134, 17550, 100995, 593988, 3556136, 21606928, 132926679, 826501640, ...
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 37 rules.
Finding the specification took 2099 seconds.
Copy 37 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_{36}\! \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 , 1\right)\\
F_{6}\! \left(x , y\right) &= F_{7}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= x^{2} F_{7}\! \left(x , y\right)^{2} y^{2}+2 x^{2} F_{7}\! \left(x , y\right) y^{2}+x^{2} y^{2}-2 x F_{7}\! \left(x , y\right)^{2} y -3 x F_{7}\! \left(x , y\right) y -y x +2 F_{7}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{36}\! \left(x \right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{7}\! \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_{20}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)+F_{21}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= x^{2} F_{16}\! \left(x , y\right)^{2} y^{2}-2 y x F_{16}\! \left(x , y\right)^{2}+x F_{16}\! \left(x , y\right) y +2 F_{16}\! \left(x , y\right)-1\\
F_{17}\! \left(x , y\right) &= -\frac{-F_{18}\! \left(x , y\right) y +F_{18}\! \left(x , 1\right)}{-1+y}\\
F_{19}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= F_{6}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= y x\\
F_{21}\! \left(x , y\right) &= F_{22}\! \left(x , y\right) F_{31}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)+F_{22}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{23}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)+F_{27}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{6}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)+F_{30}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{8}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{2}\! \left(x \right) F_{23}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= -\frac{-y F_{32}\! \left(x , y\right)+F_{32}\! \left(x , 1\right)}{-1+y}\\
F_{32}\! \left(x , y\right) &= F_{33}\! \left(x , y\right)+F_{34}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{6}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{35}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= F_{31}\! \left(x , y\right) F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= x\\
\end{align*}\)