Av(12435, 12453, 21435, 21453, 24135, 24153, 24315)
Counting Sequence
1, 1, 2, 6, 24, 113, 580, 3121, 17266, 97200, 553626, 3179393, 18369558, 106621863, 621079038, ...
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 45 rules.
Finding the specification took 2975 seconds.
Copy 45 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_{35}\! \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) &= y^{2} x^{2}+4 x F_{7}\! \left(x , y\right)^{2} y -F_{7}\! \left(x , y\right)^{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_{35}\! \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_{14}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{21}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{25}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{22}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)^{2} F_{21}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= y x\\
F_{22}\! \left(x , y\right) &= -\frac{-F_{23}\! \left(x , y\right) y +F_{23}\! \left(x , 1\right)}{-1+y}\\
F_{24}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{23}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{6}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{26}\! \left(x , y\right) F_{29}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{27}\! \left(y x \right)\\
F_{27}\! \left(x \right) &= F_{28}\! \left(x , 1\right)\\
F_{28}\! \left(x , y\right) &= -\frac{-F_{18}\! \left(x , y\right)+F_{18}\! \left(x , 1\right)}{-1+y}\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)+F_{36}\! \left(x , y\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_{32}\! \left(x , y\right)+F_{33}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{20}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{29}\! \left(x , y\right) F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= x\\
F_{36}\! \left(x , y\right) &= F_{37}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= F_{35}\! \left(x \right) F_{38}\! \left(x , y\right) F_{41}\! \left(x \right)\\
F_{38}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{39}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= F_{40}\! \left(x , y\right)\\
F_{40}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{38}\! \left(x , y\right)\\
F_{41}\! \left(x \right) &= F_{42}\! \left(x , 1\right)\\
F_{43}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{42}\! \left(x , y\right)\\
F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{31}\! \left(x , y\right)+F_{44}\! \left(x , y\right)\\
\end{align*}\)