Av(12453, 12543)
Counting Sequence
1, 1, 2, 6, 24, 118, 672, 4256, 29176, 212586, 1625704, 12930160, 106242392, 897210996, 7756325952, ...
This specification was found using the strategy pack "All The Strategies 2 Tracked Fusion Tracked Component Fusion Symmetries" and has 35 rules.
Finding the specification took 13068 seconds.
Copy 35 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 , 1\right)\\
F_{4}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{6}\! \left(x , y\right)\\
F_{5}\! \left(x \right) &= x\\
F_{6}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{7}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= -\frac{-F_{4}\! \left(x , y\right) y +F_{4}\! \left(x , 1\right)}{-1+y}\\
F_{8}\! \left(x , y\right) &= F_{9}\! \left(x , y , 1\right)\\
F_{9}\! \left(x , y , z\right) &= F_{10}\! \left(x , y\right) F_{11}\! \left(x , z , y\right)\\
F_{10}\! \left(x , y\right) &= y x\\
F_{11}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)+F_{24}\! \left(x , z , y\right)\\
F_{12}\! \left(x , y , z\right) &= F_{13}\! \left(x , y z , z\right)\\
F_{13}\! \left(x , y , z\right) &= -\frac{-F_{14}\! \left(x , y , z\right) y +F_{14}\! \left(x , 1, z\right)}{-1+y}\\
F_{14}\! \left(x , y , z\right) &= F_{15}\! \left(x , y , z\right) F_{5}\! \left(x \right)\\
F_{16}\! \left(x , y , z\right) &= F_{10}\! \left(x , y\right) F_{15}\! \left(x , y , z\right)\\
F_{17}\! \left(x , y , z\right) &= F_{16}\! \left(x , y , y z \right)\\
F_{18}\! \left(x , y , z\right) &= \frac{F_{17}\! \left(x , y , 1\right) y -F_{17}\! \left(x , y , \frac{z}{y}\right) z}{y -z}\\
F_{19}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x , y , z\right)+F_{20}\! \left(x , y , z\right)+F_{22}\! \left(x , z , y\right)\\
F_{19}\! \left(x , y , z\right) &= \frac{F_{6}\! \left(x , y\right) y -F_{6}\! \left(x , z\right) z}{y -z}\\
F_{20}\! \left(x , y , z\right) &= -\frac{-F_{21}\! \left(x , y , z\right) y +F_{21}\! \left(x , 1, z\right)}{-1+y}\\
F_{21}\! \left(x , y , z\right) &= \frac{F_{4}\! \left(x , y\right) y -F_{4}\! \left(x , z\right) z}{y -z}\\
F_{22}\! \left(x , y , z\right) &= \frac{y F_{9}\! \left(x , y , 1\right)-z F_{9}\! \left(x , y , \frac{z}{y}\right)}{y -z}\\
F_{23}\! \left(x , y , z\right) &= F_{18}\! \left(x , y z , z\right)\\
F_{24}\! \left(x , y , z\right) &= F_{10}\! \left(x , y\right) F_{25}\! \left(x , z , y\right)\\
F_{25}\! \left(x , y , z\right) &= F_{11}\! \left(x , y , z\right)+F_{26}\! \left(x , z , y\right)\\
F_{26}\! \left(x , y , z\right) &= F_{10}\! \left(x , y\right) F_{27}\! \left(x , z , y\right)\\
F_{27}\! \left(x , y , z\right) &= F_{28}\! \left(x , y z , z\right)\\
F_{29}\! \left(x , y , z\right) &= F_{10}\! \left(x , y\right) F_{28}\! \left(x , z , y\right)\\
F_{30}\! \left(x , y , z\right) &= F_{29}\! \left(x , y z , y\right)\\
F_{30}\! \left(x , y , z\right) &= F_{10}\! \left(x , z\right) F_{31}\! \left(x , y , z\right)\\
F_{32}\! \left(x , y , z\right) &= F_{10}\! \left(x , z\right) F_{31}\! \left(x , y , z\right)\\
F_{32}\! \left(x , y , z\right) &= F_{33}\! \left(x , y , z\right)\\
F_{33}\! \left(x , y , z\right) &= F_{34}\! \left(x , y , y z \right)\\
F_{15}\! \left(x , y , z\right) &= F_{34}\! \left(x , y , z\right)+F_{6}\! \left(x , y\right)\\
\end{align*}\)