Av(13254, 13524, 13542, 14253, 15243, 24153, 25143, 35142, 354162, 461325, 465132)
Counting Sequence
1, 1, 2, 6, 24, 112, 556, 2811, 14234, 71808, 360568, 1803100, 8988924, 44719588, 222221416, ...
This specification was found using the strategy pack "Row And Col Placements Tracked Fusion" and has 21 rules.
Found on January 24, 2022.Finding the specification took 111 seconds.
Copy 21 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_{4}\! \left(x \right)\\
F_{3}\! \left(x \right) &= x\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x , 1\right)\\
F_{5}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)\\
F_{6}\! \left(x , y_{0}\right) &= F_{3}\! \left(x \right) F_{7}\! \left(x , y_{0}\right)\\
F_{7}\! \left(x , y_{0}\right) &= \frac{y_{0} F_{5}\! \left(x , y_{0}\right)-F_{5}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{8}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{10}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , y_{0}\right)+F_{5}\! \left(x , y_{0}\right)\\
F_{12}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , y_{0}\right)+F_{20}\! \left(x , y_{0}\right)\\
F_{12}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}, 1\right)\\
F_{13}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} F_{14}\! \left(x , 1, y_{0}, y_{1}\right)-F_{14}\! \left(x , \frac{1}{y_{0}}, y_{0}, y_{1}\right)}{-1+y_{0}}\\
F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{15}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}, y_{1}\right)+F_{19}\! \left(x , y_{1}, y_{0}\right)\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{17}\! \left(x , y_{0}, y_{1}\right) &= F_{18}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{1} F_{14}\! \left(x , y_{0}, y_{1}, 1\right)-y_{2} F_{14}\! \left(x , y_{0}, y_{1}, \frac{y_{2}}{y_{1}}\right)}{-y_{2}+y_{1}}\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{15}\! \left(x , y_{1}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{20}\! \left(x , y_{0}\right) &= F_{15}\! \left(x , 1, y_{0}\right)\\
\end{align*}\)