Av(12345, 12354, 12435, 13245, 13254, 13425, 14235, 14325, 23415, 24315)
Counting Sequence
1, 1, 2, 6, 24, 110, 544, 2833, 15346, 85722, 490606, 2863087, 16976590, 102002124, 619728370, ...
This specification was found using the strategy pack "Col Placements Tracked Fusion" and has 32 rules.
Found on January 24, 2022.Finding the specification took 149 seconds.
Copy 32 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 , 1, y_{0}\right)\\
F_{11}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{12}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{30}\! \left(x , y_{1}, y_{0}\right)\\
F_{13}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= F_{15}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{22}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{26}\! \left(x , y_{2}, y_{0}, y_{1}\right)\\
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{3}\! \left(x \right)\\
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-y_{0} F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{15}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{1} F_{20}\! \left(x , y_{0}, y_{1}\right)-y_{2} F_{20}\! \left(x , y_{0}, y_{2}\right)}{-y_{2}+y_{1}}\\
F_{20}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} F_{21}\! \left(x , y_{0}, 1\right)-y_{1} F_{21}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}\\
F_{21}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{23}\! \left(x , y_{0}, y_{2}, y_{1}\right)\\
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{24}\! \left(x , y_{1}\right) F_{25}\! \left(x , y_{2}, y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{24}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{9}\! \left(x , y_{0}\right)\\
F_{25}\! \left(x , y_{0}, y_{1}\right) &= -\frac{y_{1} F_{11}\! \left(x , 1, y_{1}\right)-y_{0} F_{11}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}\\
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{15}\! \left(x , y_{1}, y_{2}, y_{0}\right) F_{24}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{28}\! \left(x , y_{0}, y_{1}\right) &= F_{29}\! \left(x , y_{0}, y_{1}\right)\\
F_{29}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}\right) F_{24}\! \left(x , y_{1}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{30}\! \left(x , y_{0}, y_{1}\right) &= F_{31}\! \left(x , y_{0}, y_{1}\right)\\
F_{31}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{1}, y_{0}\right) F_{24}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
\end{align*}\)