Av(12453, 12534, 12543, 13452, 13524, 13542, 14523, 14532, 23451, 23541, 24531)
Counting Sequence
1, 1, 2, 6, 24, 109, 524, 2593, 13064, 66668, 343593, 1784849, 9331901, 49055099, 259050394, ...
This specification was found using the strategy pack "Col Placements Tracked Fusion" and has 43 rules.
Found on January 24, 2022.Finding the specification took 96 seconds.
Copy 43 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_{13}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{13}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y_{0}, y_{1}\right)+F_{38}\! \left(x , y_{0}, y_{1}\right)+F_{41}\! \left(x , y_{0}, y_{1}\right)\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= F_{15}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= F_{16}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{23}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{27}\! \left(x , y_{1}, y_{2}, y_{0}\right)\\
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{3}\! \left(x \right)\\
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{0} F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{16}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{20}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}\right)\\
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{0} F_{22}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{22}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)}{-y_{1}+y_{0}}\\
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{0} y_{1} F_{13}\! \left(x , y_{0}, y_{1}\right)-y_{2} F_{13}\! \left(x , y_{0}, \frac{y_{2}}{y_{0}}\right)}{y_{0} y_{1}-y_{2}}\\
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{24}\! \left(x , y_{1}, y_{0}, y_{2}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{-y_{1} F_{25}\! \left(x , 1, y_{1}, y_{2}\right)+y_{0} F_{25}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}\\
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{2} F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{26}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{12}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)\\
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{29}\! \left(x , y_{1}, y_{0}\right) F_{31}\! \left(x , y_{1}\right) F_{5}\! \left(x , y_{2}\right) F_{9}\! \left(x , y_{1}\right)\\
F_{29}\! \left(x , y_{0}, y_{1}\right) &= F_{30}\! \left(x , y_{1}\right)+F_{9}\! \left(x , y_{0} y_{1}\right)\\
F_{30}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{9}\! \left(x , y_{0}\right)\\
F_{31}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{32}\! \left(x , y_{0}\right)\\
F_{32}\! \left(x , y_{0}\right) &= F_{33}\! \left(x , y_{0}\right)\\
F_{33}\! \left(x , y_{0}\right) &= F_{34}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{34}\! \left(x , y_{0}\right) &= F_{31}\! \left(x , y_{0}\right)+F_{35}\! \left(x , y_{0}\right)\\
F_{35}\! \left(x , y_{0}\right) &= F_{36}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)\\
F_{36}\! \left(x , y_{0}\right) &= F_{37}\! \left(x , y_{0}\right)\\
F_{37}\! \left(x , y_{0}\right) &= F_{32}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{38}\! \left(x , y_{0}, y_{1}\right) &= F_{39}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{39}\! \left(x , y_{0}, y_{1}\right) &= F_{40}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{40}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} F_{13}\! \left(x , y_{0}, 1\right)-y_{1} F_{13}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}\\
F_{41}\! \left(x , y_{0}, y_{1}\right) &= F_{42}\! \left(x , y_{0}, y_{1}\right)\\
F_{42}\! \left(x , y_{0}, y_{1}\right) &= F_{0}\! \left(x \right) F_{29}\! \left(x , y_{1}, y_{0}\right) F_{31}\! \left(x , y_{1}\right) F_{9}\! \left(x , y_{1}\right)\\
\end{align*}\)