Av(14532, 41532, 45132, 45312)
Counting Sequence
1, 1, 2, 6, 24, 116, 634, 3770, 23850, 158298, 1091984, 7776312, 56877656, 425610184, 3248113394, ...
This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 35 rules.
Found on January 23, 2022.Finding the specification took 13 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_{7}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x , 1\right)\\
F_{4}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{5}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)\\
F_{5}\! \left(x , y_{0}\right) &= F_{6}\! \left(x , y_{0}\right) F_{7}\! \left(x \right)\\
F_{6}\! \left(x , y_{0}\right) &= \frac{y_{0} F_{4}\! \left(x , y_{0}\right)-F_{4}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{7}\! \left(x \right) &= x\\
F_{8}\! \left(x , y_{0}\right) &= F_{15}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= \frac{y_{0} F_{10}\! \left(x , 1, y_{0}\right)-F_{10}\! \left(x , \frac{1}{y_{0}}, y_{0}\right)}{-1+y_{0}}\\
F_{10}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}, y_{1}\right)+F_{33}\! \left(x , y_{0}, y_{1}\right)\\
F_{11}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}, y_{1}\right) F_{15}\! \left(x , y_{1}\right)\\
F_{12}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{13}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{13}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{15}\! \left(x , y_{2}\right)\\
F_{15}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{17}\! \left(x , y_{0} y_{1}, y_{2}, y_{1}\right)\\
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{18}\! \left(x , y_{0} y_{1}, y_{2}, y_{1}\right)\\
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{15}\! \left(x , y_{2}\right) F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{-y_{1} y_{2} F_{13}\! \left(x , 1, y_{1}, y_{2}\right)+y_{0} F_{13}\! \left(x , \frac{y_{0}}{y_{1} y_{2}}, y_{1}, y_{2}\right)}{-y_{1} y_{2}+y_{0}}\\
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{15}\! \left(x , y_{2}\right) F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{22}\! \left(x , y_{0} y_{1}, y_{2}, y_{1}\right)\\
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{2} F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{23}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{24}\! \left(x , y_{0} y_{1}, y_{2}, y_{1}\right)\\
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{24}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)\\
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{-y_{1} y_{2} F_{25}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)+y_{0} F_{25}\! \left(x , y_{0}, \frac{1}{y_{2}}, y_{2}\right)}{-y_{1} y_{2}+y_{0}}\\
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{15}\! \left(x , y_{0}\right) F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{-y_{1} y_{2} F_{10}\! \left(x , y_{1}, y_{2}\right)+y_{0} F_{10}\! \left(x , \frac{y_{0}}{y_{2}}, y_{2}\right)}{-y_{1} y_{2}+y_{0}}\\
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{15}\! \left(x , y_{2}\right) F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{-y_{1} y_{2} F_{31}\! \left(x , y_{1}, y_{2}\right)+y_{0} F_{31}\! \left(x , \frac{y_{0}}{y_{2}}, y_{2}\right)}{-y_{1} y_{2}+y_{0}}\\
F_{31}\! \left(x , y_{0}, y_{1}\right) &= F_{32}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{32}\! \left(x , y_{0}, y_{1}\right) &= \frac{-y_{1} F_{10}\! \left(x , 1, y_{1}\right)+y_{0} F_{10}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}\\
F_{33}\! \left(x , y_{0}, y_{1}\right) &= F_{34}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{34}\! \left(x , y_{0}, y_{1}\right) &= F_{15}\! \left(x , y_{1}\right) F_{32}\! \left(x , y_{0}, y_{1}\right)\\
\end{align*}\)