Av(13452, 13542, 14352, 14532, 15342, 15432, 31452, 31542, 35142, 51342, 51432, 53142)
Counting Sequence
1, 1, 2, 6, 24, 108, 512, 2498, 12410, 62410, 316576, 1615962, 8287620, 42657584, 220184686, ...
This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 65 rules.
Found on January 24, 2022.Finding the specification took 305 seconds.
Copy 65 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_{15}\! \left(x \right) F_{3}\! \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_{64}\! \left(x , y_{0}\right)\\
F_{5}\! \left(x , y_{0}\right) &= F_{15}\! \left(x \right) F_{6}\! \left(x , y_{0}\right)\\
F_{6}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{55}\! \left(x , y_{0}\right)+F_{57}\! \left(x , y_{0}\right)+F_{7}\! \left(x , y_{0}\right)\\
F_{7}\! \left(x , y_{0}\right) &= F_{15}\! \left(x \right) F_{8}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{9}\! \left(x , y_{0}\right)+F_{9}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{9}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , 1, y_{0}\right)\\
F_{10}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}, y_{1}\right)+F_{49}\! \left(x , y_{0}, y_{1}\right)+F_{53}\! \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 \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_{20}\! \left(x , y_{0}, y_{1}\right)+F_{22}\! \left(x , y_{0}, y_{1}\right)+F_{48}\! \left(x , y_{0}, y_{1}\right)\\
F_{13}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}, y_{1}\right)\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= F_{15}\! \left(x \right) F_{16}\! \left(x , y_{1}\right) F_{8}\! \left(x , y_{0}\right)\\
F_{15}\! \left(x \right) &= x\\
F_{16}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{17}\! \left(x , y_{0}\right)\\
F_{17}\! \left(x , y_{0}\right) &= F_{18}\! \left(x , y_{0}\right)\\
F_{18}\! \left(x , y_{0}\right) &= F_{16}\! \left(x , y_{0}\right) F_{19}\! \left(x , y_{0}\right)\\
F_{19}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{20}\! \left(x , y_{0}, y_{1}\right) &= F_{15}\! \left(x \right) F_{21}\! \left(x , y_{0}, y_{1}\right)\\
F_{21}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{12}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{22}\! \left(x , y_{0}, y_{1}\right) &= F_{19}\! \left(x , y_{0}\right) F_{23}\! \left(x , y_{0}, y_{1}\right)\\
F_{23}\! \left(x , y_{0}, y_{1}\right) &= F_{24}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{1}, y_{2}\right)+F_{20}\! \left(x , y_{1}, y_{2}\right)+F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{12}\! \left(x , y_{1}, y_{2}\right) F_{19}\! \left(x , y_{1}\right)\\
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{19}\! \left(x , y_{1}\right) F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{15}\! \left(x \right) F_{27}\! \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_{0} y_{1}, y_{1}, y_{2}\right)\\
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{15}\! \left(x \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} F_{24}\! \left(x , 1, y_{1}, y_{2}\right)-y_{0} F_{24}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}, y_{2}\right)}{-y_{1}+y_{0}}\\
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{32}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)\\
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{19}\! \left(x , y_{2}\right) F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{0} F_{34}\! \left(x , y_{0}, y_{2}\right)-y_{1} F_{34}\! \left(x , y_{1}, y_{2}\right)}{-y_{1}+y_{0}}\\
F_{34}\! \left(x , y_{0}, y_{1}\right) &= -\frac{y_{1} F_{35}\! \left(x , 1, y_{1}\right)-y_{0} F_{35}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}\\
F_{36}\! \left(x , y_{0}, y_{1}\right) &= F_{15}\! \left(x \right) F_{35}\! \left(x , y_{0}, y_{1}\right)\\
F_{37}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{36}\! \left(x , y_{0}, y_{1}\right)+F_{45}\! \left(x , y_{0}, y_{1}\right)+F_{46}\! \left(x , y_{0}, y_{1}\right)\\
F_{37}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{38}\! \left(x , y_{1}\right)+F_{39}\! \left(x , y_{0}, y_{1}\right)+F_{43}\! \left(x , y_{0}, y_{1}\right)\\
F_{38}\! \left(x , y_{0}\right) &= F_{15}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)\\
F_{39}\! \left(x , y_{0}, y_{1}\right) &= F_{19}\! \left(x , y_{1}\right) F_{40}\! \left(x , y_{1}\right)\\
F_{40}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{38}\! \left(x , y_{0}\right)+F_{41}\! \left(x , y_{0}\right)\\
F_{41}\! \left(x , y_{0}\right) &= F_{19}\! \left(x , y_{0}\right) F_{42}\! \left(x , y_{0}\right)\\
F_{42}\! \left(x , y_{0}\right) &= F_{37}\! \left(x , 1, y_{0}\right)\\
F_{43}\! \left(x , y_{0}, y_{1}\right) &= F_{19}\! \left(x , y_{1}\right) F_{44}\! \left(x , y_{0}, y_{1}\right)\\
F_{44}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{37}\! \left(x , y_{0}, y_{1}\right)+F_{37}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{45}\! \left(x , y_{0}, y_{1}\right) &= F_{16}\! \left(x , y_{1}\right) F_{19}\! \left(x , y_{1}\right)\\
F_{46}\! \left(x , y_{0}, y_{1}\right) &= F_{47}\! \left(x , y_{0}, y_{1}\right)\\
F_{47}\! \left(x , y_{0}, y_{1}\right) &= F_{16}\! \left(x , y_{1}\right) F_{19}\! \left(x , y_{1}\right) F_{37}\! \left(x , y_{0}, y_{1}\right)\\
F_{48}\! \left(x , y_{0}, y_{1}\right) &= F_{19}\! \left(x , y_{1}\right) F_{34}\! \left(x , y_{0}, y_{1}\right)\\
F_{49}\! \left(x , y_{0}, y_{1}\right) &= F_{50}\! \left(x , y_{0}, y_{1}\right)\\
F_{50}\! \left(x , y_{0}, y_{1}\right) &= F_{16}\! \left(x , y_{1}\right) F_{19}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{0}\right)\\
F_{51}\! \left(x , y_{0}\right) &= F_{52}\! \left(x , 1, y_{0}\right)\\
F_{52}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{53}\! \left(x , y_{0}, y_{1}\right) &= F_{54}\! \left(x , y_{0}, y_{1}\right)\\
F_{54}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}, y_{1}\right) F_{16}\! \left(x , y_{1}\right) F_{19}\! \left(x , y_{1}\right)\\
F_{55}\! \left(x , y_{0}\right) &= F_{15}\! \left(x \right) F_{56}\! \left(x , y_{0}\right)\\
F_{56}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{6}\! \left(x , y_{0}\right)+F_{6}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{57}\! \left(x , y_{0}\right) &= F_{19}\! \left(x , y_{0}\right) F_{58}\! \left(x , y_{0}\right)\\
F_{58}\! \left(x , y_{0}\right) &= F_{59}\! \left(x , 1, y_{0}\right)\\
F_{59}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{55}\! \left(x , y_{1}\right)+F_{60}\! \left(x , y_{0}, y_{1}\right)+F_{61}\! \left(x , y_{0}, y_{1}\right)+F_{7}\! \left(x , y_{1}\right)\\
F_{60}\! \left(x , y_{0}, y_{1}\right) &= F_{19}\! \left(x , y_{1}\right) F_{6}\! \left(x , y_{1}\right)\\
F_{61}\! \left(x , y_{0}, y_{1}\right) &= F_{62}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{62}\! \left(x , y_{0}, y_{1}\right) &= F_{19}\! \left(x , y_{1}\right) F_{63}\! \left(x , y_{0}, y_{1}\right)\\
F_{63}\! \left(x , y_{0}, y_{1}\right) &= -\frac{y_{1} F_{59}\! \left(x , 1, y_{1}\right)-y_{0} F_{59}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}\\
F_{64}\! \left(x , y_{0}\right) &= F_{19}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{0}\right)\\
\end{align*}\)