Av(12345, 12354, 12435, 12453, 12534, 12543, 13425, 13452, 13524, 13542, 14523, 14532, 23415, 23514, 24513)
Counting Sequence
1, 1, 2, 6, 24, 105, 474, 2160, 9869, 45118, 206266, 942828, 4308667, 19685861, 89922650, ...
This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 62 rules.
Found on January 23, 2022.Finding the specification took 292 seconds.
Copy 62 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_{14}\! \left(x \right) F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{14}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x \right)+F_{57}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{14}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{8}\! \left(x , 1\right)\\
F_{8}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)+F_{23}\! \left(x \right)+F_{57}\! \left(x \right)+F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{11}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= y x\\
F_{11}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{15}\! \left(x \right)+F_{9}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{14}\! \left(x \right)\\
F_{13}\! \left(x , y\right) &= -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}\\
F_{14}\! \left(x \right) &= x\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x \right)\\
F_{16}\! \left(x \right) &= F_{14}\! \left(x \right) F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)+F_{3}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{0}\! \left(x \right) F_{14}\! \left(x \right) F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{14}\! \left(x \right) F_{19}\! \left(x \right)\\
F_{21}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{22}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= -\frac{-y F_{8}\! \left(x , y\right)+F_{8}\! \left(x , 1\right)}{-1+y}\\
F_{23}\! \left(x \right) &= F_{14}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{28}\! \left(x \right)+F_{56}\! \left(x \right)\\
F_{25}\! \left(x \right) &= F_{14}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{14}\! \left(x \right) F_{27}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{22}\! \left(x , 1\right)\\
F_{28}\! \left(x \right) &= F_{14}\! \left(x \right) F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{30}\! \left(x , 1\right)\\
F_{30}\! \left(x , y\right) &= -\frac{-y F_{31}\! \left(x , y\right)+F_{31}\! \left(x , 1\right)}{-1+y}\\
F_{31}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)+F_{32}\! \left(x , y\right)+F_{33}\! \left(x , y\right)+F_{34}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{31}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{30}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{35}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= -\frac{-y F_{36}\! \left(x , y\right)+F_{36}\! \left(x , 1\right)}{-1+y}\\
F_{36}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x \right)+F_{37}\! \left(x , y\right)+F_{44}\! \left(x \right)+F_{54}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{38}\! \left(x , y\right)\\
F_{38}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{37}\! \left(x , y\right)+F_{39}\! \left(x , y\right)+F_{41}\! \left(x \right)\\
F_{39}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{40}\! \left(x , y\right)\\
F_{40}\! \left(x , y\right) &= -\frac{-y F_{38}\! \left(x , y\right)+F_{38}\! \left(x , 1\right)}{-1+y}\\
F_{41}\! \left(x \right) &= F_{14}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x \right)+F_{43}\! \left(x \right)+F_{44}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{14}\! \left(x \right) F_{42}\! \left(x \right)\\
F_{44}\! \left(x \right) &= F_{14}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{28}\! \left(x \right)+F_{46}\! \left(x \right)+F_{47}\! \left(x \right)+F_{49}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{14}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{14}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{35}\! \left(x , 1\right)\\
F_{49}\! \left(x \right) &= F_{14}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x , 1\right)\\
F_{51}\! \left(x , y\right) &= -\frac{-y F_{52}\! \left(x , y\right)+F_{52}\! \left(x , 1\right)}{-1+y}\\
F_{52}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)+F_{53}\! \left(x , y\right)+F_{54}\! \left(x , y\right)+F_{55}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{52}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{35}\! \left(x , y\right)\\
F_{55}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{51}\! \left(x , y\right)\\
F_{56}\! \left(x \right) &= F_{14}\! \left(x \right) F_{48}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{14}\! \left(x \right) F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{36}\! \left(x , 1\right)\\
F_{59}\! \left(x \right) &= F_{14}\! \left(x \right) F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x \right)+F_{44}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{14}\! \left(x \right) F_{58}\! \left(x \right)\\
\end{align*}\)