Av(12354, 12453, 12543, 13254, 13452, 13542, 14253, 14352, 21354, 21453, 21543, 23154, 24153, 31254, 32154)
Counting Sequence
1, 1, 2, 6, 24, 105, 481, 2274, 11014, 54382, 272737, 1385583, 7115727, 36880923, 192673918, ...
This specification was found using the strategy pack "Col Placements Tracked Fusion" and has 71 rules.
Found on January 23, 2022.Finding the specification took 310 seconds.
Copy 71 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_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{3}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{61}\! \left(x \right)+F_{63}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{3}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{9}\! \left(x , 1\right)\\
F_{9}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{60}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{3}\! \left(x \right)\\
F_{11}\! \left(x , y\right) &= -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{3}\! \left(x \right)\\
F_{13}\! \left(x , y\right) &= -\frac{-y F_{14}\! \left(x , y\right)+F_{14}\! \left(x , 1\right)}{-1+y}\\
F_{14}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{37}\! \left(x , y\right)+F_{59}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{3}\! \left(x \right)\\
F_{16}\! \left(x , y\right) &= -\frac{-y F_{17}\! \left(x , y\right)+F_{17}\! \left(x , 1\right)}{-1+y}\\
F_{17}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{18}\! \left(x , y\right)+F_{29}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{3}\! \left(x \right)\\
F_{19}\! \left(x , y\right) &= -\frac{-y F_{20}\! \left(x , y\right)+F_{20}\! \left(x , 1\right)}{-1+y}\\
F_{20}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x , y\right)+F_{47}\! \left(x , y\right)+F_{48}\! \left(x , y\right)+F_{56}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{22}\! \left(x , y\right) F_{3}\! \left(x \right)\\
F_{22}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{23}\! \left(x , y\right)+F_{25}\! \left(x , y\right)+F_{27}\! \left(x , y\right)+F_{29}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{3}\! \left(x \right)\\
F_{24}\! \left(x , y\right) &= -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}\\
F_{25}\! \left(x , y\right) &= F_{26}\! \left(x , y\right) F_{3}\! \left(x \right)\\
F_{26}\! \left(x , y\right) &= -\frac{-y F_{13}\! \left(x , y\right)+F_{13}\! \left(x , 1\right)}{-1+y}\\
F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{3}\! \left(x \right)\\
F_{28}\! \left(x , y\right) &= -\frac{-y F_{19}\! \left(x , y\right)+F_{19}\! \left(x , 1\right)}{-1+y}\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{31}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= y x\\
F_{31}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{32}\! \left(x , y\right)+F_{33}\! \left(x , y\right)+F_{47}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{3}\! \left(x \right)\\
F_{33}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{34}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{37}\! \left(x , y\right)+F_{41}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{36}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= -\frac{-y F_{34}\! \left(x , y\right)+F_{34}\! \left(x , 1\right)}{-1+y}\\
F_{37}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{38}\! \left(x , y\right)\\
F_{38}\! \left(x , y\right) &= -\frac{-y F_{39}\! \left(x , y\right)+F_{39}\! \left(x , 1\right)}{-1+y}\\
F_{39}\! \left(x , y\right) &= -\frac{-y F_{40}\! \left(x , y\right)+F_{40}\! \left(x , 1\right)}{-1+y}\\
F_{40}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{32}\! \left(x , y\right)+F_{33}\! \left(x , y\right)+F_{41}\! \left(x , y\right)\\
F_{41}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{42}\! \left(x , y\right)\\
F_{42}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{41}\! \left(x , y\right)+F_{43}\! \left(x , y\right)\\
F_{43}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{44}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{29}\! \left(x , y\right)+F_{45}\! \left(x , y\right)+F_{46}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{9}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{3}\! \left(x \right)\\
F_{47}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{40}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{49}\! \left(x , y\right)\\
F_{49}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{37}\! \left(x , y\right)+F_{41}\! \left(x , y\right)+F_{50}\! \left(x , y\right)+F_{52}\! \left(x , y\right)+F_{54}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{51}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= -\frac{-y F_{16}\! \left(x , y\right)+F_{16}\! \left(x , 1\right)}{-1+y}\\
F_{52}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{53}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= -\frac{-y F_{36}\! \left(x , y\right)+F_{36}\! \left(x , 1\right)}{-1+y}\\
F_{54}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{55}\! \left(x , y\right)\\
F_{55}\! \left(x , y\right) &= -\frac{-y F_{38}\! \left(x , y\right)+F_{38}\! \left(x , 1\right)}{-1+y}\\
F_{56}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{57}\! \left(x , y\right)\\
F_{57}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{35}\! \left(x , y\right)+F_{41}\! \left(x , y\right)+F_{58}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{39}\! \left(x , y\right)\\
F_{59}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{39}\! \left(x , y\right)\\
F_{60}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{30}\! \left(x , y\right)\\
F_{61}\! \left(x \right) &= F_{3}\! \left(x \right) F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{14}\! \left(x , 1\right)\\
F_{63}\! \left(x \right) &= F_{60}\! \left(x , 1\right)\\
F_{64}\! \left(x \right) &= F_{3}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{66}\! \left(x \right)+F_{67}\! \left(x \right)+F_{68}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{32}\! \left(x , 1\right)\\
F_{67}\! \left(x \right) &= F_{33}\! \left(x , 1\right)\\
F_{68}\! \left(x \right) &= F_{3}\! \left(x \right) F_{69}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x , 1\right)\\
F_{70}\! \left(x , y\right) &= -\frac{-y F_{40}\! \left(x , y\right)+F_{40}\! \left(x , 1\right)}{-1+y}\\
\end{align*}\)