Av(13452, 14352, 23451, 24351, 34251)
Counting Sequence
1, 1, 2, 6, 24, 115, 614, 3507, 20951, 129199, 815721, 5244547, 34208870, 225772609, 1504679134, ...
This specification was found using the strategy pack "Row And Col Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 53 rules.
Finding the specification took 2299 seconds.
Copy 53 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_{5}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{5}\! \left(x \right) &= x\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x , 1\right)\\
F_{7}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{44}\! \left(x , y\right)+F_{45}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= -\frac{-F_{10}\! \left(x , y\right) y +F_{10}\! \left(x , 1\right)}{-1+y}\\
F_{10}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{14}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{12}\! \left(x , y\right) &= -\frac{-F_{7}\! \left(x , y\right) y +F_{7}\! \left(x , 1\right)}{-1+y}\\
F_{13}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{9}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{16}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= y x\\
F_{16}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{17}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{19}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)+F_{20}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{3}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{22}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{21}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{22}\! \left(x , y\right)+F_{30}\! \left(x , y\right)+F_{38}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= -\frac{-F_{24}\! \left(x , y\right) y +F_{24}\! \left(x , 1\right)}{-1+y}\\
F_{24}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)+F_{26}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{26}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{27}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)+F_{28}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)+F_{29}\! \left(x \right)\\
F_{29}\! \left(x \right) &= F_{29}\! \left(x \right) x +F_{29} \left(x \right)^{2}-2 F_{29}\! \left(x \right)+2\\
F_{30}\! \left(x , y\right) &= F_{31}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{31}\! \left(x , y\right) &= -\frac{-F_{32}\! \left(x , y\right) y +F_{32}\! \left(x , 1\right)}{-1+y}\\
F_{33}\! \left(x , y\right) &= F_{32}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{24}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)+F_{34}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{35}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)+F_{36}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{37}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{29}\! \left(x \right) F_{35}\! \left(x , y\right)\\
F_{38}\! \left(x , y\right) &= F_{39}\! \left(x , y\right) F_{5}\! \left(x \right)\\
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_{41}\! \left(x \right)+F_{42}\! \left(x , y\right)\\
F_{41}\! \left(x \right) &= F_{24}\! \left(x , 1\right)\\
F_{42}\! \left(x , y\right) &= F_{43}\! \left(x , y\right)\\
F_{43}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{29}\! \left(x \right) F_{40}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{45}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{46}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)+F_{7}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)+F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{49}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{49}\! \left(x \right) &= F_{5}\! \left(x \right) F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{10}\! \left(x , 1\right)\\
F_{51}\! \left(x \right) &= F_{5}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{5}\! \left(x \right) F_{50}\! \left(x \right)\\
\end{align*}\)