Av(12354, 12453, 12543, 13254, 13452, 13542, 14253, 14352, 23451, 23541, 24351)
Counting Sequence
1, 1, 2, 6, 24, 109, 525, 2622, 13448, 70412, 374783, 2021818, 11029479, 60738890, 337198042, ...
This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 68 rules.
Finding the specification took 369 seconds.
Copy 68 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_{3}\! \left(x \right) &= F_{11}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)+F_{65}\! \left(x \right)+F_{7}\! \left(x \right)\\
F_{6}\! \left(x \right) &= 0\\
F_{7}\! \left(x \right) &= F_{11}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{13}\! \left(x \right)+F_{6}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{11}\! \left(x \right) &= x\\
F_{12}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{11}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x , 1\right)\\
F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)+F_{22}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)+F_{19}\! \left(x \right)+F_{21}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{18}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= y x\\
F_{19}\! \left(x \right) &= F_{11}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{20}\! \left(x \right) &= F_{16}\! \left(x , 1\right)\\
F_{21}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{15}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)+F_{60}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)+F_{26}\! \left(x , y\right)+F_{44}\! \left(x , y\right)+F_{58}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{24}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{27}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= -\frac{-y F_{28}\! \left(x , y\right)+F_{28}\! \left(x , 1\right)}{-1+y}\\
F_{28}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)+F_{29}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= F_{31}\! \left(x \right)+F_{33}\! \left(x \right)+F_{42}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{31}\! \left(x \right) &= F_{32}\! \left(x \right)\\
F_{32}\! \left(x \right) &= F_{11}\! \left(x \right) F_{30}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{11}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)+F_{37}\! \left(x \right)+F_{38}\! \left(x \right)+F_{39}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{11}\! \left(x \right) F_{34}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{10}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{11}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{41}\! \left(x , 1\right)\\
F_{41}\! \left(x , y\right) &= -\frac{-y F_{15}\! \left(x , y\right)+F_{15}\! \left(x , 1\right)}{-1+y}\\
F_{42}\! \left(x \right) &= F_{11}\! \left(x \right) F_{43}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{24}\! \left(x , 1\right)\\
F_{44}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{45}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{46}\! \left(x , y\right)+F_{47}\! \left(x , y\right)+F_{51}\! \left(x , y\right)+F_{54}\! \left(x , y\right)+F_{56}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{45}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{48}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= -\frac{-F_{49}\! \left(x , y\right) y +F_{49}\! \left(x , 1\right)}{-1+y}\\
F_{49}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)+F_{50}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{34}\! \left(x \right)\\
F_{52}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x \right)+F_{25}\! \left(x , y\right)+F_{26}\! \left(x , y\right)+F_{51}\! \left(x , y\right)+F_{54}\! \left(x , y\right)\\
F_{52}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)+F_{53}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{8}\! \left(x \right)\\
F_{54}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{55}\! \left(x , y\right)\\
F_{55}\! \left(x , y\right) &= -\frac{-y F_{52}\! \left(x , y\right)+F_{52}\! \left(x , 1\right)}{-1+y}\\
F_{56}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{57}\! \left(x , y\right)\\
F_{57}\! \left(x , y\right) &= -\frac{-F_{41}\! \left(x , y\right) y +F_{41}\! \left(x , 1\right)}{-1+y}\\
F_{58}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{59}\! \left(x , y\right)\\
F_{59}\! \left(x , y\right) &= -\frac{-y F_{24}\! \left(x , y\right)+F_{24}\! \left(x , 1\right)}{-1+y}\\
F_{60}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{61}\! \left(x , y\right)+F_{62}\! \left(x , y\right)+F_{64}\! \left(x , y\right)\\
F_{61}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{60}\! \left(x , y\right)\\
F_{62}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{63}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= -\frac{-y F_{16}\! \left(x , y\right)+F_{16}\! \left(x , 1\right)}{-1+y}\\
F_{64}\! \left(x , y\right) &= F_{11}\! \left(x \right) F_{24}\! \left(x , y\right)\\
F_{65}\! \left(x \right) &= F_{11}\! \left(x \right) F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{30}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{19}\! \left(x \right)+F_{65}\! \left(x \right)\\
\end{align*}\)
This specification was found using the strategy pack "Col Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 33 rules.
Finding the specification took 25 seconds.
Copy 33 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\right) &= F_{1}\! \left(x \right)+F_{5}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\
F_{5}\! \left(x , y\right) &= F_{6}\! \left(x , y\right) F_{7}\! \left(x \right)\\
F_{6}\! \left(x , y\right) &= -\frac{-F_{4}\! \left(x , y\right) y +F_{4}\! \left(x , 1\right)}{-1+y}\\
F_{7}\! \left(x \right) &= x\\
F_{8}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , 1, y\right)\\
F_{10}\! \left(x , y , z\right) &= -\frac{F_{11}\! \left(x , 1, z\right) z -F_{11}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}\\
F_{11}\! \left(x , y , z\right) &= F_{12}\! \left(z x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{31}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{16}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{15}\! \left(x , y\right)+F_{17}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{16}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= y x\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{7}\! \left(x \right)\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , 1, y\right)\\
F_{19}\! \left(x , y , z\right) &= -\frac{-F_{20}\! \left(x , y z \right) y +F_{20}\! \left(x , z\right)}{-1+y}\\
F_{20}\! \left(x , y\right) &= F_{21}\! \left(x , y , 1\right)\\
F_{21}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{22}\! \left(x , z , y\right)+F_{23}\! \left(x , y , z\right)+F_{29}\! \left(x , y , z\right)\\
F_{22}\! \left(x , y , z\right) &= F_{16}\! \left(x , z\right) F_{21}\! \left(x , z , y\right)\\
F_{23}\! \left(x , y , z\right) &= F_{16}\! \left(x , z\right) F_{24}\! \left(x , y , z\right)\\
F_{24}\! \left(x , y , z\right) &= -\frac{-F_{25}\! \left(x , y , z\right) y +F_{25}\! \left(x , 1, z\right)}{-1+y}\\
F_{25}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{26}\! \left(x , z , y\right)+F_{27}\! \left(x , z\right)+F_{29}\! \left(x , y , z\right)\\
F_{26}\! \left(x , y , z\right) &= F_{16}\! \left(x , z\right) F_{25}\! \left(x , z , y\right)\\
F_{27}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{25}\! \left(x , 1, y\right)\\
F_{29}\! \left(x , y , z\right) &= F_{16}\! \left(x , z\right) F_{30}\! \left(x , y , z\right)\\
F_{30}\! \left(x , y , z\right) &= -\frac{-y F_{21}\! \left(x , y , z\right)+F_{21}\! \left(x , 1, z\right)}{-1+y}\\
F_{31}\! \left(x , y\right) &= F_{32}\! \left(x , y , 1\right)\\
F_{32}\! \left(x , y , z\right) &= F_{16}\! \left(x , z\right) F_{21}\! \left(x , y , z\right)\\
\end{align*}\)