Av(12345, 12354, 13245, 13254, 13425)
Counting Sequence
1, 1, 2, 6, 24, 115, 615, 3534, 21380, 134488, 872134, 5794510, 39263562, 270396422, 1887558230, ...
This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 53 rules.
Finding the specification took 1841 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_{3}\! \left(x \right) &= F_{16}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{51}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{16}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x , 1\right)\\
F_{7}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y_{0}\right)+F_{48}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}, 1\right)\\
F_{10}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{11}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}, y_{1}\right)+F_{14}\! \left(x , y_{1}\right)+F_{17}\! \left(x , y_{0}, y_{1}\right)+F_{8}\! \left(x , y_{1}\right)\\
F_{12}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{0}, y_{1}\right) F_{13}\! \left(x , y_{0}\right)\\
F_{13}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{14}\! \left(x , y_{0}\right) &= F_{15}\! \left(x , y_{0}\right) F_{16}\! \left(x \right)\\
F_{15}\! \left(x , y_{0}\right) &= -\frac{-F_{7}\! \left(x , y_{0}\right) y_{0}+F_{7}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{16}\! \left(x \right) &= x\\
F_{17}\! \left(x , y_{0}, y_{1}\right) &= F_{16}\! \left(x \right) F_{18}\! \left(x , y_{0}, y_{1}\right)\\
F_{18}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{19}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{19}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{20}\! \left(x , y_{0}, y_{1}\right)+F_{21}\! \left(x , y_{1}\right)+F_{24}\! \left(x , y_{0}, y_{1}\right)+F_{46}\! \left(x , y_{0}, y_{1}\right)\\
F_{20}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}\right) F_{19}\! \left(x , y_{0}, y_{1}\right)\\
F_{21}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}\right)\\
F_{22}\! \left(x , y_{0}\right) &= F_{23}\! \left(x , y_{0}, 1\right)\\
F_{23}\! \left(x , y_{0}, y_{1}\right) &= F_{19}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{24}\! \left(x , y_{0}, y_{1}\right) &= F_{16}\! \left(x \right) F_{25}\! \left(x , y_{0}, y_{1}\right)\\
F_{25}\! \left(x , y_{0}, y_{1}\right) &= F_{26}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{28}\! \left(x , y_{1}, y_{2}\right)+F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{27}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{13}\! \left(x , y_{0}\right) F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{28}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}\right) F_{29}\! \left(x , y_{0}, y_{1}\right)\\
F_{29}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{10}\! \left(x , y_{0}, 1\right) y_{0}-F_{10}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{13}\! \left(x , y_{2}\right) F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{32}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{32}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{32}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{33}\! \left(x , 1, y_{1}\right) y_{1}-F_{33}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{33}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{16}\! \left(x \right) F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{26}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{16}\! \left(x \right) F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{38}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{40}\! \left(x , y_{1}, y_{2}\right)+F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{13}\! \left(x , y_{0}\right) F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{40}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}\right) F_{41}\! \left(x , y_{0}, y_{1}\right)\\
F_{41}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{23}\! \left(x , y_{0}, 1\right) y_{0}-F_{23}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{13}\! \left(x , y_{2}\right) F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{44}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{44}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{44}\! \left(x , y_{0}, y_{1}\right) &= -\frac{y_{1} F_{45}\! \left(x , 1, y_{1}\right)-y_{0} F_{45}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)}{-y_{1}+y_{0}}\\
F_{45}\! \left(x , y_{0}, y_{1}\right) &= F_{19}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{46}\! \left(x , y_{0}, y_{1}\right) &= F_{16}\! \left(x \right) F_{47}\! \left(x , y_{0}, y_{1}\right)\\
F_{47}\! \left(x , y_{0}, y_{1}\right) &= F_{38}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{48}\! \left(x , y_{0}\right) &= F_{16}\! \left(x \right) F_{49}\! \left(x , y_{0}\right)\\
F_{49}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{50}\! \left(x , y_{0}\right)+F_{50}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{50}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y_{0}\right)+F_{21}\! \left(x , y_{0}\right)+F_{48}\! \left(x , y_{0}\right)\\
F_{51}\! \left(x \right) &= F_{16}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{50}\! \left(x , 1\right)\\
\end{align*}\)