Av(12345, 12435, 12453, 14235, 14253)
Counting Sequence
1, 1, 2, 6, 24, 115, 614, 3510, 21029, 130414, 830603, 5403282, 35759301, 240038812, 1630507394, ...
This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 67 rules.
Finding the specification took 1309 seconds.
Copy 67 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_{4}\! \left(x \right) F_{45}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x , 1\right)\\
F_{5}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{66}\! \left(x , y_{0}\right)\\
F_{6}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{7}\! \left(x , y_{0}\right)\\
F_{7}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{61}\! \left(x , y_{0}\right)+F_{64}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , 1, y_{0}\right)\\
F_{10}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{11}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{13}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{12}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{14}\! \left(x , y_{0}\right)\\
F_{14}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{14}\! \left(x , y_{2}\right) F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{F_{17}\! \left(x , 1, y_{1}, y_{2}\right) y_{1} y_{2}-F_{17}\! \left(x , \frac{y_{0}}{y_{1} y_{2}}, y_{1}, y_{2}\right) y_{0}}{-y_{1} y_{2}+y_{0}}\\
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{18}\! \left(x , y_{0} y_{1}, y_{2}, y_{1}\right)\\
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{12}\! \left(x , y_{0} y_{1}, y_{2}, y_{1}\right)\\
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{20}\! \left(x , y_{0}, y_{1} y_{2}, y_{2}\right)\\
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{14}\! \left(x , y_{2}\right) F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{22}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{22}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{22}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x , y_{0}, y_{1}\right)+F_{24}\! \left(x , y_{0}, y_{1}\right)+F_{27}\! \left(x , y_{0}, y_{1}\right)+F_{8}\! \left(x , y_{1}\right)\\
F_{23}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}\right) F_{22}\! \left(x , y_{0}, y_{1}\right)\\
F_{24}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{25}\! \left(x , y_{0}, y_{1}\right)\\
F_{25}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{26}\! \left(x , 1, y_{1}\right) y_{1}-F_{26}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{26}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{27}\! \left(x , y_{0}, y_{1}\right) &= F_{28}\! \left(x , y_{0}, y_{1}\right) F_{45}\! \left(x \right)\\
F_{28}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{29}\! \left(x , 1, y_{1}\right) y_{1}-F_{29}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{29}\! \left(x , y_{0}, y_{1}\right) &= F_{30}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{32}\! \left(x , y_{1}, y_{2}\right)+F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{14}\! \left(x , y_{1}\right) F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{33}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{32}\! \left(x , y_{0}, y_{1}\right)+F_{34}\! \left(x , y_{0}, y_{1}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)\\
F_{33}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} F_{5}\! \left(x , y_{0}\right)-F_{5}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{34}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{35}\! \left(x , y_{0}, y_{1}\right)\\
F_{35}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{24}\! \left(x , y_{0}, y_{1}\right)+F_{27}\! \left(x , y_{0}, y_{1}\right)+F_{36}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}, y_{1}\right)\\
F_{36}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}\right) F_{37}\! \left(x , y_{0}, y_{1}\right)\\
F_{37}\! \left(x , y_{0}, y_{1}\right) &= F_{38}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{39}\! \left(x , y_{0}, \frac{y_{1}}{y_{2}}, y_{2}\right) y_{0} y_{1}+F_{39}\! \left(x , y_{0}, \frac{1}{y_{0}}, y_{2}\right) y_{2}}{y_{0} y_{1}-y_{2}}\\
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{12}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)\\
F_{40}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{41}\! \left(x , y_{0}, y_{1}\right)\\
F_{41}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{10}\! \left(x , 1, y_{1}\right) y_{1}-F_{10}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{42}\! \left(x , y_{0}, y_{1}\right) &= F_{43}\! \left(x , y_{0}, y_{1}\right) F_{45}\! \left(x \right)\\
F_{43}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{44}\! \left(x , y_{0}\right) y_{0}-F_{44}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{44}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{5}\! \left(x , y_{0}\right)+F_{5}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{45}\! \left(x \right) &= x\\
F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{14}\! \left(x , y_{2}\right) F_{47}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{47}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{36}\! \left(x , y_{1}, y_{2}\right)+F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{51}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{14}\! \left(x , y_{1}\right) F_{47}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{14}\! \left(x , y_{2}\right) F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{41}\! \left(x , y_{0} y_{1}, y_{2}\right) y_{0}+F_{41}\! \left(x , y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{51}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{52}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)\\
F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{14}\! \left(x , y_{2}\right) F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{25}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{25}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{55}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)\\
F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{45}\! \left(x \right) F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{56}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{28}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{28}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{45}\! \left(x \right) F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{58}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{30}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{30}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{45}\! \left(x \right) F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{y_{1} y_{2} F_{29}\! \left(x , y_{1}, y_{2}\right)-y_{0} F_{29}\! \left(x , \frac{y_{0}}{y_{2}}, y_{2}\right)}{-y_{1} y_{2}+y_{0}}\\
F_{61}\! \left(x , y_{0}\right) &= F_{62}\! \left(x , y_{0}, 1\right)\\
F_{62}\! \left(x , y_{0}, y_{1}\right) &= F_{63}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{63}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{22}\! \left(x , y_{0}, y_{1}\right)\\
F_{64}\! \left(x , y_{0}\right) &= F_{65}\! \left(x , 1, y_{0}\right)\\
F_{65}\! \left(x , y_{0}, y_{1}\right) &= F_{29}\! \left(x , y_{0}, y_{1}\right) F_{45}\! \left(x \right)\\
F_{66}\! \left(x , y_{0}\right) &= F_{44}\! \left(x , y_{0}\right) F_{45}\! \left(x \right)\\
\end{align*}\)