Av(12453, 13452, 14352, 23451, 24351)
Counting Sequence
1, 1, 2, 6, 24, 115, 614, 3511, 21050, 130686, 833434, 5429428, 35984323, 241893577, 1645390651, ...
This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 60 rules.
Finding the specification took 4873 seconds.
Copy 60 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_{10}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{10}\! \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_{11}\! \left(x , y_{0}\right)+F_{56}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= F_{10}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \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_{10}\! \left(x \right) &= x\\
F_{11}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right) F_{24}\! \left(x , y_{0}\right)\\
F_{12}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}, 1\right)\\
F_{13}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}\right)+F_{35}\! \left(x , y_{0}, y_{1}\right)\\
F_{14}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}\right)+F_{15}\! \left(x , y_{0}\right)+F_{17}\! \left(x , y_{0}\right)\\
F_{15}\! \left(x , y_{0}\right) &= F_{10}\! \left(x \right) F_{16}\! \left(x , y_{0}\right)\\
F_{16}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{14}\! \left(x , y_{0}\right)+F_{14}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{17}\! \left(x , y_{0}\right) &= F_{10}\! \left(x \right) F_{18}\! \left(x , y_{0}\right)\\
F_{18}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{17}\! \left(x , y_{0}\right)+F_{19}\! \left(x , y_{0}\right)+F_{21}\! \left(x , y_{0}\right)+F_{25}\! \left(x , y_{0}\right)\\
F_{19}\! \left(x , y_{0}\right) &= F_{10}\! \left(x \right) F_{20}\! \left(x , y_{0}\right)\\
F_{20}\! \left(x , y_{0}\right) &= -\frac{-F_{18}\! \left(x , y_{0}\right) y_{0}+F_{18}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{21}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right) F_{24}\! \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) &= \frac{F_{13}\! \left(x , y_{0}, y_{1}\right) y_{0} y_{1}-F_{13}\! \left(x , y_{0}, \frac{1}{y_{0}}\right)}{y_{0} y_{1}-1}\\
F_{24}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{25}\! \left(x , y_{0}\right) &= F_{10}\! \left(x \right) F_{26}\! \left(x , y_{0}\right)\\
F_{26}\! \left(x , y_{0}\right) &= F_{27}\! \left(x , y_{0}, 1\right)\\
F_{27}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{1} F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{28}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{28}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{29}\! \left(x , y_{0}, y_{1}\right)+F_{31}\! \left(x , y_{0}, y_{1}\right)+F_{33}\! \left(x , y_{0}, y_{1}\right)+F_{34}\! \left(x , y_{0}, y_{1}\right)\\
F_{29}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x \right) F_{30}\! \left(x , y_{0}, y_{1}\right)\\
F_{30}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{28}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{28}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{31}\! \left(x , y_{0}, y_{1}\right) &= F_{24}\! \left(x , y_{0}\right) F_{32}\! \left(x , y_{0}, y_{1}\right)\\
F_{32}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{13}\! \left(x , y_{0}, 1\right) y_{0}-F_{13}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{33}\! \left(x , y_{0}, y_{1}\right) &= F_{24}\! \left(x , y_{1}\right) F_{28}\! \left(x , y_{0}, y_{1}\right)\\
F_{34}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x \right) F_{27}\! \left(x , y_{0}, y_{1}\right)\\
F_{35}\! \left(x , y_{0}, y_{1}\right) &= 2 F_{36}\! \left(x \right)+F_{37}\! \left(x , y_{0}, y_{1}\right)+F_{51}\! \left(x , y_{0}, y_{1}\right)+F_{52}\! \left(x , y_{0}, y_{1}\right)\\
F_{36}\! \left(x \right) &= 0\\
F_{37}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x \right) F_{38}\! \left(x , y_{0}, y_{1}\right)\\
F_{38}\! \left(x , y_{0}, y_{1}\right) &= F_{39}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= 2 F_{36}\! \left(x \right)+F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{10}\! \left(x \right) F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{39}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{24}\! \left(x , y_{0}\right) F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{y_{2} \left(F_{44}\! \left(x , y_{0}, y_{1}\right)-F_{44}\! \left(x , y_{0}, y_{1} y_{2}\right)\right)}{y_{2}-1}\\
F_{44}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{1} \left(F_{35}\! \left(x , y_{0}, 1\right)-F_{35}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)\right)}{-y_{1}+y_{0}}\\
F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{24}\! \left(x , y_{2}\right) F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{46}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{47}\! \left(x , y_{0}, y_{1}\right)\\
F_{47}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} F_{14}\! \left(x , y_{0}\right)-F_{14}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{10}\! \left(x \right) F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{1} y_{2} \left(F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)-F_{39}\! \left(x , y_{0}, y_{1}, \frac{1}{y_{1}}\right)\right)}{y_{1} y_{2}-1}\\
F_{51}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}, y_{1}\right) F_{24}\! \left(x , y_{1}\right)\\
F_{52}\! \left(x , y_{0}, y_{1}\right) &= F_{53}\! \left(x , y_{0}, y_{1}\right)\\
F_{53}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x \right) F_{54}\! \left(x , y_{0}, y_{1}\right)\\
F_{54}\! \left(x , y_{0}, y_{1}\right) &= F_{55}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{55}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{0} y_{1} \left(F_{35}\! \left(x , y_{0}, y_{1}\right)-F_{35}\! \left(x , y_{0}, \frac{y_{2}}{y_{0}}\right)\right)}{y_{0} y_{1}-y_{2}}\\
F_{56}\! \left(x , y_{0}\right) &= F_{10}\! \left(x \right) F_{57}\! \left(x , y_{0}\right)\\
F_{57}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{14}\! \left(x , y_{0}\right)+F_{14}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{58}\! \left(x \right) &= F_{10}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{14}\! \left(x , 1\right)\\
\end{align*}\)