Av(12345, 12354, 12435, 13245, 13254, 13524)
Counting Sequence
1, 1, 2, 6, 24, 114, 598, 3340, 19491, 117502, 726259, 4577820, 29314065, 190155745, 1246878942, ...
This specification was found using the strategy pack "Row Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 97 rules.
Finding the specification took 32266 seconds.
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\(\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_{17}\! \left(x \right) F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{95}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{17}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x \right)+F_{91}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{17}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{8}\! \left(x , 1\right)\\
F_{8}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}\right)+F_{6}\! \left(x \right)+F_{9}\! \left(x , y_{0}\right)+F_{90}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{8}\! \left(x , y_{0}\right)\\
F_{10}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{11}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right) F_{17}\! \left(x \right)\\
F_{12}\! \left(x , y_{0}\right) &= -\frac{-F_{13}\! \left(x , y_{0}\right) y_{0}+F_{13}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{13}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}\right)+F_{14}\! \left(x , y_{0}\right)+F_{15}\! \left(x , y_{0}\right)+F_{18}\! \left(x , y_{0}\right)\\
F_{14}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{13}\! \left(x , y_{0}\right)\\
F_{15}\! \left(x , y_{0}\right) &= F_{16}\! \left(x , y_{0}\right) F_{17}\! \left(x \right)\\
F_{16}\! \left(x , y_{0}\right) &= -\frac{-F_{8}\! \left(x , y_{0}\right) y_{0}+F_{8}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{17}\! \left(x \right) &= x\\
F_{18}\! \left(x , y_{0}\right) &= F_{17}\! \left(x \right) F_{19}\! \left(x , y_{0}\right)\\
F_{19}\! \left(x , y_{0}\right) &= F_{20}\! \left(x , y_{0}, 1\right)\\
F_{20}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{21}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{21}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{21}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{22}\! \left(x , y_{0}, y_{1}\right)+F_{23}\! \left(x , y_{0}, y_{1}\right)+F_{83}\! \left(x , y_{0}, y_{1}\right)+F_{89}\! \left(x , y_{0}, y_{1}\right)\\
F_{22}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}\right) F_{21}\! \left(x , y_{0}, y_{1}\right)\\
F_{23}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{1}\right) F_{24}\! \left(x , y_{0}, y_{1}\right)\\
F_{24}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{25}\! \left(x , 1, y_{1}\right) y_{1}-F_{25}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{25}\! \left(x , y_{0}, y_{1}\right) &= F_{26}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{26}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{27}\! \left(x , y_{0}, y_{1}\right)+F_{28}\! \left(x , y_{1}\right)+F_{31}\! \left(x , y_{1}\right)+F_{82}\! \left(x , y_{0}, y_{1}\right)\\
F_{27}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}\right) F_{26}\! \left(x , y_{0}, y_{1}\right)\\
F_{28}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{29}\! \left(x , y_{0}\right)\\
F_{29}\! \left(x , y_{0}\right) &= F_{30}\! \left(x , y_{0}, 1\right)\\
F_{30}\! \left(x , y_{0}, y_{1}\right) &= F_{26}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{31}\! \left(x , y_{0}\right) &= F_{17}\! \left(x \right) F_{32}\! \left(x , y_{0}\right)\\
F_{32}\! \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_{33}\! \left(x , y_{0}\right)+F_{77}\! \left(x , y_{0}\right)\\
F_{33}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{34}\! \left(x , y_{0}\right)\\
F_{34}\! \left(x , y_{0}\right) &= F_{35}\! \left(x , y_{0}, 1\right)\\
F_{35}\! \left(x , y_{0}, y_{1}\right) &= F_{36}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{36}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{1}\right)+F_{15}\! \left(x , y_{1}\right)+F_{33}\! \left(x , y_{1}\right)+F_{37}\! \left(x , y_{0}, y_{1}\right)+F_{38}\! \left(x , y_{0}, y_{1}\right)\\
F_{37}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}\right) F_{36}\! \left(x , y_{0}, y_{1}\right)\\
F_{38}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x \right) F_{39}\! \left(x , y_{0}, y_{1}\right)\\
F_{39}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{40}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{40}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{40}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{41}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{41}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{41}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{1}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)+F_{43}\! \left(x , y_{0}, y_{1}\right)+F_{75}\! \left(x , y_{0}, y_{1}\right)\\
F_{42}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}\right) F_{41}\! \left(x , y_{0}, y_{1}\right)\\
F_{43}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x \right) F_{44}\! \left(x , y_{0}, y_{1}\right)\\
F_{44}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{33}\! \left(x , y_{1}\right)+F_{45}\! \left(x , y_{0}, y_{1}\right)+F_{46}\! \left(x , y_{0}, y_{1}\right)+F_{48}\! \left(x , y_{0}, y_{1}\right)+F_{50}\! \left(x , y_{0}, y_{1}\right)\\
F_{45}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}\right) F_{44}\! \left(x , y_{0}, y_{1}\right)\\
F_{46}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x \right) F_{47}\! \left(x , y_{0}, y_{1}\right)\\
F_{47}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{16}\! \left(x , y_{0}\right) y_{0}-F_{16}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{48}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x \right) F_{49}\! \left(x , y_{0}, y_{1}\right)\\
F_{49}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{12}\! \left(x , y_{0}\right) y_{0}-F_{12}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{50}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x \right) F_{51}\! \left(x , y_{0}, y_{1}\right)\\
F_{51}\! \left(x , y_{0}, y_{1}\right) &= F_{52}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{53}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{55}\! \left(x , y_{1}, y_{2}\right)+F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{74}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{54}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{10}\! \left(x , y_{0}\right) F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{55}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}\right) F_{56}\! \left(x , y_{0}, y_{1}\right)\\
F_{56}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{30}\! \left(x , y_{0}, 1\right) y_{0}-F_{30}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{57}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{10}\! \left(x , y_{2}\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_{24}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{24}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{17}\! \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) &= F_{1}\! \left(x \right)+F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{62}\! \left(x , y_{1}, y_{2}\right)+F_{64}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{70}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{72}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{10}\! \left(x , y_{0}\right) F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{62}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}\right) F_{63}\! \left(x , y_{0}, y_{1}\right)\\
F_{63}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{35}\! \left(x , y_{0}, 1\right) y_{0}-F_{35}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{64}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{10}\! \left(x , y_{2}\right) F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{66}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{66}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{66}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{67}\! \left(x , 1, y_{1}\right) y_{1}-F_{67}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{67}\! \left(x , y_{0}, y_{1}\right) &= F_{36}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{17}\! \left(x \right) F_{69}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{69}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{47}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{47}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{70}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{17}\! \left(x \right) F_{71}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{71}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{49}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{49}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{72}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{17}\! \left(x \right) F_{73}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{73}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{52}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{74}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{17}\! \left(x \right) F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{75}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x \right) F_{76}\! \left(x , y_{0}, y_{1}\right)\\
F_{76}\! \left(x , y_{0}, y_{1}\right) &= F_{53}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{77}\! \left(x , y_{0}\right) &= F_{17}\! \left(x \right) F_{78}\! \left(x , y_{0}\right)\\
F_{78}\! \left(x , y_{0}\right) &= -\frac{-F_{79}\! \left(x , y_{0}\right) y_{0}+F_{79}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{79}\! \left(x , y_{0}\right) &= -\frac{-F_{80}\! \left(x , y_{0}\right) y_{0}+F_{80}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{80}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{0}\right)+F_{31}\! \left(x , y_{0}\right)+F_{81}\! \left(x , y_{0}\right)\\
F_{81}\! \left(x , y_{0}\right) &= F_{17}\! \left(x \right) F_{79}\! \left(x , y_{0}\right)\\
F_{82}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x \right) F_{40}\! \left(x , y_{0}, y_{1}\right)\\
F_{83}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x \right) F_{84}\! \left(x , y_{0}, y_{1}\right)\\
F_{84}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{46}\! \left(x , y_{0}, y_{1}\right)+F_{48}\! \left(x , y_{0}, y_{1}\right)+F_{85}\! \left(x , y_{0}, y_{1}\right)+F_{86}\! \left(x , y_{0}, y_{1}\right)+F_{87}\! \left(x , y_{0}, y_{1}\right)\\
F_{85}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{0}\right) F_{84}\! \left(x , y_{0}, y_{1}\right)\\
F_{86}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x , y_{1}\right) F_{66}\! \left(x , y_{0}, y_{1}\right)\\
F_{87}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x \right) F_{88}\! \left(x , y_{0}, y_{1}\right)\\
F_{88}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{1} F_{20}\! \left(x , y_{0}, y_{1}\right)+F_{20}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{89}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x \right) F_{20}\! \left(x , y_{0}, y_{1}\right)\\
F_{90}\! \left(x , y_{0}\right) &= F_{75}\! \left(x , y_{0}, 1\right)\\
F_{91}\! \left(x \right) &= F_{17}\! \left(x \right) F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{13}\! \left(x , 1\right)\\
F_{93}\! \left(x \right) &= F_{17}\! \left(x \right) F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{79}\! \left(x , 1\right)\\
F_{95}\! \left(x \right) &= F_{17}\! \left(x \right) F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{80}\! \left(x , 1\right)\\
\end{align*}\)