Av(13524, 13542)
Counting Sequence
1, 1, 2, 6, 24, 118, 672, 4254, 29116, 211464, 1608744, 12702238, 103391268, 863161152, 7362170304, ...
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 115 rules.
Finding the specification took 135835 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_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{4}\! \left(x \right) &= x\\
F_{5}\! \left(x \right) &= F_{0}\! \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_{8}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= x F_{8}\! \left(x , y_{0}\right) y_{0}+y_{0} x +F_{8}\! \left(x , y_{0}\right)^{2}\\
F_{9}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right)\\
F_{10}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , y_{0}\right) F_{23}\! \left(x , y_{0}\right)\\
F_{11}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right)+F_{27}\! \left(x , y_{0}\right)\\
F_{12}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{2}\! \left(x \right)\\
F_{13}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right)+F_{15}\! \left(x , y_{0}\right)\\
F_{14}\! \left(x , y_{0}\right) &= x F_{14}\! \left(x , y_{0}\right) y_{0}+F_{14}\! \left(x , y_{0}\right)^{2}-2 F_{14}\! \left(x , y_{0}\right)+2\\
F_{15}\! \left(x , y_{0}\right) &= F_{16}\! \left(x , 1, y_{0}\right)\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(y_{1} x , y_{0}\right)\\
F_{17}\! \left(x , y_{0}\right) &= F_{18}\! \left(x , y_{0}\right)\\
F_{18}\! \left(x , y_{0}\right) &= F_{19}\! \left(x , y_{0}\right) F_{23}\! \left(x , y_{0}\right) F_{26}\! \left(x \right)\\
F_{19}\! \left(x , y_{0}\right) &= F_{20}\! \left(x , y_{0}\right)+F_{24}\! \left(x , y_{0}\right)\\
F_{20}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right)+F_{21}\! \left(x , y_{0}\right)\\
F_{21}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right)\\
F_{22}\! \left(x , y_{0}\right) &= F_{20}\! \left(x , y_{0}\right)^{2} F_{23}\! \left(x , y_{0}\right)\\
F_{23}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{24}\! \left(x , y_{0}\right) &= F_{25}\! \left(x , y_{0}\right)\\
F_{25}\! \left(x , y_{0}\right) &= F_{19}\! \left(x , y_{0}\right) F_{20}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)\\
F_{26}\! \left(x \right) &= F_{26}\! \left(x \right) x +F_{26} \left(x \right)^{2}-2 F_{26}\! \left(x \right)+2\\
F_{27}\! \left(x , y_{0}\right) &= F_{113}\! \left(x , y_{0}\right)+F_{28}\! \left(x , y_{0}\right)\\
F_{29}\! \left(x , y_{0}\right) &= F_{112}\! \left(x , y_{0}\right)+F_{28}\! \left(x , y_{0}\right)\\
F_{29}\! \left(x , y_{0}\right) &= F_{30}\! \left(x , y_{0}\right)+F_{31}\! \left(x , y_{0}\right)\\
F_{30}\! \left(x , y_{0}\right) &= F_{0}\! \left(x \right)+F_{7}\! \left(x , y_{0}\right)\\
F_{31}\! \left(x , y_{0}\right) &= F_{32}\! \left(x , y_{0}\right)\\
F_{32}\! \left(x , y_{0}\right) &= F_{33}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)\\
F_{33}\! \left(x , y_{0}\right) &= F_{34}\! \left(x , 1, y_{0}\right)\\
F_{34}\! \left(x , y_{0}, y_{1}\right) &= F_{35}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{36}\! \left(x , y_{0}, y_{1}\right) &= F_{107}\! \left(x , y_{0}, y_{1}\right)+F_{35}\! \left(x , y_{0}, y_{1}\right)\\
F_{36}\! \left(x , y_{0}, y_{1}\right) &= F_{37}\! \left(x , y_{0}, y_{1}\right)+F_{92}\! \left(x , y_{0}, y_{1}\right)\\
F_{37}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{38}\! \left(x , 1, y_{1}\right) y_{1}-F_{38}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{38}\! \left(x , y_{0}, y_{1}\right) &= F_{39}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{39}\! \left(x , y_{0}, y_{1}\right) &= F_{29}\! \left(x , y_{1}\right)+F_{40}\! \left(x , y_{0}, y_{1}\right)\\
F_{40}\! \left(x , y_{0}, y_{1}\right) &= F_{41}\! \left(x , y_{0}, y_{1}\right)\\
F_{41}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , y_{0}\right) F_{42}\! \left(x , y_{0}, y_{1}\right)\\
F_{42}\! \left(x , y_{0}, y_{1}\right) &= F_{43}\! \left(x , y_{0}, y_{1}\right)+F_{89}\! \left(x , y_{0}, y_{1}\right)\\
F_{43}\! \left(x , y_{0}, y_{1}\right) &= F_{35}\! \left(x , y_{0}, y_{1}\right)+F_{44}\! \left(x , y_{0}, y_{1}\right)\\
F_{44}\! \left(x , y_{0}, y_{1}\right) &= F_{45}\! \left(x , y_{0}, y_{1}\right)\\
F_{45}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , y_{1}\right) F_{46}\! \left(x , y_{0}, y_{1}\right)\\
F_{46}\! \left(x , y_{0}, y_{1}\right) &= F_{47}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{47}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{48}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)\\
F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{42}\! \left(x , y_{1}, y_{2}\right)+F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{23}\! \left(x , y_{1}\right) F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{50}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{51}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{51}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{75}\! \left(x , y_{0}, y_{2}\right)\\
F_{52}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{53}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{54}\! \left(x , y_{1}, y_{2}\right) F_{7}\! \left(x , y_{0}\right)\\
F_{55}\! \left(x , y_{0}, y_{1}\right) &= F_{0}\! \left(x \right) F_{54}\! \left(x , y_{0}, y_{1}\right)\\
F_{39}\! \left(x , y_{0}, y_{1}\right) &= F_{55}\! \left(x , y_{0}, y_{1}\right)+F_{56}\! \left(x , y_{0}, y_{1}\right)\\
F_{56}\! \left(x , y_{0}, y_{1}\right) &= F_{28}\! \left(x , y_{1}\right)+F_{57}\! \left(x , y_{0}, y_{1}\right)\\
F_{40}\! \left(x , y_{0}, y_{1}\right) &= F_{57}\! \left(x , y_{0}, y_{1}\right)+F_{58}\! \left(x , y_{0}, y_{1}\right)\\
F_{59}\! \left(x , y_{0}, y_{1}\right) &= F_{58}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{59}\! \left(x , y_{0}, y_{1}\right) &= F_{0}\! \left(x \right) F_{16}\! \left(x , y_{0}, y_{1}\right)\\
F_{60}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{4}\! \left(x \right) F_{62}\! \left(x , y_{1}, y_{2}\right) F_{7}\! \left(x , y_{0}\right)\\
F_{62}\! \left(x , y_{0}, y_{1}\right) &= F_{63}\! \left(x , y_{0}, y_{1}\right)+F_{69}\! \left(x , y_{0}, y_{1}\right)\\
F_{64}\! \left(x , y_{0}, y_{1}\right) &= F_{4}\! \left(x \right) F_{63}\! \left(x , y_{0}, y_{1}\right)\\
F_{64}\! \left(x , y_{0}, y_{1}\right) &= F_{65}\! \left(x , y_{0}, y_{1}\right)\\
F_{66}\! \left(x , y_{0}, y_{1}\right) &= F_{54}\! \left(x , y_{0}, y_{1}\right)+F_{65}\! \left(x , y_{0}, y_{1}\right)\\
F_{66}\! \left(x , y_{0}, y_{1}\right) &= F_{30}\! \left(x , y_{1}\right)+F_{67}\! \left(x , y_{0}, y_{1}\right)\\
F_{67}\! \left(x , y_{0}, y_{1}\right) &= F_{68}\! \left(x , y_{0}, y_{1}\right)\\
F_{68}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , y_{0}\right) F_{43}\! \left(x , y_{0}, y_{1}\right)\\
F_{69}\! \left(x , y_{0}, y_{1}\right) &= F_{70}\! \left(x , y_{0}, y_{1}\right)\\
F_{71}\! \left(x , y_{0}, y_{1}\right) &= F_{70}\! \left(x , y_{0}, y_{1}\right)+F_{73}\! \left(x , y_{0}, y_{1}\right)\\
F_{72}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , y_{0}\right) F_{71}\! \left(x , y_{0}, y_{1}\right)\\
F_{72}\! \left(x , y_{0}, y_{1}\right) &= F_{40}\! \left(x , y_{0}, y_{1}\right)\\
F_{74}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , y_{0}\right) F_{73}\! \left(x , y_{0}, y_{1}\right)\\
F_{74}\! \left(x , y_{0}, y_{1}\right) &= F_{67}\! \left(x , y_{0}, y_{1}\right)\\
F_{75}\! \left(x , y_{0}, y_{1}\right) &= F_{76}\! \left(x , y_{0}, y_{1}\right)+F_{77}\! \left(x , y_{0}, y_{1}\right)\\
F_{76}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right) F_{7}\! \left(x , y_{0}\right)\\
F_{77}\! \left(x , y_{0}, y_{1}\right) &= F_{78}\! \left(x , y_{0}, y_{1}\right)\\
F_{78}\! \left(x , y_{0}, y_{1}\right) &= F_{4}\! \left(x \right) F_{7}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{1}\right)\\
F_{79}\! \left(x , y_{0}\right) &= F_{80}\! \left(x , y_{0}\right)+F_{85}\! \left(x , y_{0}\right)\\
F_{80}\! \left(x , y_{0}\right) &= F_{29}\! \left(x , y_{0}\right)+F_{81}\! \left(x , y_{0}\right)\\
F_{81}\! \left(x , y_{0}\right) &= F_{82}\! \left(x , y_{0}\right)\\
F_{82}\! \left(x , y_{0}\right) &= F_{23}\! \left(x , y_{0}\right) F_{83}\! \left(x , y_{0}\right)\\
F_{83}\! \left(x , y_{0}\right) &= F_{84}\! \left(x , y_{0}, 1\right)\\
F_{84}\! \left(x , y_{0}, y_{1}\right) &= F_{62}\! \left(x , y_{0} y_{1}, y_{0}\right)\\
F_{85}\! \left(x , y_{0}\right) &= F_{86}\! \left(x , y_{0}\right)\\
F_{86}\! \left(x , y_{0}\right) &= F_{4}\! \left(x \right) F_{87}\! \left(x , y_{0}\right)\\
F_{87}\! \left(x , y_{0}\right) &= F_{88}\! \left(x , 1, y_{0}\right)\\
F_{88}\! \left(x , y_{0}, y_{1}\right) &= F_{47}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{89}\! \left(x , y_{0}, y_{1}\right) &= F_{90}\! \left(x , y_{0}, y_{1}\right)\\
F_{90}\! \left(x , y_{0}, y_{1}\right) &= F_{4}\! \left(x \right) F_{91}\! \left(x , y_{0}, y_{1}\right)\\
F_{91}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{88}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{88}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{93}\! \left(x , y_{0}, y_{1}\right) &= F_{105}\! \left(x , y_{0}, y_{1}\right)+F_{92}\! \left(x , y_{0}, y_{1}\right)\\
F_{94}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , y_{1}\right) F_{93}\! \left(x , y_{0}, y_{1}\right)\\
F_{94}\! \left(x , y_{0}, y_{1}\right) &= F_{95}\! \left(x , y_{0}, y_{1}\right)\\
F_{95}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , y_{0}\right) F_{96}\! \left(x , y_{0}, y_{1}\right)\\
F_{96}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{1} \left(F_{97}\! \left(x , y_{0}\right)-F_{97}\! \left(x , y_{1}\right)\right)}{-y_{1}+y_{0}}\\
F_{97}\! \left(x , y_{0}\right) &= F_{101}\! \left(x , y_{0}\right)+F_{98}\! \left(x , y_{0}\right)\\
F_{99}\! \left(x , y_{0}\right) &= F_{81}\! \left(x , y_{0}\right)+F_{98}\! \left(x , y_{0}\right)\\
F_{100}\! \left(x , y_{0}\right) &= F_{4}\! \left(x \right) F_{99}\! \left(x , y_{0}\right)\\
F_{100}\! \left(x , y_{0}\right) &= F_{9}\! \left(x , y_{0}\right)\\
F_{101}\! \left(x , y_{0}\right) &= F_{102}\! \left(x , y_{0}\right)\\
F_{102}\! \left(x , y_{0}\right) &= F_{103}\! \left(x , y_{0}\right) F_{23}\! \left(x , y_{0}\right)\\
F_{103}\! \left(x , y_{0}\right) &= F_{104}\! \left(x , y_{0}, 1\right)\\
F_{104}\! \left(x , y_{0}, y_{1}\right) &= F_{71}\! \left(x , y_{0} y_{1}, y_{0}\right)\\
F_{105}\! \left(x , y_{0}, y_{1}\right) &= -\frac{y_{0} \left(F_{106}\! \left(x , 1, y_{1}\right)-F_{106}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right)\right)}{-y_{1}+y_{0}}\\
F_{106}\! \left(x , y_{0}, y_{1}\right) &= F_{40}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{107}\! \left(x , y_{0}, y_{1}\right) &= F_{108}\! \left(x , y_{0}, y_{1}\right)\\
F_{108}\! \left(x , y_{0}, y_{1}\right) &= F_{109}\! \left(x , y_{0}, y_{1}\right) F_{23}\! \left(x , y_{1}\right)\\
F_{109}\! \left(x , y_{0}, y_{1}\right) &= F_{110}\! \left(x , y_{0}, 1, y_{1}\right)\\
F_{110}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-y_{0} y_{1} F_{111}\! \left(x , y_{0}, y_{2}, \frac{y_{1}}{y_{2}}\right)+y_{2} F_{111}\! \left(x , y_{0}, y_{2}, \frac{1}{y_{0}}\right)}{y_{0} y_{1}-y_{2}}\\
F_{111}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{47}\! \left(x , y_{0}, y_{1} y_{2}, y_{1}\right)\\
F_{112}\! \left(x , y_{0}\right) &= F_{0}\! \left(x \right) F_{14}\! \left(x , y_{0}\right)\\
F_{113}\! \left(x , y_{0}\right) &= F_{114}\! \left(x , 1, y_{0}\right)\\
F_{114}\! \left(x , y_{0}, y_{1}\right) &= F_{57}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
\end{align*}\)