Av(12345, 12354, 12435, 13245, 13254, 13524, 31245, 31254, 31524)
Counting Sequence
1, 1, 2, 6, 24, 111, 548, 2793, 14501, 76235, 404508, 2161812, 11619764, 62748103, 340153636, ...
This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Req Corrob Symmetries" and has 135 rules.
Finding the specification took 3807 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_{12}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x , 1\right)\\
F_{6}\! \left(x , y\right) &= F_{7}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= F_{77}\! \left(x , y\right) F_{8}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{13}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{6}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{12}\! \left(x \right)\\
F_{11}\! \left(x , y\right) &= -\frac{-F_{8}\! \left(x , y\right) y +F_{8}\! \left(x , 1\right)}{-1+y}\\
F_{12}\! \left(x \right) &= x\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{77}\! \left(x , y\right) F_{79}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{133}\! \left(x , y\right)+F_{16}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{132}\! \left(x , y\right)+F_{17}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{128}\! \left(x , y\right)+F_{18}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{19}\! \left(x , y\right)\\
F_{19}\! \left(x , y\right) &= F_{20}\! \left(x \right)+F_{25}\! \left(x , y\right)\\
F_{20}\! \left(x \right) &= \frac{F_{21}\! \left(x \right)}{F_{12}\! \left(x \right)}\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= F_{12}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= F_{8}\! \left(x , 1\right)\\
F_{25}\! \left(x , y\right) &= F_{124}\! \left(x , y\right)+F_{126}\! \left(x , y\right)+F_{26}\! \left(x \right)+F_{27}\! \left(x , y\right)\\
F_{26}\! \left(x \right) &= 0\\
F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{29}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= -\frac{y \left(F_{30}\! \left(x , 1\right)-F_{30}\! \left(x , y\right)\right)}{-1+y}\\
F_{30}\! \left(x , y\right) &= F_{119}\! \left(x , y\right)+F_{31}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= F_{118}\! \left(x , y\right)+F_{32}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{26}\! \left(x \right)+F_{33}\! \left(x , y\right)+F_{35}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{30}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= F_{36}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{37}\! \left(x , y\right) F_{77}\! \left(x , y\right) F_{79}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{35}\! \left(x , y\right)+F_{38}\! \left(x , y\right)\\
F_{38}\! \left(x , y\right) &= F_{39}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{40}\! \left(x , y\right)\\
F_{40}\! \left(x , y\right) &= F_{41}\! \left(x , y\right)+F_{70}\! \left(x , y\right)\\
F_{41}\! \left(x , y\right) &= F_{37}\! \left(x , y\right)+F_{42}\! \left(x , y\right)\\
F_{42}\! \left(x , y\right) &= F_{43}\! \left(x , y\right)\\
F_{43}\! \left(x , y\right) &= F_{117}\! \left(x , y\right)+F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= -F_{116}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= -F_{46}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{26}\! \left(x \right)+F_{47}\! \left(x \right)+F_{50}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{49}\! \left(x , 1\right)\\
F_{49}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{25}\! \left(x , y\right)\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{12}\! \left(x \right) F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{54}\! \left(x \right) &= F_{41}\! \left(x , 1\right)\\
F_{55}\! \left(x \right) &= F_{56}\! \left(x , 1\right)\\
F_{56}\! \left(x , y\right) &= F_{57}\! \left(x , y\right)+F_{67}\! \left(x , y\right)\\
F_{57}\! \left(x , y\right) &= F_{58}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{16}\! \left(x , y\right) F_{59}\! \left(x \right) F_{60}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{12}\! \left(x \right) F_{63}\! \left(x \right)\\
F_{63}\! \left(x \right) &= F_{59}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= F_{61}\! \left(x \right)+F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{12}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{67}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{68}\! \left(x , y\right)\\
F_{68}\! \left(x , y\right) &= -\frac{-F_{56}\! \left(x , y\right) y +F_{56}\! \left(x , 1\right)}{-1+y}\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x , 1\right)\\
F_{70}\! \left(x , y\right) &= F_{113}\! \left(x , y\right)+F_{71}\! \left(x , y\right)\\
F_{71}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{72}\! \left(x , y\right)\\
F_{72}\! \left(x , y\right) &= F_{73}\! \left(x , y\right)+F_{98}\! \left(x , y\right)\\
F_{73}\! \left(x , y\right) &= F_{74}\! \left(x , y\right)+F_{83}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{75}\! \left(x , y\right)\\
F_{75}\! \left(x , y\right) &= F_{76}\! \left(x , y\right)\\
F_{76}\! \left(x , y\right) &= F_{77}\! \left(x , y\right) F_{78}\! \left(x , y\right)\\
F_{77}\! \left(x , y\right) &= y x\\
F_{78}\! \left(x , y\right) &= F_{79}\! \left(x , y\right)+F_{80}\! \left(x , y\right)\\
F_{79}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{77}\! \left(x , y\right)\\
F_{80}\! \left(x , y\right) &= F_{75}\! \left(x , y\right)+F_{81}\! \left(x , y\right)\\
F_{81}\! \left(x , y\right) &= F_{82}\! \left(x , y\right)\\
F_{82}\! \left(x , y\right) &= F_{75}\! \left(x , y\right) F_{77}\! \left(x , y\right)\\
F_{83}\! \left(x , y\right) &= F_{84}\! \left(x \right)+F_{87}\! \left(x , y\right)\\
F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)\\
F_{85}\! \left(x \right) &= F_{12}\! \left(x \right) F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{84}\! \left(x \right)\\
F_{87}\! \left(x , y\right) &= F_{26}\! \left(x \right)+F_{88}\! \left(x , y\right)+F_{90}\! \left(x , y\right)\\
F_{88}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{89}\! \left(x , y\right)\\
F_{89}\! \left(x , y\right) &= F_{75}\! \left(x , y\right)+F_{87}\! \left(x , y\right)\\
F_{90}\! \left(x , y\right) &= F_{77}\! \left(x , y\right) F_{91}\! \left(x , y\right)\\
F_{91}\! \left(x , y\right) &= F_{92}\! \left(x , y\right)+F_{95}\! \left(x , y\right)\\
F_{92}\! \left(x , y\right) &= F_{84}\! \left(x \right)+F_{93}\! \left(x , y\right)\\
F_{93}\! \left(x , y\right) &= F_{94}\! \left(x , y\right)\\
F_{94}\! \left(x , y\right) &= F_{77}\! \left(x , y\right) F_{84}\! \left(x \right)\\
F_{95}\! \left(x , y\right) &= F_{87}\! \left(x , y\right)+F_{96}\! \left(x , y\right)\\
F_{96}\! \left(x , y\right) &= F_{97}\! \left(x , y\right)\\
F_{97}\! \left(x , y\right) &= F_{77}\! \left(x , y\right) F_{87}\! \left(x , y\right)\\
F_{98}\! \left(x , y\right) &= F_{111}\! \left(x , y\right)+F_{2}\! \left(x \right)+F_{99}\! \left(x , y\right)\\
F_{99}\! \left(x , y\right) &= F_{100}\! \left(x , y\right) F_{12}\! \left(x \right)\\
F_{100}\! \left(x , y\right) &= F_{101}\! \left(x , y\right)+F_{98}\! \left(x , y\right)\\
F_{101}\! \left(x , y\right) &= F_{102}\! \left(x , y\right)\\
F_{102}\! \left(x , y\right) &= F_{103}\! \left(x \right) F_{74}\! \left(x , y\right)\\
F_{103}\! \left(x \right) &= -F_{108}\! \left(x \right)+F_{104}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x , 1\right)\\
F_{105}\! \left(x , y\right) &= F_{106}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\
F_{106}\! \left(x , y\right) &= F_{107}\! \left(x , y\right) F_{12}\! \left(x \right)\\
F_{107}\! \left(x , y\right) &= -\frac{-y F_{105}\! \left(x , y\right)+F_{105}\! \left(x , 1\right)}{-1+y}\\
F_{108}\! \left(x \right) &= -F_{5}\! \left(x \right)+F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{110}\! \left(x \right) &= F_{104}\! \left(x \right) F_{12}\! \left(x \right)\\
F_{111}\! \left(x , y\right) &= F_{112}\! \left(x , y\right)\\
F_{112}\! \left(x , y\right) &= F_{77}\! \left(x , y\right) F_{79}\! \left(x , y\right) F_{98}\! \left(x , y\right)\\
F_{113}\! \left(x , y\right) &= F_{114}\! \left(x , y\right)\\
F_{114}\! \left(x , y\right) &= F_{115}\! \left(x , y\right) F_{12}\! \left(x \right)\\
F_{115}\! \left(x , y\right) &= F_{102}\! \left(x , y\right)+F_{55}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{22}\! \left(x \right)\\
F_{117}\! \left(x , y\right) &= F_{103}\! \left(x \right) F_{75}\! \left(x , y\right)\\
F_{118}\! \left(x , y\right) &= F_{117}\! \left(x , y\right)\\
F_{119}\! \left(x , y\right) &= F_{120}\! \left(x , y\right)\\
F_{70}\! \left(x , y\right) &= F_{120}\! \left(x , y\right)+F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{12}\! \left(x \right) F_{123}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{55}\! \left(x \right)\\
F_{124}\! \left(x , y\right) &= F_{12}\! \left(x \right) F_{125}\! \left(x , y\right)\\
F_{125}\! \left(x , y\right) &= -\frac{y \left(F_{25}\! \left(x , 1\right)-F_{25}\! \left(x , y\right)\right)}{-1+y}\\
F_{126}\! \left(x , y\right) &= F_{127}\! \left(x , y\right)\\
F_{127}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{77}\! \left(x , y\right) F_{79}\! \left(x , y\right)\\
F_{128}\! \left(x , y\right) &= F_{129}\! \left(x , y\right)\\
F_{129}\! \left(x , y\right) &= F_{130}\! \left(x , y\right) F_{77}\! \left(x , y\right)\\
F_{130}\! \left(x , y\right) &= F_{131}\! \left(x , y\right)+F_{37}\! \left(x , y\right)\\
F_{131}\! \left(x , y\right) &= F_{72}\! \left(x , y\right) F_{77}\! \left(x , y\right)\\
F_{132}\! \left(x , y\right) &= F_{6}\! \left(x , y\right) F_{74}\! \left(x , y\right)\\
F_{133}\! \left(x , y\right) &= F_{134}\! \left(x , y\right)\\
F_{134}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{77}\! \left(x , y\right) F_{79}\! \left(x , y\right)\\
\end{align*}\)