Av(12345, 12354, 12453, 21345, 21354, 21453, 31245, 31254, 31452, 41253, 41352)
Counting Sequence
1, 1, 2, 6, 24, 109, 522, 2551, 12554, 61872, 304700, 1498140, 7352556, 36020720, 176183388, ...
This specification was found using the strategy pack "Col Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 181 rules.
Finding the specification took 2467 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_{14}\! \left(x \right) F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{180}\! \left(x \right)+F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{14}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x , 1\right)\\
F_{7}\! \left(x , y\right) &= -\frac{-F_{6}\! \left(x , y\right) y +F_{6}\! \left(x , 1\right)}{-1+y}\\
F_{7}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)+F_{178}\! \left(x , y\right)+F_{179}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= F_{58}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{163}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{162}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x \right)+F_{148}\! \left(x , y\right)\\
F_{12}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{112}\! \left(x \right)+F_{13}\! \left(x \right)+F_{15}\! \left(x \right)+F_{17}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right) F_{3}\! \left(x \right)\\
F_{14}\! \left(x \right) &= x\\
F_{15}\! \left(x \right) &= F_{16}\! \left(x , 1\right)\\
F_{16}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{14}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{14}\! \left(x \right) F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x , 1\right)\\
F_{19}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{124}\! \left(x , y\right)+F_{143}\! \left(x , y\right)+F_{146}\! \left(x , y\right)+F_{20}\! \left(x , y\right)+F_{21}\! \left(x , y\right)\\
F_{20}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{6}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{22}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{141}\! \left(x , y\right)+F_{23}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{12}\! \left(x \right)+F_{24}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)\\
F_{25}\! \left(x , y\right) &= F_{26}\! \left(x , y\right) F_{58}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)+F_{31}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{27}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)+F_{6}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{7}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= F_{32}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{134}\! \left(x , y\right)+F_{135}\! \left(x , y\right)+F_{137}\! \left(x , y\right)+F_{33}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)+F_{96}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{35}\! \left(x , y\right) F_{58}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{36}\! \left(x , y\right)+F_{37}\! \left(x , y\right)+F_{38}\! \left(x , y\right)+F_{41}\! \left(x , y\right)\\
F_{37}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{23}\! \left(x , y\right)\\
F_{38}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{39}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= F_{40}\! \left(x , y\right)\\
F_{40}\! \left(x , y\right) &= -\frac{-F_{7}\! \left(x , y\right) y +F_{7}\! \left(x , 1\right)}{-1+y}\\
F_{41}\! \left(x , y\right) &= F_{14}\! \left(x \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) &= -\frac{-F_{44}\! \left(x , y\right) y +F_{44}\! \left(x , 1\right)}{-1+y}\\
F_{44}\! \left(x , y\right) &= F_{45}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{41}\! \left(x , y\right)+F_{46}\! \left(x , y\right)+F_{50}\! \left(x , y\right)+F_{90}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{47}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= -\frac{-F_{48}\! \left(x , y\right) y +F_{48}\! \left(x , 1\right)}{-1+y}\\
F_{48}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{103}\! \left(x , y\right)+F_{49}\! \left(x \right)+F_{50}\! \left(x , y\right)+F_{90}\! \left(x , y\right)\\
F_{49}\! \left(x \right) &= F_{0}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{50}\! \left(x , y\right) &= F_{51}\! \left(x , y\right) F_{58}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= F_{48}\! \left(x , y\right)+F_{52}\! \left(x , y\right)\\
F_{52}\! \left(x , y\right) &= F_{53}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= y F_{54}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= F_{49}\! \left(x \right)+F_{55}\! \left(x \right)+F_{56}\! \left(x , y\right)+F_{59}\! \left(x , y\right)+F_{67}\! \left(x , y\right)\\
F_{55}\! \left(x \right) &= 0\\
F_{56}\! \left(x , y\right) &= F_{57}\! \left(x , y\right)\\
F_{57}\! \left(x , y\right) &= F_{54}\! \left(x , y\right) F_{58}\! \left(x , y\right)\\
F_{58}\! \left(x , y\right) &= y x\\
F_{59}\! \left(x , y\right) &= F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{14}\! \left(x \right) F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{62}\! \left(x , 1\right)\\
F_{62}\! \left(x , y\right) &= F_{49}\! \left(x \right)+F_{55}\! \left(x \right)+F_{63}\! \left(x , y\right)+F_{65}\! \left(x , y\right)+F_{67}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= F_{64}\! \left(x , y\right)\\
F_{64}\! \left(x , y\right) &= F_{58}\! \left(x , y\right) F_{62}\! \left(x , y\right)\\
F_{65}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{66}\! \left(x , y\right)\\
F_{66}\! \left(x , y\right) &= -\frac{-F_{62}\! \left(x , y\right) y +F_{62}\! \left(x , 1\right)}{-1+y}\\
F_{67}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{68}\! \left(x , y\right)\\
F_{68}\! \left(x , y\right) &= F_{69}\! \left(x \right)+F_{86}\! \left(x , y\right)\\
F_{69}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{55}\! \left(x \right)+F_{70}\! \left(x \right)+F_{73}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{14}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{54}\! \left(x , 1\right)\\
F_{73}\! \left(x \right) &= F_{60}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{14}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= F_{76}\! \left(x , 1\right)\\
F_{76}\! \left(x , y\right) &= F_{55}\! \left(x \right)+F_{77}\! \left(x , y\right)+F_{79}\! \left(x , y\right)+F_{82}\! \left(x , y\right)+F_{83}\! \left(x , y\right)+F_{84}\! \left(x , y\right)\\
F_{77}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{78}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= -\frac{-F_{78}\! \left(x , y\right) y +F_{78}\! \left(x , 1\right)}{-1+y}\\
F_{79}\! \left(x , y\right) &= F_{80}\! \left(x , y\right)\\
F_{80}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{81}\! \left(x , y\right)\\
F_{81}\! \left(x , y\right) &= -\frac{-y F_{54}\! \left(x , y\right)+F_{54}\! \left(x , 1\right)}{-1+y}\\
F_{82}\! \left(x , y\right) &= F_{57}\! \left(x , y\right)\\
F_{83}\! \left(x , y\right) &= F_{60}\! \left(x \right)\\
F_{84}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{85}\! \left(x , y\right)\\
F_{85}\! \left(x , y\right) &= -\frac{-F_{76}\! \left(x , y\right) y +F_{76}\! \left(x , 1\right)}{-1+y}\\
F_{86}\! \left(x , y\right) &= F_{58}\! \left(x , y\right) F_{87}\! \left(x , y\right)\\
F_{87}\! \left(x , y\right) &= -\frac{-F_{88}\! \left(x , y\right) y +F_{88}\! \left(x , 1\right)}{-1+y}\\
F_{88}\! \left(x , y\right) &= F_{54}\! \left(x , y\right)+F_{89}\! \left(x , y\right)\\
F_{89}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{87}\! \left(x , y\right)\\
F_{90}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{91}\! \left(x , y\right)\\
F_{91}\! \left(x , y\right) &= F_{133}\! \left(x , y\right)+F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{93}\! \left(x , 1\right)\\
F_{93}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{101}\! \left(x , y\right)+F_{103}\! \left(x , y\right)+F_{49}\! \left(x \right)+F_{94}\! \left(x , y\right)\\
F_{94}\! \left(x , y\right) &= F_{58}\! \left(x , y\right) F_{95}\! \left(x , y\right)\\
F_{95}\! \left(x , y\right) &= F_{100}\! \left(x , y\right)+F_{96}\! \left(x , y\right)\\
F_{97}\! \left(x , y\right) &= F_{58}\! \left(x , y\right) F_{96}\! \left(x , y\right)\\
F_{6}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{97}\! \left(x , y\right)+F_{98}\! \left(x , y\right)+F_{99}\! \left(x , y\right)\\
F_{98}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{7}\! \left(x , y\right)\\
F_{99}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{44}\! \left(x , y\right)\\
F_{100}\! \left(x , y\right) &= F_{62}\! \left(x , y\right)\\
F_{101}\! \left(x , y\right) &= F_{102}\! \left(x , y\right) F_{14}\! \left(x \right)\\
F_{102}\! \left(x , y\right) &= -\frac{-F_{93}\! \left(x , y\right) y +F_{93}\! \left(x , 1\right)}{-1+y}\\
F_{103}\! \left(x , y\right) &= F_{104}\! \left(x , y\right) F_{14}\! \left(x \right)\\
F_{104}\! \left(x , y\right) &= F_{105}\! \left(x \right)+F_{126}\! \left(x , y\right)\\
F_{105}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{106}\! \left(x \right)+F_{107}\! \left(x \right)+F_{112}\! \left(x \right)+F_{13}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{50}\! \left(x , 1\right)\\
F_{107}\! \left(x \right) &= F_{108}\! \left(x , 1\right)\\
F_{108}\! \left(x , y\right) &= F_{109}\! \left(x , y\right) F_{14}\! \left(x \right)\\
F_{109}\! \left(x , y\right) &= F_{110}\! \left(x , y\right)+F_{92}\! \left(x \right)\\
F_{110}\! \left(x , y\right) &= F_{111}\! \left(x , y\right)\\
F_{111}\! \left(x , y\right) &= y F_{61}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right) F_{14}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x , 1\right)\\
F_{114}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{115}\! \left(x , y\right)+F_{118}\! \left(x , y\right)+F_{121}\! \left(x , y\right)+F_{124}\! \left(x , y\right)+F_{77}\! \left(x , y\right)\\
F_{115}\! \left(x , y\right) &= F_{116}\! \left(x , y\right) F_{14}\! \left(x \right)\\
F_{116}\! \left(x , y\right) &= F_{117}\! \left(x , y\right)+F_{47}\! \left(x , y\right)\\
F_{117}\! \left(x , y\right) &= F_{81}\! \left(x , y\right)\\
F_{118}\! \left(x , y\right) &= F_{119}\! \left(x , y\right) F_{58}\! \left(x , y\right)\\
F_{119}\! \left(x , y\right) &= F_{120}\! \left(x , y\right)+F_{51}\! \left(x , y\right)\\
F_{120}\! \left(x , y\right) &= F_{54}\! \left(x , y\right)\\
F_{121}\! \left(x , y\right) &= F_{122}\! \left(x , y\right) F_{14}\! \left(x \right)\\
F_{122}\! \left(x , y\right) &= F_{123}\! \left(x , y\right)+F_{91}\! \left(x , y\right)\\
F_{123}\! \left(x , y\right) &= F_{61}\! \left(x \right)\\
F_{124}\! \left(x , y\right) &= F_{125}\! \left(x , y\right) F_{14}\! \left(x \right)\\
F_{125}\! \left(x , y\right) &= -\frac{-F_{114}\! \left(x , y\right) y +F_{114}\! \left(x , 1\right)}{-1+y}\\
F_{126}\! \left(x , y\right) &= F_{127}\! \left(x , y\right)\\
F_{127}\! \left(x , y\right) &= F_{128}\! \left(x , y\right) F_{58}\! \left(x , y\right)\\
F_{128}\! \left(x , y\right) &= F_{129}\! \left(x , y\right)+F_{87}\! \left(x , y\right)\\
F_{130}\! \left(x , y\right) &= F_{129}\! \left(x , y\right) F_{58}\! \left(x , y\right)\\
F_{130}\! \left(x , y\right) &= F_{131}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{131}\! \left(x , y\right)+F_{132}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{78}\! \left(x , 1\right)\\
F_{133}\! \left(x , y\right) &= F_{111}\! \left(x , y\right)\\
F_{134}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{32}\! \left(x , y\right)\\
F_{135}\! \left(x , y\right) &= F_{136}\! \left(x , y\right) F_{14}\! \left(x \right)\\
F_{136}\! \left(x , y\right) &= -\frac{-F_{32}\! \left(x , y\right) y +F_{32}\! \left(x , 1\right)}{-1+y}\\
F_{137}\! \left(x , y\right) &= F_{138}\! \left(x , y\right) F_{14}\! \left(x \right)\\
F_{138}\! \left(x , y\right) &= -\frac{-F_{139}\! \left(x , y\right) y +F_{139}\! \left(x , 1\right)}{-1+y}\\
F_{139}\! \left(x , y\right) &= F_{137}\! \left(x , y\right)+F_{140}\! \left(x , y\right)+F_{54}\! \left(x , y\right)\\
F_{140}\! \left(x , y\right) &= F_{139}\! \left(x , y\right) F_{14}\! \left(x \right)\\
F_{141}\! \left(x , y\right) &= F_{142}\! \left(x , y\right)\\
F_{142}\! \left(x , y\right) &= -\frac{-F_{33}\! \left(x , y\right) y +F_{33}\! \left(x , 1\right)}{-1+y}\\
F_{143}\! \left(x , y\right) &= F_{144}\! \left(x , y\right) F_{58}\! \left(x , y\right)\\
F_{144}\! \left(x , y\right) &= F_{145}\! \left(x , y\right)+F_{35}\! \left(x , y\right)\\
F_{145}\! \left(x , y\right) &= F_{33}\! \left(x , y\right)\\
F_{146}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{147}\! \left(x , y\right)\\
F_{147}\! \left(x , y\right) &= -\frac{-F_{19}\! \left(x , y\right) y +F_{19}\! \left(x , 1\right)}{-1+y}\\
F_{148}\! \left(x , y\right) &= F_{149}\! \left(x , y\right)\\
F_{149}\! \left(x , y\right) &= y F_{150}\! \left(x \right)\\
F_{150}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{151}\! \left(x \right)+F_{153}\! \left(x \right)+F_{55}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{151}\! \left(x \right) &= F_{152}\! \left(x \right)\\
F_{152}\! \left(x \right) &= F_{14}\! \left(x \right) F_{150}\! \left(x \right)\\
F_{153}\! \left(x \right) &= F_{14}\! \left(x \right) F_{154}\! \left(x \right)\\
F_{154}\! \left(x \right) &= F_{155}\! \left(x , 1\right)\\
F_{155}\! \left(x , y\right) &= F_{156}\! \left(x , y\right)+F_{158}\! \left(x , y\right)+F_{160}\! \left(x , y\right)+F_{20}\! \left(x , y\right)+F_{55}\! \left(x \right)+F_{84}\! \left(x , y\right)\\
F_{156}\! \left(x , y\right) &= F_{157}\! \left(x , y\right)\\
F_{157}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{142}\! \left(x , y\right)\\
F_{158}\! \left(x , y\right) &= F_{159}\! \left(x , y\right)\\
F_{159}\! \left(x , y\right) &= F_{33}\! \left(x , y\right) F_{58}\! \left(x , y\right)\\
F_{160}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{161}\! \left(x , y\right)\\
F_{161}\! \left(x , y\right) &= -\frac{-F_{155}\! \left(x , y\right) y +F_{155}\! \left(x , 1\right)}{-1+y}\\
F_{162}\! \left(x , y\right) &= F_{150}\! \left(x \right)\\
F_{163}\! \left(x , y\right) &= F_{164}\! \left(x , y\right)\\
F_{164}\! \left(x , y\right) &= F_{165}\! \left(x , y\right) F_{58}\! \left(x , y\right)\\
F_{165}\! \left(x , y\right) &= F_{166}\! \left(x , y\right)+F_{169}\! \left(x , y\right)\\
F_{167}\! \left(x , y\right) &= F_{166}\! \left(x , y\right) F_{58}\! \left(x , y\right)\\
F_{167}\! \left(x , y\right) &= F_{168}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= F_{168}\! \left(x , y\right)+F_{5}\! \left(x \right)\\
F_{169}\! \left(x , y\right) &= F_{170}\! \left(x , y\right)\\
F_{170}\! \left(x , y\right) &= y F_{171}\! \left(x , y\right)\\
F_{171}\! \left(x , y\right) &= F_{172}\! \left(x , y\right)\\
F_{173}\! \left(x , y\right) &= F_{166}\! \left(x , y\right)+F_{172}\! \left(x , y\right)\\
F_{174}\! \left(x , y\right) &= F_{173}\! \left(x , y\right) F_{58}\! \left(x , y\right)\\
F_{174}\! \left(x , y\right) &= F_{175}\! \left(x , y\right)\\
F_{176}\! \left(x , y\right) &= F_{12}\! \left(x \right)+F_{175}\! \left(x , y\right)\\
F_{176}\! \left(x , y\right) &= -\frac{-y F_{177}\! \left(x , y\right)+F_{177}\! \left(x , 1\right)}{-1+y}\\
F_{23}\! \left(x , y\right) &= -\frac{-y F_{177}\! \left(x , y\right)+F_{177}\! \left(x , 1\right)}{-1+y}\\
F_{178}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{40}\! \left(x , y\right)\\
F_{179}\! \left(x , y\right) &= F_{14}\! \left(x \right) F_{43}\! \left(x , y\right)\\
F_{180}\! \left(x \right) &= F_{132}\! \left(x \right) F_{14}\! \left(x \right)\\
\end{align*}\)