Av(13425, 13452, 31425, 31452, 34125, 34152, 34215)
Counting Sequence
1, 1, 2, 6, 24, 113, 580, 3116, 17162, 95874, 540190, 3060318, 17402163, 99222951, 566921455, ...
This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 167 rules.
Finding the specification took 6421 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_{49}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x , 1\right)\\
F_{5}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{6}\! \left(x , y\right)\\
F_{6}\! \left(x , y\right) &= F_{7}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= F_{8}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= y x\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{165}\! \left(x , y\right)+F_{5}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{8}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , 1, y\right)\\
F_{13}\! \left(x , y , z\right) &= F_{14}\! \left(x , y z , z\right)\\
F_{14}\! \left(x , y , z\right) &= F_{15}\! \left(x , y , z\right)+F_{97}\! \left(x , y , z\right)\\
F_{15}\! \left(x , y , z\right) &= F_{16}\! \left(x , z\right)+F_{96}\! \left(x , y , z\right)\\
F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{93}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{18}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x \right)+F_{20}\! \left(x , y\right)+F_{83}\! \left(x , y\right)\\
F_{19}\! \left(x \right) &= 0\\
F_{20}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{22}\! \left(x , y\right) F_{8}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y , 1\right)\\
F_{23}\! \left(x , y , z\right) &= F_{24}\! \left(x , y , y z \right)\\
F_{24}\! \left(x , y , z\right) &= F_{25}\! \left(x , y , z\right)+F_{57}\! \left(x , y , z\right)\\
F_{25}\! \left(x , y , z\right) &= F_{26}\! \left(x , y , z\right)+F_{9}\! \left(x , z\right)\\
F_{26}\! \left(x , y , z\right) &= F_{19}\! \left(x \right)+F_{27}\! \left(x , y , z\right)+F_{50}\! \left(x , y , z\right)+F_{55}\! \left(x , y , z\right)\\
F_{27}\! \left(x , y , z\right) &= F_{28}\! \left(x , y , z\right)\\
F_{28}\! \left(x , y , z\right) &= F_{29}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)\\
F_{29}\! \left(x , y , z\right) &= F_{30}\! \left(x , y , z\right)+F_{31}\! \left(x , y , z\right)\\
F_{30}\! \left(x , y , z\right) &= F_{17}\! \left(x , z\right)+F_{26}\! \left(x , y , z\right)\\
F_{31}\! \left(x , y , z\right) &= F_{32}\! \left(x , y , z\right)\\
F_{32}\! \left(x , y , z\right) &= F_{0}\! \left(x \right) F_{33}\! \left(x , y\right) F_{41}\! \left(x , y , z\right)\\
F_{33}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{35}\! \left(x , y\right) F_{8}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= F_{36}\! \left(x , 1, y\right)\\
F_{36}\! \left(x , y , z\right) &= F_{37}\! \left(x , y z , z\right)\\
F_{37}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{38}\! \left(x , y , z\right)+F_{39}\! \left(x , y , z\right)\\
F_{38}\! \left(x , y , z\right) &= F_{37}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)\\
F_{39}\! \left(x , y , z\right) &= F_{40}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)\\
F_{40}\! \left(x , y , z\right) &= -\frac{F_{36}\! \left(x , 1, z\right) z -F_{36}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}\\
F_{42}\! \left(x , y , z\right) &= F_{41}\! \left(x , y , y z \right)\\
F_{42}\! \left(x , y , z\right) &= -\frac{-F_{43}\! \left(x , y z \right) z +F_{43}\! \left(x , y\right)}{z -1}\\
F_{43}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{44}\! \left(x , y\right)+F_{47}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{45}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{43}\! \left(x , y\right) F_{46}\! \left(x , y\right) F_{8}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{33}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{48}\! \left(x , y\right) F_{49}\! \left(x \right)\\
F_{48}\! \left(x , y\right) &= -\frac{-F_{43}\! \left(x , y\right) y +F_{43}\! \left(x , 1\right)}{-1+y}\\
F_{49}\! \left(x \right) &= x\\
F_{50}\! \left(x , y , z\right) &= F_{51}\! \left(x , y , z\right)\\
F_{51}\! \left(x , y , z\right) &= F_{0}\! \left(x \right) F_{43}\! \left(x , z\right) F_{52}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)\\
F_{53}\! \left(x , y , z\right) &= F_{52}\! \left(x , y z , z\right)\\
F_{53}\! \left(x , y , z\right) &= F_{54}\! \left(z x , y\right)\\
F_{54}\! \left(x , y\right) &= -\frac{y \left(F_{33}\! \left(x , 1\right)-F_{33}\! \left(x , y\right)\right)}{-1+y}\\
F_{55}\! \left(x , y , z\right) &= F_{49}\! \left(x \right) F_{56}\! \left(x , y , z\right)\\
F_{56}\! \left(x , y , z\right) &= -\frac{-F_{26}\! \left(x , y , z\right) z +F_{26}\! \left(x , y , 1\right)}{z -1}\\
F_{58}\! \left(x , y , z\right) &= F_{57}\! \left(x , y , z\right)+F_{77}\! \left(x , y , z\right)\\
F_{59}\! \left(x , y , z\right) &= F_{58}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)\\
F_{59}\! \left(x , y , z\right) &= F_{60}\! \left(x , y , z\right)\\
F_{61}\! \left(x , y , z\right) &= F_{60}\! \left(x , y , z\right)+F_{63}\! \left(x , y\right)\\
F_{61}\! \left(x , y , z\right) &= F_{62}\! \left(x , y , z\right)\\
F_{62}\! \left(x , y , z\right) &= F_{14}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)\\
F_{64}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{63}\! \left(x , y\right)\\
F_{65}\! \left(x , y , z\right) &= F_{64}\! \left(x , y\right)+F_{67}\! \left(x , y , z\right)\\
F_{65}\! \left(x , y , z\right) &= F_{66}\! \left(x , y , y z \right)\\
F_{66}\! \left(x , y , z\right) &= F_{5}\! \left(x , z\right)+F_{61}\! \left(x , y , z\right)\\
F_{68}\! \left(x , y , z\right) &= \frac{z \left(F_{67}\! \left(x , y , 1\right)-F_{67}\! \left(x , y , \frac{z}{y}\right)\right)}{-z +y}\\
F_{69}\! \left(x , y , z\right) &= F_{68}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)\\
F_{70}\! \left(x , y , z\right) &= F_{19}\! \left(x \right)+F_{69}\! \left(x , y , z\right)+F_{71}\! \left(x , y , z\right)+F_{74}\! \left(x , y , z\right)\\
F_{70}\! \left(x , y , z\right) &= \frac{z \left(F_{6}\! \left(x , y\right)-F_{6}\! \left(x , z\right)\right)}{-z +y}\\
F_{71}\! \left(x , y , z\right) &= F_{72}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)\\
F_{72}\! \left(x , y , z\right) &= -\frac{F_{73}\! \left(x , 1, z\right) z -F_{73}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}\\
F_{73}\! \left(x , y , z\right) &= F_{66}\! \left(x , y z , z\right)\\
F_{74}\! \left(x , y , z\right) &= F_{49}\! \left(x \right) F_{75}\! \left(x , y , z\right)\\
F_{75}\! \left(x , y , z\right) &= \frac{z \left(F_{76}\! \left(x , y\right)-F_{76}\! \left(x , z\right)\right)}{-z +y}\\
F_{76}\! \left(x , y\right) &= -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}\\
F_{77}\! \left(x , y , z\right) &= F_{78}\! \left(x , y , z\right)\\
F_{78}\! \left(x , y , z\right) &= F_{79}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)\\
F_{79}\! \left(x , y , z\right) &= F_{17}\! \left(x , z\right)+F_{80}\! \left(x , y , z\right)+F_{81}\! \left(x , y , z\right)\\
F_{80}\! \left(x , y , z\right) &= F_{79}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)\\
F_{81}\! \left(x , y , z\right) &= F_{82}\! \left(x , y , z\right)\\
F_{82}\! \left(x , y , z\right) &= F_{0}\! \left(x \right) F_{35}\! \left(x , y\right) F_{43}\! \left(x , z\right) F_{46}\! \left(x , y\right) F_{8}\! \left(x , y\right)\\
F_{83}\! \left(x , y\right) &= F_{84}\! \left(x , y\right)\\
F_{84}\! \left(x , y\right) &= F_{49}\! \left(x \right) F_{85}\! \left(x , y\right)\\
F_{85}\! \left(x , y\right) &= F_{86}\! \left(x , y\right)+F_{91}\! \left(x , y\right)\\
F_{86}\! \left(x , y\right) &= -\frac{y \left(F_{87}\! \left(x , 1\right)-F_{87}\! \left(x , y\right)\right)}{-1+y}\\
F_{87}\! \left(x , y\right) &= F_{6}\! \left(x , y\right)+F_{88}\! \left(x , y\right)\\
F_{88}\! \left(x , y\right) &= F_{89}\! \left(x , y\right)\\
F_{89}\! \left(x , y\right) &= F_{49}\! \left(x \right) F_{90}\! \left(x , y\right)\\
F_{90}\! \left(x , y\right) &= F_{57}\! \left(x , y , 1\right)\\
F_{91}\! \left(x , y\right) &= F_{49}\! \left(x \right) F_{92}\! \left(x , y\right)\\
F_{92}\! \left(x , y\right) &= -\frac{y \left(F_{85}\! \left(x , 1\right)-F_{85}\! \left(x , y\right)\right)}{-1+y}\\
F_{93}\! \left(x , y\right) &= F_{8}\! \left(x , y\right) F_{94}\! \left(x , y\right)\\
F_{94}\! \left(x , y\right) &= F_{95}\! \left(x , 1, y\right)\\
F_{95}\! \left(x , y , z\right) &= F_{30}\! \left(x , y z , z\right)\\
F_{96}\! \left(x , y , z\right) &= F_{61}\! \left(x , y , z\right)\\
F_{97}\! \left(x , y , z\right) &= F_{98}\! \left(x , y , z\right)\\
F_{98}\! \left(x , y , z\right) &= F_{8}\! \left(x , y\right) F_{99}\! \left(x , y , z\right)\\
F_{99}\! \left(x , y , z\right) &= F_{100}\! \left(x , y , z\right)+F_{158}\! \left(x , y , z\right)\\
F_{100}\! \left(x , y , z\right) &= F_{101}\! \left(x , y , z\right) F_{46}\! \left(x , y\right)\\
F_{101}\! \left(x , y , z\right) &= F_{102}\! \left(x , y , z\right)+F_{97}\! \left(x , y , z\right)\\
F_{102}\! \left(x , y , z\right) &= F_{103}\! \left(x , z\right)+F_{154}\! \left(x , y , z\right)\\
F_{103}\! \left(x , y\right) &= F_{104}\! \left(x , y\right)+F_{150}\! \left(x , y\right)\\
F_{104}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{105}\! \left(x , y\right)+F_{148}\! \left(x , y\right)\\
F_{105}\! \left(x , y\right) &= F_{106}\! \left(x , y\right) F_{8}\! \left(x , y\right)\\
F_{106}\! \left(x , y\right) &= F_{107}\! \left(x , 1, y\right)\\
F_{107}\! \left(x , y , z\right) &= F_{0}\! \left(x \right)+F_{108}\! \left(x , y , z\right)+F_{109}\! \left(x , y , z\right)+F_{111}\! \left(x , y , z\right)\\
F_{108}\! \left(x , y , z\right) &= F_{107}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)\\
F_{109}\! \left(x , y , z\right) &= F_{110}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)\\
F_{110}\! \left(x , y , z\right) &= -\frac{-F_{107}\! \left(x , y , z\right) y +F_{107}\! \left(x , 1, z\right)}{-1+y}\\
F_{111}\! \left(x , y , z\right) &= F_{112}\! \left(x , y , z\right)\\
F_{112}\! \left(x , y , z\right) &= F_{113}\! \left(x , y , z\right) F_{49}\! \left(x \right)\\
F_{113}\! \left(x , y , z\right) &= -\frac{-F_{114}\! \left(x , y z \right) y +F_{114}\! \left(x , z\right)}{-1+y}\\
F_{114}\! \left(x , y\right) &= F_{115}\! \left(x , y\right)+F_{144}\! \left(x , y\right)\\
F_{115}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{116}\! \left(x , y\right)+F_{117}\! \left(x , y\right)+F_{119}\! \left(x , y\right)\\
F_{116}\! \left(x , y\right) &= F_{115}\! \left(x , y\right) F_{8}\! \left(x , y\right)\\
F_{117}\! \left(x , y\right) &= F_{118}\! \left(x , y\right) F_{49}\! \left(x \right)\\
F_{118}\! \left(x , y\right) &= -\frac{-F_{115}\! \left(x , y\right) y +F_{115}\! \left(x , 1\right)}{-1+y}\\
F_{119}\! \left(x , y\right) &= F_{120}\! \left(x , y\right)\\
F_{120}\! \left(x , y\right) &= F_{121}\! \left(x , y\right) F_{49}\! \left(x \right)\\
F_{121}\! \left(x , y\right) &= -\frac{-F_{122}\! \left(x , y\right) y +F_{122}\! \left(x , 1\right)}{-1+y}\\
F_{122}\! \left(x , y\right) &= F_{123}\! \left(x , y\right)+F_{124}\! \left(x , y\right)\\
F_{123}\! \left(x , y\right) &= F_{107}\! \left(x , y , 1\right)\\
F_{124}\! \left(x , y\right) &= F_{125}\! \left(x , y\right)\\
F_{125}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{126}\! \left(x , y\right) F_{49}\! \left(x \right)\\
F_{126}\! \left(x , y\right) &= F_{127}\! \left(x , y , 1\right)\\
F_{127}\! \left(x , y , z\right) &= -\frac{-F_{128}\! \left(x , y , z\right) z +F_{128}\! \left(x , y , 1\right)}{z -1}\\
F_{128}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{129}\! \left(x , y , z\right)+F_{130}\! \left(x , y , z\right)+F_{133}\! \left(x , y , z\right)\\
F_{129}\! \left(x , y , z\right) &= F_{128}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)\\
F_{130}\! \left(x , y , z\right) &= F_{131}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)\\
F_{131}\! \left(x , y , z\right) &= -\frac{F_{132}\! \left(x , 1, z\right) z -F_{132}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}\\
F_{132}\! \left(x , y , z\right) &= F_{128}\! \left(x , y z , z\right)\\
F_{133}\! \left(x , y , z\right) &= F_{134}\! \left(x , y , z\right) F_{49}\! \left(x \right)\\
F_{134}\! \left(x , y , z\right) &= \frac{F_{135}\! \left(x , y\right) y -F_{135}\! \left(x , z\right) z}{-z +y}\\
F_{135}\! \left(x , y\right) &= F_{136}\! \left(x , y , 1\right)\\
F_{136}\! \left(x , y , z\right) &= F_{137}\! \left(x , y z , z\right)\\
F_{137}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{138}\! \left(x , y , z\right)+F_{139}\! \left(x , y , z\right)+F_{141}\! \left(x , y , z\right)\\
F_{138}\! \left(x , y , z\right) &= F_{137}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)\\
F_{139}\! \left(x , y , z\right) &= F_{140}\! \left(x , y , z\right) F_{8}\! \left(x , z\right)\\
F_{140}\! \left(x , y , z\right) &= -\frac{F_{136}\! \left(x , 1, z\right) z -F_{136}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}\\
F_{141}\! \left(x , y , z\right) &= F_{142}\! \left(x , y , z\right) F_{49}\! \left(x \right)\\
F_{142}\! \left(x , y , z\right) &= \frac{F_{143}\! \left(x , y\right) y -F_{143}\! \left(x , z\right) z}{-z +y}\\
F_{143}\! \left(x , y\right) &= F_{132}\! \left(x , y , 1\right)\\
F_{144}\! \left(x , y\right) &= F_{145}\! \left(x , y\right)\\
F_{145}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{146}\! \left(x , y\right) F_{49}\! \left(x \right)\\
F_{146}\! \left(x , y\right) &= F_{147}\! \left(x , y , 1\right)\\
F_{147}\! \left(x , y , z\right) &= -\frac{-F_{137}\! \left(x , y , z\right) z +F_{137}\! \left(x , y , 1\right)}{z -1}\\
F_{148}\! \left(x , y\right) &= F_{149}\! \left(x , y\right)\\
F_{149}\! \left(x , y\right) &= F_{114}\! \left(x , y\right) F_{49}\! \left(x \right)\\
F_{150}\! \left(x , y\right) &= F_{151}\! \left(x , y\right)\\
F_{151}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{152}\! \left(x , y\right) F_{8}\! \left(x , y\right)\\
F_{152}\! \left(x , y\right) &= F_{153}\! \left(x , 1, y\right)\\
F_{153}\! \left(x , y , z\right) &= -\frac{-F_{43}\! \left(x , y z \right) y +F_{43}\! \left(x , z\right)}{-1+y}\\
F_{154}\! \left(x , y , z\right) &= F_{155}\! \left(x , y , z\right) F_{8}\! \left(x , y\right)\\
F_{155}\! \left(x , y , z\right) &= F_{102}\! \left(x , y , z\right)+F_{156}\! \left(x , y , z\right)\\
F_{156}\! \left(x , y , z\right) &= F_{157}\! \left(x , y , z\right)\\
F_{157}\! \left(x , y , z\right) &= F_{8}\! \left(x , y\right) F_{99}\! \left(x , y , z\right)\\
F_{158}\! \left(x , y , z\right) &= F_{159}\! \left(x , y , z\right)\\
F_{159}\! \left(x , y , z\right) &= F_{46}\! \left(x , y\right)^{2} F_{0}\! \left(x \right) F_{160}\! \left(x , y\right) F_{43}\! \left(x , z\right)\\
F_{160}\! \left(x , y\right) &= y F_{161}\! \left(x , y\right)\\
F_{161}\! \left(x , y\right) &= F_{162}\! \left(x , y\right)\\
F_{162}\! \left(x , y\right) &= F_{163}\! \left(x , y\right) F_{49}\! \left(x \right)\\
F_{163}\! \left(x , y\right) &= F_{164}\! \left(x , 1, y\right)\\
F_{164}\! \left(x , y , z\right) &= -\frac{-F_{46}\! \left(x , y z \right) y +F_{46}\! \left(x , z\right)}{-1+y}\\
F_{165}\! \left(x , y\right) &= F_{166}\! \left(x , y\right) F_{49}\! \left(x \right)\\
F_{166}\! \left(x , y\right) &= -\frac{-y F_{9}\! \left(x , y\right)+F_{9}\! \left(x , 1\right)}{-1+y}\\
\end{align*}\)