Av(12435, 12453, 12543)
Counting Sequence
1, 1, 2, 6, 24, 117, 652, 3986, 26050, 178963, 1277820, 9407127, 70990882, 546790230, 4284188730, ...
This specification was found using the strategy pack "All The Strategies 2 Tracked Fusion Tracked Component Fusion Symmetries" and has 79 rules.
Finding the specification took 9691 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 , 1\right)\\
F_{4}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{6}\! \left(x , y\right)\\
F_{5}\! \left(x \right) &= x\\
F_{6}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{7}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= F_{8}\! \left(x , y\right)\\
F_{8}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{12}\! \left(x , y\right)+F_{6}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= -\frac{-F_{11}\! \left(x , y\right) y +F_{11}\! \left(x , 1\right)}{-1+y}\\
F_{11}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{9}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{15}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= y x\\
F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y , 1\right)\\
F_{16}\! \left(x , y , z\right) &= F_{17}\! \left(x , y , y z \right)\\
F_{18}\! \left(x , y , z\right) &= F_{14}\! \left(x , z\right) F_{17}\! \left(x , y , z\right)\\
F_{18}\! \left(x , y , z\right) &= F_{19}\! \left(x , y , z\right)\\
F_{19}\! \left(x , y , z\right) &= F_{20}\! \left(x , y , z\right)\\
F_{20}\! \left(x , y , z\right) &= z F_{21}\! \left(x , y , z\right)\\
F_{21}\! \left(x , y , z\right) &= F_{22}\! \left(x \right)+F_{23}\! \left(x , y , z\right)+F_{25}\! \left(x , y , z\right)+F_{28}\! \left(x , z , y\right)+F_{30}\! \left(x , y , z\right)\\
F_{22}\! \left(x \right) &= 0\\
F_{23}\! \left(x , y , z\right) &= -\frac{-F_{24}\! \left(x , y , z\right) y +F_{24}\! \left(x , 1, z\right)}{-1+y}\\
F_{24}\! \left(x , y , z\right) &= F_{21}\! \left(x , y , z\right) F_{5}\! \left(x \right)\\
F_{25}\! \left(x , y , z\right) &= \frac{F_{26}\! \left(x , y , 1\right) y -F_{26}\! \left(x , y , \frac{z}{y}\right) z}{-z +y}\\
F_{26}\! \left(x , y , z\right) &= F_{14}\! \left(x , y\right) F_{27}\! \left(x , y , z\right)\\
F_{27}\! \left(x , y , z\right) &= F_{21}\! \left(x , y , y z \right)\\
F_{28}\! \left(x , y , z\right) &= F_{29}\! \left(x , y , z\right)\\
F_{29}\! \left(x , y , z\right) &= F_{14}\! \left(x , y\right) F_{21}\! \left(x , z , y\right)\\
F_{30}\! \left(x , y , z\right) &= F_{31}\! \left(x , y , z\right) F_{5}\! \left(x \right)\\
F_{32}\! \left(x , y , z\right) &= F_{31}\! \left(x , y , z\right)+F_{33}\! \left(x , y , z\right)\\
F_{32}\! \left(x , y , z\right) &= \frac{F_{6}\! \left(x , y\right) y -F_{6}\! \left(x , z\right) z}{-z +y}\\
F_{33}\! \left(x , y , z\right) &= F_{34}\! \left(x , y , z\right)\\
F_{34}\! \left(x , y , z\right) &= -\frac{F_{35}\! \left(x , 1, z\right) z -y F_{35}\! \left(x , \frac{y}{z}, z\right)}{-z +y}\\
F_{35}\! \left(x , y , z\right) &= F_{36}\! \left(x , y z , z\right)\\
F_{36}\! \left(x , y , z\right) &= z F_{37}\! \left(x , y , z\right)\\
F_{37}\! \left(x , y , z\right) &= F_{38}\! \left(x , z , y\right)\\
F_{38}\! \left(x , y , z\right) &= F_{39}\! \left(x , y , z\right) F_{5}\! \left(x \right)\\
F_{39}\! \left(x , y , z\right) &= F_{22}\! \left(x \right)+F_{40}\! \left(x , y , z\right)+F_{42}\! \left(x , y , z\right)+F_{65}\! \left(x , y , z\right)\\
F_{40}\! \left(x , y , z\right) &= -\frac{-F_{41}\! \left(x , y , z\right) z +F_{41}\! \left(x , y , 1\right)}{-1+z}\\
F_{41}\! \left(x , y , z\right) &= F_{39}\! \left(x , y , z\right) F_{5}\! \left(x \right)\\
F_{42}\! \left(x , y , z\right) &= F_{14}\! \left(x , z\right) F_{43}\! \left(x , y , z\right)\\
F_{43}\! \left(x , y , z\right) &= y F_{44}\! \left(x , z\right)\\
F_{45}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{44}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{22}\! \left(x \right)+F_{45}\! \left(x , y\right)+F_{62}\! \left(x , y\right)+F_{64}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{48}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{48}\! \left(x , y\right) &= F_{49}\! \left(x , y\right)+F_{51}\! \left(x , y\right)+F_{9}\! \left(x , y\right)\\
F_{49}\! \left(x , y\right) &= -\frac{-F_{50}\! \left(x , y\right) y +F_{50}\! \left(x , 1\right)}{-1+y}\\
F_{50}\! \left(x , y\right) &= F_{48}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{51}\! \left(x , y\right) &= F_{52}\! \left(x , y\right)\\
F_{52}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{53}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{54}\! \left(x , y , 1\right)\\
F_{55}\! \left(x , y , z\right) &= F_{14}\! \left(x , z\right) F_{54}\! \left(x , y , z\right)\\
F_{16}\! \left(x , y , z\right) &= F_{55}\! \left(x , y , z\right)+F_{56}\! \left(x , y , z\right)\\
F_{16}\! \left(x , y , z\right) &= F_{56}\! \left(x , y , z\right)+F_{57}\! \left(x , y , z\right)\\
F_{57}\! \left(x , y , z\right) &= F_{58}\! \left(x , y , y z \right)\\
F_{59}\! \left(x , y , z\right) &= F_{14}\! \left(x , z\right) F_{58}\! \left(x , y , z\right)\\
F_{59}\! \left(x , y , z\right) &= F_{60}\! \left(x , y , z\right)\\
F_{61}\! \left(x , y , z\right) &= F_{31}\! \left(x , y , z\right)+F_{60}\! \left(x , y , z\right)\\
F_{61}\! \left(x , y , z\right) &= F_{19}\! \left(x , y , z\right)+F_{6}\! \left(x , y\right)\\
F_{62}\! \left(x , y\right) &= -\frac{-y F_{63}\! \left(x , y\right)+F_{63}\! \left(x , 1\right)}{-1+y}\\
F_{63}\! \left(x , y\right) &= F_{46}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{64}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{9}\! \left(x , y\right)\\
F_{65}\! \left(x , y , z\right) &= F_{66}\! \left(x , y\right) F_{68}\! \left(x , y , z\right)\\
F_{66}\! \left(x , y\right) &= F_{67}\! \left(x , y\right)\\
F_{67}\! \left(x , y\right) &= y x\\
F_{69}\! \left(x , y , z\right) &= F_{14}\! \left(x , z\right) F_{68}\! \left(x , y , z\right)\\
F_{69}\! \left(x , y , z\right) &= F_{70}\! \left(x , z , y\right)\\
F_{71}\! \left(x , y , z\right) &= F_{70}\! \left(x , y , y z \right)\\
F_{72}\! \left(x , y , z\right) &= F_{71}\! \left(x , y , z\right)+F_{73}\! \left(x , y z \right)\\
F_{72}\! \left(x , y , z\right) &= F_{31}\! \left(x , y , y z \right)\\
F_{73}\! \left(x , y\right) &= F_{74}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{75}\! \left(x , y\right)+F_{78}\! \left(x , y\right)\\
F_{75}\! \left(x , y\right) &= F_{5}\! \left(x \right) F_{76}\! \left(x , y\right)\\
F_{76}\! \left(x , y\right) &= F_{77}\! \left(x , y\right)\\
F_{77}\! \left(x , y\right) &= F_{31}\! \left(x , 1, y\right)\\
F_{78}\! \left(x , y\right) &= F_{66}\! \left(x , y\right) F_{74}\! \left(x , y\right)\\
\end{align*}\)