Av(12354, 12453, 12543, 13254)
Counting Sequence
1, 1, 2, 6, 24, 116, 635, 3791, 24134, 161486, 1124514, 8091104, 59831778, 452835816, 3496384939, ...
This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 66 rules.
Finding the specification took 6101 seconds.
Copy 66 equations to clipboard:
\(\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_{8}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x , 1\right)\\
F_{5}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)\\
F_{6}\! \left(x , y_{0}\right) &= F_{7}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)\\
F_{7}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{5}\! \left(x , y_{0}\right)+F_{5}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{8}\! \left(x \right) &= x\\
F_{9}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)\\
F_{10}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , 1, y_{0}\right)\\
F_{11}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{12}\! \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_{12}\! \left(x , y_{0}, y_{1}\right) &= F_{13}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)\\
F_{13}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{1}\right)+F_{52}\! \left(x , y_{0}, y_{1}\right)\\
F_{15}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)\\
F_{16}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}\right)+F_{45}\! \left(x , y_{0}\right)\\
F_{16}\! \left(x , y_{0}\right) &= F_{0}\! \left(x \right)+F_{17}\! \left(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_{35}\! \left(x , y_{0}\right)\\
F_{19}\! \left(x , y_{0}\right) &= F_{20}\! \left(x , y_{0}\right)+F_{40}\! \left(x , y_{0}\right)+F_{44}\! \left(x , y_{0}\right)\\
F_{20}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x , y_{0}\right)+F_{37}\! \left(x , y_{0}\right)\\
F_{21}\! \left(x , y_{0}\right) &= F_{22}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)\\
F_{22}\! \left(x , y_{0}\right) &= F_{23}\! \left(x , 1, y_{0}\right)\\
F_{23}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{1}\right)+F_{24}\! \left(x , y_{0}, y_{1}\right)\\
F_{24}\! \left(x , y_{0}, y_{1}\right) &= F_{25}\! \left(x \right)+F_{26}\! \left(x , y_{0}, y_{1}\right)+F_{28}\! \left(x , y_{0}, y_{1}\right)+F_{36}\! \left(x , y_{0}, y_{1}\right)\\
F_{25}\! \left(x \right) &= 0\\
F_{26}\! \left(x , y_{0}, y_{1}\right) &= F_{27}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)\\
F_{27}\! \left(x , y_{0}, y_{1}\right) &= -\frac{y_{0} \left(F_{24}\! \left(x , 1, y_{1}\right)-F_{24}\! \left(x , y_{0}, y_{1}\right)\right)}{-1+y_{0}}\\
F_{28}\! \left(x , y_{0}, y_{1}\right) &= F_{29}\! \left(x , y_{0}, y_{1}\right) F_{35}\! \left(x , y_{0}\right)\\
F_{29}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , y_{0}, y_{1}\right)+F_{30}\! \left(x , y_{0}, y_{1}\right)\\
F_{30}\! \left(x , y_{0}, y_{1}\right) &= F_{31}\! \left(x , y_{0}, y_{1}\right)\\
F_{31}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} \left(F_{32}\! \left(x , y_{0}, 1\right)-F_{32}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)\right)}{-y_{1}+y_{0}}\\
F_{32}\! \left(x , y_{0}, y_{1}\right) &= F_{33}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{34}\! \left(x , y_{0}, y_{1}\right) &= F_{33}\! \left(x , y_{0}, y_{1}\right)+F_{5}\! \left(x , y_{0}\right)\\
F_{11}\! \left(x , y_{0}, y_{1}\right) &= F_{34}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{35}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{36}\! \left(x , y_{0}, y_{1}\right) &= F_{24}\! \left(x , y_{0}, y_{1}\right) F_{35}\! \left(x , y_{1}\right)\\
F_{37}\! \left(x , y_{0}\right) &= F_{38}\! \left(x , y_{0}, 1\right)\\
F_{38}\! \left(x , y_{0}, y_{1}\right) &= F_{39}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{39}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{1}\right) F_{35}\! \left(x , y_{0}\right)\\
F_{40}\! \left(x , y_{0}\right) &= F_{41}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)\\
F_{41}\! \left(x , y_{0}\right) &= F_{42}\! \left(x , 1, y_{0}\right)\\
F_{43}\! \left(x , y_{0}, y_{1}\right) &= F_{35}\! \left(x , y_{0}\right) F_{42}\! \left(x , y_{0}, y_{1}\right)\\
F_{43}\! \left(x , y_{0}, y_{1}\right) &= F_{24}\! \left(x , y_{0}, y_{1}\right)\\
F_{44}\! \left(x , y_{0}\right) &= F_{19}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right)\\
F_{45}\! \left(x , y_{0}\right) &= F_{35}\! \left(x , y_{0}\right) F_{46}\! \left(x , y_{0}\right)\\
F_{46}\! \left(x , y_{0}\right) &= F_{47}\! \left(x , y_{0}, 1\right)\\
F_{47}\! \left(x , y_{0}, y_{1}\right) &= F_{48}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{48}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{1}\right)+F_{49}\! \left(x , y_{0}, y_{1}\right)\\
F_{49}\! \left(x , y_{0}, y_{1}\right) &= y_{0} F_{50}\! \left(x , y_{1}\right)\\
F_{50}\! \left(x , y_{0}\right) &= F_{51}\! \left(x , y_{0}\right)\\
F_{51}\! \left(x , y_{0}\right) &= F_{19}\! \left(x , y_{0}\right) F_{8}\! \left(x \right)\\
F_{52}\! \left(x , y_{0}, y_{1}\right) &= F_{53}\! \left(x , y_{0}, y_{1}\right)\\
F_{53}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} y_{1} \left(F_{54}\! \left(x , y_{0}, y_{1}\right)-F_{54}\! \left(x , \frac{1}{y_{1}}, y_{1}\right)\right)}{y_{0} y_{1}-1}\\
F_{11}\! \left(x , y_{0}, y_{1}\right) &= F_{16}\! \left(x , y_{1}\right)+F_{54}\! \left(x , y_{0}, y_{1}\right)\\
F_{55}\! \left(x , y_{0}, y_{1}\right) &= F_{28}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{56}\! \left(x , y_{0}, y_{1}\right) &= F_{35}\! \left(x , y_{1}\right) F_{57}\! \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_{60}\! \left(x , y_{0}, y_{1}\right)\\
F_{58}\! \left(x , y_{0}, y_{1}\right) &= F_{59}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{59}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{23}\! \left(x , y_{0} y_{1}, y_{1} y_{2}\right)\\
F_{60}\! \left(x , y_{0}, y_{1}\right) &= y_{1} F_{61}\! \left(x , y_{0}, y_{1}\right)\\
F_{61}\! \left(x , y_{0}, y_{1}\right) &= F_{62}\! \left(x , y_{0}, y_{1}\right)\\
F_{62}\! \left(x , y_{0}, y_{1}\right) &= F_{63}\! \left(x , y_{0}, y_{1}\right) F_{8}\! \left(x \right)\\
F_{64}\! \left(x , y_{0}, y_{1}\right) &= F_{35}\! \left(x , y_{1}\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_{65}\! \left(x , y_{0}, y_{1}\right) &= F_{33}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
\end{align*}\)