Av(12354, 12453, 13254, 13452, 14253, 14352, 23451, 24351)
Counting Sequence
1, 1, 2, 6, 24, 112, 568, 3040, 16933, 97295, 572976, 3441666, 21009275, 129977901, 813245131, ...
This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 73 rules.
Finding the specification took 481 seconds.
Copy 73 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_{10}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{5}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{10}\! \left(x \right) F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x , 1\right)\\
F_{7}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x , y_{0}\right)+F_{48}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= F_{10}\! \left(x \right) F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= -\frac{-F_{7}\! \left(x , y_{0}\right) y_{0}+F_{7}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{10}\! \left(x \right) &= x\\
F_{11}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right) F_{24}\! \left(x , y_{0}\right)\\
F_{12}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , 1, y_{0}\right)\\
F_{13}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{14}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)+F_{46}\! \left(x , y_{0}, y_{1}\right)\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x \right) F_{16}\! \left(x , y_{0}, y_{1}\right)\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= F_{17}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{10}\! \left(x \right) F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{17}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{24}\! \left(x , y_{0}\right)\\
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{22}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{22}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}\\
F_{22}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{23}\! \left(x , y_{0}, 1\right) y_{0}-F_{23}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{23}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{24}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{25}\! \left(x , y_{0}, y_{1}\right) &= F_{24}\! \left(x , y_{1}\right) F_{26}\! \left(x , y_{0}, y_{1}\right)\\
F_{26}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{27}\! \left(x , 1, y_{1}\right) y_{1}-F_{27}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{27}\! \left(x , y_{0}, y_{1}\right) &= F_{28}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{28}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{29}\! \left(x , y_{0}, y_{1}\right)+F_{40}\! \left(x , y_{0}\right)+F_{42}\! \left(x , y_{0}, y_{1}\right)+F_{43}\! \left(x , y_{0}, y_{1}\right)\\
F_{29}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x \right) F_{30}\! \left(x , y_{0}, y_{1}\right)\\
F_{30}\! \left(x , y_{0}, y_{1}\right) &= F_{31}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{32}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{10}\! \left(x \right) F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{33}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{31}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{34}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{24}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{35}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{36}\! \left(x , y_{0}, y_{1}\right) y_{1}-F_{36}\! \left(x , y_{0}, y_{2}\right) y_{2}}{-y_{2}+y_{1}}\\
F_{36}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{37}\! \left(x , y_{0}, 1\right) y_{0}-F_{37}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{37}\! \left(x , y_{0}, y_{1}\right) &= F_{28}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{24}\! \left(x , y_{2}\right) F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{10}\! \left(x \right) F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{40}\! \left(x , y_{0}\right) &= F_{24}\! \left(x , y_{0}\right) F_{41}\! \left(x , y_{0}\right)\\
F_{41}\! \left(x , y_{0}\right) &= F_{27}\! \left(x , 1, y_{0}\right)\\
F_{42}\! \left(x , y_{0}, y_{1}\right) &= F_{24}\! \left(x , y_{1}\right) F_{28}\! \left(x , y_{0}, y_{1}\right)\\
F_{43}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x \right) F_{28}\! \left(x , y_{0}, y_{1}\right)\\
F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{10}\! \left(x \right) F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{45}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{31}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{31}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{46}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x \right) F_{47}\! \left(x , y_{0}, y_{1}\right)\\
F_{47}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{28}\! \left(x , y_{0}, y_{1}\right) y_{1}+F_{28}\! \left(x , y_{0}, 1\right)}{-1+y_{1}}\\
F_{48}\! \left(x , y_{0}\right) &= F_{10}\! \left(x \right) F_{49}\! \left(x , y_{0}\right)\\
F_{49}\! \left(x , y_{0}\right) &= -\frac{-F_{50}\! \left(x , y_{0}\right) y_{0}+F_{50}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{50}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{40}\! \left(x , y_{0}\right)+F_{51}\! \left(x , y_{0}\right)+F_{69}\! \left(x , y_{0}\right)\\
F_{51}\! \left(x , y_{0}\right) &= F_{10}\! \left(x \right) F_{52}\! \left(x , y_{0}\right)\\
F_{52}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{53}\! \left(x , y_{0}\right)+F_{62}\! \left(x , y_{0}\right)+F_{65}\! \left(x , y_{0}\right)+F_{67}\! \left(x , y_{0}\right)\\
F_{53}\! \left(x , y_{0}\right) &= F_{10}\! \left(x \right) F_{54}\! \left(x , y_{0}\right)\\
F_{54}\! \left(x , y_{0}\right) &= F_{55}\! \left(x , 1, y_{0}\right)\\
F_{55}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{56}\! \left(x , y_{0}, y_{1}\right)+F_{56}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{56}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x , y_{0}, y_{1}\right)+F_{57}\! \left(x , y_{0}, y_{1}\right)+F_{59}\! \left(x , y_{0}, y_{1}\right)+F_{60}\! \left(x , y_{0}, y_{1}\right)\\
F_{57}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x \right) F_{58}\! \left(x , y_{0}, y_{1}\right)\\
F_{58}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{56}\! \left(x , y_{0}, y_{1}\right)+F_{56}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{59}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{0}, y_{1}\right) F_{24}\! \left(x , y_{0}\right)\\
F_{60}\! \left(x , y_{0}, y_{1}\right) &= F_{10}\! \left(x \right) F_{61}\! \left(x , y_{0}, y_{1}\right)\\
F_{61}\! \left(x , y_{0}, y_{1}\right) &= F_{31}\! \left(x , y_{0}, y_{1}, 1\right)\\
F_{62}\! \left(x , y_{0}\right) &= F_{10}\! \left(x \right) F_{63}\! \left(x , y_{0}\right)\\
F_{63}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{64}\! \left(x , y_{0}\right)+F_{64}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{64}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , 1, y_{0}\right)\\
F_{65}\! \left(x , y_{0}\right) &= F_{24}\! \left(x , y_{0}\right) F_{66}\! \left(x , y_{0}\right)\\
F_{66}\! \left(x , y_{0}\right) &= F_{26}\! \left(x , 1, y_{0}\right)\\
F_{67}\! \left(x , y_{0}\right) &= F_{10}\! \left(x \right) F_{68}\! \left(x , y_{0}\right)\\
F_{68}\! \left(x , y_{0}\right) &= F_{30}\! \left(x , y_{0}, 1\right)\\
F_{69}\! \left(x , y_{0}\right) &= F_{70}\! \left(x , y_{0}, 1\right)\\
F_{70}\! \left(x , y_{0}, y_{1}\right) &= F_{42}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{71}\! \left(x \right) &= F_{10}\! \left(x \right) F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{50}\! \left(x , 1\right)\\
\end{align*}\)
This specification was found using the strategy pack "All The Strategies 2 Tracked Fusion Tracked Component Fusion Symmetries" and has 34 rules.
Finding the specification took 37581 seconds.
Copy 34 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 , 1\right)\\
F_{4}\! \left(x , y_{0}\right) &= F_{5}\! \left(x \right) F_{6}\! \left(x , y_{0}\right)\\
F_{5}\! \left(x \right) &= x\\
F_{6}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{7}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)\\
F_{7}\! \left(x , y_{0}\right) &= -\frac{-F_{4}\! \left(x , y_{0}\right) y_{0}+F_{4}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{8}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{10}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , y_{0}, 1\right)\\
F_{11}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{12}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}, y_{1}\right)+F_{30}\! \left(x , y_{0}, y_{1}\right)+F_{32}\! \left(x , y_{1}, y_{0}\right)\\
F_{13}\! \left(x , y_{0}, y_{1}\right) &= F_{14}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{5}\! \left(x \right)\\
F_{15}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{20}\! \left(x , y_{1}, y_{0}, y_{2}\right)+F_{28}\! \left(x , y_{2}, y_{0}, y_{1}\right)\\
F_{16}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{14}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{14}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{17}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{18}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{18}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{y_{0}-y_{1}}\\
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{19}\! \left(x , y_{0}, y_{1}\right) y_{0} y_{1}-F_{19}\! \left(x , y_{0}, \frac{y_{2}}{y_{0}}\right) y_{2}}{y_{0} y_{1}-y_{2}}\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{y_{0} F_{22}\! \left(x , y_{0}, 1, y_{2}\right)-y_{1} F_{22}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right)}{y_{0}-y_{1}}\\
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{23}\! \left(x , y_{1}, y_{0}\right) F_{24}\! \left(x , y_{2}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{23}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{24}\! \left(x , y_{0}\right) &= F_{25}\! \left(x , y_{0}\right)\\
F_{25}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{26}\! \left(x , y_{0}\right)\\
F_{26}\! \left(x , y_{0}\right) &= F_{27}\! \left(x , y_{0}\right)\\
F_{27}\! \left(x , y_{0}\right) &= F_{25}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{28}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{29}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{15}\! \left(x , y_{1}, y_{2}, y_{0}\right) F_{24}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\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) &= F_{10}\! \left(x , y_{0}\right) F_{24}\! \left(x , y_{1}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{32}\! \left(x , y_{0}, y_{1}\right) &= F_{33}\! \left(x , y_{0}, y_{1}\right)\\
F_{33}\! \left(x , y_{0}, y_{1}\right) &= F_{12}\! \left(x , y_{1}, y_{0}\right) F_{24}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
\end{align*}\)