Av(12435, 13425, 14325, 15324, 23415, 24315, 25314)
Counting Sequence
1, 1, 2, 6, 24, 113, 580, 3129, 17442, 99574, 579108, 3419056, 20440024, 123494294, 752913720, ...
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 76 rules.
Finding the specification took 2975 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_{5}\! \left(x \right)\\
F_{4}\! \left(x \right) &= x\\
F_{5}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x , 1\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^{2} x^{2}+4 x F_{8}\! \left(x , y\right)^{2} y -F_{8}\! \left(x , y\right)^{2}+F_{8}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right)+F_{13}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= -\frac{y \left(F_{7}\! \left(x , 1\right)-F_{7}\! \left(x , y\right)\right)}{-1+y}\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{16}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= y x\\
F_{17}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)\\
F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , 1, y\right)\\
F_{19}\! \left(x , y , z\right) &= -\frac{-F_{20}\! \left(x , y z \right) y +F_{20}\! \left(x , z\right)}{-1+y}\\
F_{20}\! \left(x , y\right) &= F_{2}\! \left(x \right)+F_{21}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{22}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{23}\! \left(x , y\right) F_{70}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{20}\! \left(x , y\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_{4}\! \left(x \right)\\
F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)+F_{74}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= -\frac{-F_{28}\! \left(x , y\right) y +F_{28}\! \left(x , 1\right)}{-1+y}\\
F_{28}\! \left(x , y\right) &= F_{29}\! \left(x \right)+F_{31}\! \left(x , y\right)\\
F_{29}\! \left(x \right) &= \frac{F_{30}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{30}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{31}\! \left(x , y\right) &= F_{32}\! \left(x , y\right)\\
F_{32}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{33}\! \left(x , y\right) F_{70}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)+F_{34}\! \left(x , y\right)\\
F_{34}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)+F_{35}\! \left(x , y\right)\\
F_{35}\! \left(x , y\right) &= F_{36}\! \left(x , y\right)\\
F_{36}\! \left(x , y\right) &= F_{37}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{37}\! \left(x , y\right) &= F_{38}\! \left(x , y\right)+F_{54}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= F_{26}\! \left(x , y\right)+F_{38}\! \left(x , y\right)\\
F_{39}\! \left(x , y\right) &= F_{40}\! \left(x \right)+F_{58}\! \left(x , y\right)\\
F_{40}\! \left(x \right) &= -F_{57}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= -F_{49}\! \left(x \right)+F_{42}\! \left(x \right)\\
F_{42}\! \left(x \right) &= \frac{F_{43}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= -F_{48}\! \left(x \right)+F_{45}\! \left(x \right)\\
F_{45}\! \left(x \right) &= \frac{F_{46}\! \left(x \right)}{F_{4}\! \left(x \right)}\\
F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{29}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{28}\! \left(x , 1\right)\\
F_{49}\! \left(x \right) &= F_{50}\! \left(x \right)\\
F_{50}\! \left(x \right) &= F_{4}\! \left(x \right) F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= F_{52}\! \left(x , 1\right)\\
F_{52}\! \left(x , y\right) &= -\frac{-y F_{53}\! \left(x , y\right)+F_{53}\! \left(x , 1\right)}{-1+y}\\
F_{53}\! \left(x , y\right) &= F_{39}\! \left(x , y\right)+F_{54}\! \left(x , y\right)\\
F_{54}\! \left(x , y\right) &= F_{55}\! \left(x , y\right)\\
F_{55}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{56}\! \left(x , y\right)\\
F_{56}\! \left(x , y\right) &= -\frac{-y F_{53}\! \left(x , y\right)+F_{53}\! \left(x , 1\right)}{-1+y}\\
F_{57}\! \left(x \right) &= F_{58}\! \left(x , 1\right)\\
F_{58}\! \left(x , y\right) &= F_{59}\! \left(x , y\right)+F_{73}\! \left(x , y\right)\\
F_{59}\! \left(x , y\right) &= -\frac{y \left(F_{60}\! \left(x , 1\right)-F_{60}\! \left(x , y\right)\right)}{-1+y}\\
F_{60}\! \left(x , y\right) &= F_{61}\! \left(x , y\right)\\
F_{61}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{62}\! \left(x , y\right) F_{70}\! \left(x , y\right)\\
F_{63}\! \left(x , y\right) &= -\frac{-y F_{62}\! \left(x , y\right)+F_{62}\! \left(x , 1\right)}{-1+y}\\
F_{64}\! \left(x , y\right) &= F_{63}\! \left(x , y\right)+F_{66}\! \left(x , y\right)\\
F_{65}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{64}\! \left(x , y\right)\\
F_{65}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)\\
F_{67}\! \left(x , y\right) &= F_{66}\! \left(x , y\right)+F_{69}\! \left(x , y\right)\\
F_{68}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{67}\! \left(x , y\right)\\
F_{68}\! \left(x , y\right) &= F_{35}\! \left(x , y\right)\\
F_{69}\! \left(x , y\right) &= F_{38}\! \left(x , y\right)\\
F_{70}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{71}\! \left(x , y\right)\\
F_{71}\! \left(x , y\right) &= F_{72}\! \left(x , y\right)\\
F_{72}\! \left(x , y\right) &= F_{70}\! \left(x , y\right)^{2} F_{15}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= F_{44}\! \left(x \right)+F_{73}\! \left(x , y\right)\\
F_{74}\! \left(x , y\right) &= F_{75}\! \left(x , y\right)\\
F_{75}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{56}\! \left(x , y\right)\\
\end{align*}\)
This specification was found using the strategy pack "Col Placements Tracked Fusion" and has 38 rules.
Finding the specification took 15 seconds.
Copy 38 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_{4}\! \left(x \right)\\
F_{3}\! \left(x \right) &= x\\
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_{8}\! \left(x , y_{0}\right)\\
F_{6}\! \left(x , y_{0}\right) &= F_{3}\! \left(x \right) F_{7}\! \left(x , y_{0}\right)\\
F_{7}\! \left(x , y_{0}\right) &= -\frac{-F_{5}\! \left(x , y_{0}\right) y_{0}+F_{5}\! \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 , 1, y_{0}\right)\\
F_{11}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{12}\! \left(x , y_{0} y_{1}\right) y_{0}+F_{12}\! \left(x , y_{1}\right)}{-1+y_{0}}\\
F_{12}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}\right)+F_{36}\! \left(x , y_{0}\right)\\
F_{13}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)\\
F_{14}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}\right)+F_{30}\! \left(x , y_{0}\right)+F_{33}\! \left(x , y_{0}\right)\\
F_{15}\! \left(x , y_{0}\right) &= F_{16}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)\\
F_{16}\! \left(x , y_{0}\right) &= F_{17}\! \left(x , 1, y_{0}\right)\\
F_{17}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{18}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{18}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{18}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{19}\! \left(x , y_{0}, y_{1}\right)+F_{21}\! \left(x , y_{0}, y_{1}\right)+F_{25}\! \left(x , y_{1}, y_{0}\right)\\
F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)\\
F_{20}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{18}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{18}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{21}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{22}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{24}\! \left(x , y_{0} y_{1}, y_{2}\right) y_{0}+F_{24}\! \left(x , y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{24}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} F_{12}\! \left(x , y_{0}\right)-F_{12}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{25}\! \left(x , y_{0}, y_{1}\right) &= F_{26}\! \left(x , y_{0}, y_{1}\right)\\
F_{26}\! \left(x , y_{0}, y_{1}\right) &= F_{24}\! \left(x , y_{1}, y_{0}\right) F_{27}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{27}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{28}\! \left(x , y_{0}\right)\\
F_{28}\! \left(x , y_{0}\right) &= F_{29}\! \left(x , y_{0}\right)\\
F_{29}\! \left(x , y_{0}\right) &= F_{27}\! \left(x , y_{0}\right)^{2} F_{9}\! \left(x , y_{0}\right)\\
F_{30}\! \left(x , y_{0}\right) &= F_{3}\! \left(x \right) F_{31}\! \left(x , y_{0}\right)\\
F_{31}\! \left(x , y_{0}\right) &= F_{32}\! \left(x , 1, y_{0}\right)\\
F_{32}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{24}\! \left(x , y_{0}, y_{1}\right)+F_{24}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{33}\! \left(x , y_{0}\right) &= F_{34}\! \left(x , y_{0}\right)\\
F_{34}\! \left(x , y_{0}\right) &= F_{27}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
F_{35}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{12}\! \left(x , y_{0}\right)+F_{12}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{36}\! \left(x , y_{0}\right) &= F_{37}\! \left(x , y_{0}\right)\\
F_{37}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right) F_{27}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Tracked Fusion" and has 54 rules.
Finding the specification took 2398 seconds.
Copy 54 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_{5}\! \left(x \right)\\
F_{4}\! \left(x \right) &= x\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x , 1\right)\\
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_{45}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{49}\! \left(x , y\right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , 1, y\right)\\
F_{11}\! \left(x , y , z\right) &= -\frac{-F_{12}\! \left(x , y z \right) y +F_{12}\! \left(x , z\right)}{-1+y}\\
F_{12}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{13}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{42}\! \left(x , y\right) F_{45}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{12}\! \left(x , y\right)+F_{16}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{18}\! \left(x , y\right) &= -\frac{-F_{19}\! \left(x , y\right) y +F_{19}\! \left(x , 1\right)}{-1+y}\\
F_{19}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)+F_{20}\! \left(x , y\right)\\
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_{4}\! \left(x \right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)+F_{47}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{23}\! \left(x , y\right) F_{42}\! \left(x , y\right) F_{45}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)+F_{46}\! \left(x \right)\\
F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)+F_{28}\! \left(x , y\right)\\
F_{27}\! \left(x , y\right) &= -\frac{-F_{12}\! \left(x , y\right) y +F_{12}\! \left(x , 1\right)}{-1+y}\\
F_{28}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right) F_{4}\! \left(x \right)\\
F_{30}\! \left(x , y\right) &= F_{31}\! \left(x , 1, y\right)\\
F_{31}\! \left(x , y , z\right) &= -\frac{-F_{32}\! \left(x , y , z\right) y +F_{32}\! \left(x , 1, z\right)}{-1+y}\\
F_{32}\! \left(x , y , z\right) &= F_{33}\! \left(x , y , z\right)+F_{38}\! \left(x , y , z\right)\\
F_{33}\! \left(x , y , z\right) &= F_{34}\! \left(x , y , z\right)+F_{35}\! \left(x , y , z\right)\\
F_{34}\! \left(x , y , z\right) &= \frac{F_{12}\! \left(x , y\right) y -F_{12}\! \left(x , z\right) z}{-z +y}\\
F_{35}\! \left(x , y , z\right) &= F_{36}\! \left(x , y , z\right)\\
F_{36}\! \left(x , y , z\right) &= F_{37}\! \left(x , y , z\right) F_{4}\! \left(x \right)\\
F_{37}\! \left(x , y , z\right) &= -\frac{-F_{32}\! \left(x , y , z\right) y +F_{32}\! \left(x , 1, z\right)}{-1+y}\\
F_{38}\! \left(x , y , z\right) &= F_{39}\! \left(x , z , y\right)\\
F_{39}\! \left(x , y , z\right) &= F_{4}\! \left(x \right) F_{40}\! \left(x , z\right) F_{42}\! \left(x , y\right)\\
F_{41}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{40}\! \left(x , y\right)\\
F_{41}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)\\
F_{42}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{43}\! \left(x , y\right)\\
F_{43}\! \left(x , y\right) &= F_{44}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{42}\! \left(x , y\right)^{2} F_{45}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= y x\\
F_{46}\! \left(x \right) &= F_{15}\! \left(x , 1\right)\\
F_{47}\! \left(x , y\right) &= F_{48}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= F_{38}\! \left(x , 1, y\right)\\
F_{49}\! \left(x , y\right) &= F_{50}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{4}\! \left(x \right) F_{51}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= F_{52}\! \left(x , 1, y\right)\\
F_{52}\! \left(x , y , z\right) &= -\frac{z F_{53}\! \left(x , 1, z\right)-y F_{53}\! \left(x , \frac{y}{z}, z\right)}{-z +y}\\
F_{53}\! \left(x , y , z\right) &= F_{32}\! \left(x , y z , z\right)\\
\end{align*}\)