Av(13425, 13452, 14325, 14352, 14532)
Counting Sequence
1, 1, 2, 6, 24, 115, 614, 3510, 21011, 129960, 823630, 5318320, 34853269, 231165135, 1548495034, ...
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 88 rules.
Finding the specification took 48023 seconds.
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Copy 88 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_{37}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{6}\! \left(x , 1\right)\\
F_{6}\! \left(x , y\right) &= F_{7}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\
F_{7}\! \left(x , y\right) &= x F_{7}\! \left(x , y\right) y +y x +F_{7}\! \left(x , y\right)^{2}\\
F_{8}\! \left(x , y\right) &= F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{37}\! \left(x \right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)+F_{12}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}\\
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_{24}\! \left(x , y\right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y , 1\right)\\
F_{15}\! \left(x , y , z\right) &= F_{16}\! \left(x , y , y z \right)\\
F_{16}\! \left(x , y , z\right) &= F_{17}\! \left(x , y , z\right)+F_{81}\! \left(x , y , z\right)\\
F_{17}\! \left(x , y , z\right) &= F_{18}\! \left(x , y\right) F_{19}\! \left(x , y , z\right)\\
F_{18}\! \left(x , y\right) &= x F_{18}\! \left(x , y\right) y +F_{18}\! \left(x , y\right)^{2}-2 F_{18}\! \left(x , y\right)+2\\
F_{19}\! \left(x , y , z\right) &= -\frac{-F_{20}\! \left(x , y , z\right) z +F_{20}\! \left(x , y , 1\right)}{-1+z}\\
F_{20}\! \left(x , y , z\right) &= F_{21}\! \left(x , y , z\right)+F_{75}\! \left(x , y , z\right)\\
F_{21}\! \left(x , y , z\right) &= F_{18}\! \left(x , z\right)+F_{22}\! \left(x , y , z\right)\\
F_{22}\! \left(x , y , z\right) &= F_{23}\! \left(x , y , z\right)\\
F_{23}\! \left(x , y , z\right) &= F_{24}\! \left(x , y\right) F_{25}\! \left(x , y , z\right)\\
F_{24}\! \left(x , y\right) &= y x\\
F_{26}\! \left(x , y , z\right) &= F_{25}\! \left(x , y , z\right) F_{56}\! \left(x \right)\\
F_{27}\! \left(x , y , z\right) &= F_{26}\! \left(x , y z , z\right)\\
F_{27}\! \left(x , y , z\right) &= F_{28}\! \left(x , y , z\right) F_{56}\! \left(x \right)\\
F_{28}\! \left(x , y , z\right) &= F_{29}\! \left(z x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)+F_{41}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{31}\! \left(x , y\right) F_{38}\! \left(x \right)\\
F_{31}\! \left(x , y\right) &= F_{32}\! \left(y x \right)\\
F_{32}\! \left(x \right) &= F_{33}\! \left(x \right)+F_{34}\! \left(x \right)\\
F_{33}\! \left(x \right) &= F_{33}\! \left(x \right) x +F_{33} \left(x \right)^{2}-2 F_{33}\! \left(x \right)+2\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{36}\! \left(x \right) F_{37}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{29}\! \left(x , 1\right)\\
F_{37}\! \left(x \right) &= x\\
F_{38}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= F_{37}\! \left(x \right) F_{38}\! \left(x \right)\\
F_{41}\! \left(x , y\right) &= F_{42}\! \left(x , y\right)\\
F_{42}\! \left(x , y\right) &= F_{31}\! \left(x , y\right) F_{37}\! \left(x \right) F_{43}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{18}\! \left(x , y\right) F_{37}\! \left(x \right) F_{43}\! \left(x , y\right)\\
F_{44}\! \left(x , y\right) &= F_{45}\! \left(x , y\right)\\
F_{45}\! \left(x , y\right) &= F_{46}\! \left(x , y\right)+F_{48}\! \left(x , y\right)\\
F_{46}\! \left(x , y\right) &= F_{47}\! \left(x , y , 1\right)\\
F_{21}\! \left(x , y , z\right) &= F_{18}\! \left(x , y\right)+F_{47}\! \left(x , y , z\right)\\
F_{48}\! \left(x , y\right) &= F_{49}\! \left(x , y\right)\\
F_{49}\! \left(x , y\right) &= F_{37}\! \left(x \right) F_{50}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{51}\! \left(x , y\right)+F_{52}\! \left(x , y\right)\\
F_{51}\! \left(x , y\right) &= F_{38}\! \left(x \right) F_{46}\! \left(x , y\right)\\
F_{52}\! \left(x , y\right) &= F_{53}\! \left(x , y\right)\\
F_{53}\! \left(x , y\right) &= F_{37}\! \left(x \right) F_{54}\! \left(x , y\right) F_{55}\! \left(x \right)\\
F_{54}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)+F_{46}\! \left(x , y\right)\\
F_{55}\! \left(x \right) &= F_{43}\! \left(x , 1\right)\\
F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{74}\! \left(x \right)\\
F_{57}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= F_{37}\! \left(x \right) F_{60}\! \left(x \right)\\
F_{60}\! \left(x \right) &= F_{57}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)+F_{64}\! \left(x \right)+F_{67}\! \left(x \right)\\
F_{63}\! \left(x \right) &= 0\\
F_{64}\! \left(x \right) &= F_{37}\! \left(x \right) F_{65}\! \left(x \right)\\
F_{65}\! \left(x \right) &= F_{66}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{62}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{37}\! \left(x \right) F_{68}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{70}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{63}\! \left(x \right)+F_{67}\! \left(x \right)+F_{72}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{37}\! \left(x \right) F_{73}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{58}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{39}\! \left(x \right)+F_{71}\! \left(x \right)\\
F_{75}\! \left(x , y , z\right) &= F_{76}\! \left(x , y , z\right)\\
F_{76}\! \left(x , y , z\right) &= F_{37}\! \left(x \right) F_{77}\! \left(x , y , z\right)\\
F_{77}\! \left(x , y , z\right) &= F_{78}\! \left(x , y , z\right)+F_{81}\! \left(x , y , z\right)\\
F_{78}\! \left(x , y , z\right) &= F_{18}\! \left(x , y\right) F_{79}\! \left(x , z\right)\\
F_{79}\! \left(x , y\right) &= -\frac{-F_{80}\! \left(x , y\right) y +F_{80}\! \left(x , 1\right)}{-1+y}\\
F_{80}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{6}\! \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_{24}\! \left(x , z\right) F_{83}\! \left(x , y , z\right) F_{85}\! \left(x , z\right)\\
F_{84}\! \left(x , y , z\right) &= F_{24}\! \left(x , z\right) F_{83}\! \left(x , y , z\right)\\
F_{84}\! \left(x , y , z\right) &= F_{47}\! \left(x , y , z\right)\\
F_{85}\! \left(x , y\right) &= F_{86}\! \left(x , y , 1\right)\\
F_{86}\! \left(x , y , z\right) &= \frac{y z F_{87}\! \left(x , y , z\right)-F_{87}\! \left(x , y , \frac{1}{y}\right)}{y z -1}\\
F_{87}\! \left(x , y , z\right) &= F_{20}\! \left(x , y , y z \right)\\
\end{align*}\)
This specification was found using the strategy pack "Point And Row Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 59 rules.
Finding the specification took 42043 seconds.
Copy 59 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_{47}\! \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_{58}\! \left(x , y\right)+F_{7}\! \left(x \right)+F_{8}\! \left(x , y\right)\\
F_{7}\! \left(x \right) &= 0\\
F_{8}\! \left(x , y\right) &= F_{34}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\
F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y , 1\right)\\
F_{10}\! \left(x , y , z\right) &= F_{11}\! \left(x , y , z\right)+F_{57}\! \left(x , y , z\right)\\
F_{11}\! \left(x , y , z\right) &= F_{12}\! \left(y x , z\right)\\
F_{12}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{55}\! \left(x , y\right)\\
F_{13}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{47}\! \left(x \right)\\
F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , 1, y\right)\\
F_{15}\! \left(x , y , z\right) &= F_{12}\! \left(x , y\right)+F_{16}\! \left(x , y , z\right)\\
F_{16}\! \left(x , y , z\right) &= F_{17}\! \left(x , y , z\right)\\
F_{17}\! \left(x , y , z\right) &= F_{12}\! \left(x , y\right) F_{18}\! \left(x , y , z\right) F_{34}\! \left(x , z\right)\\
F_{18}\! \left(x , y , z\right) &= F_{19}\! \left(x , y , y z \right)\\
F_{20}\! \left(x , y , z\right) &= F_{19}\! \left(x , y , z\right) F_{34}\! \left(x , z\right)\\
F_{21}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{20}\! \left(x , y , z\right)+F_{53}\! \left(x , y , z\right)\\
F_{22}\! \left(x , y , z\right) &= F_{21}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)\\
F_{10}\! \left(x , y , z\right) &= F_{22}\! \left(x , y , y z \right)\\
F_{23}\! \left(x , y , z\right) &= F_{24}\! \left(x , y\right)+F_{48}\! \left(x , y , z\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_{27}\! \left(x , y\right) F_{47}\! \left(x \right)\\
F_{26}\! \left(x , y\right) &= x F_{26}\! \left(x , y\right) y +F_{26}\! \left(x , y\right)^{2}-2 F_{26}\! \left(x , y\right)+2\\
F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y , 1\right)\\
F_{28}\! \left(x , y , z\right) &= F_{29}\! \left(x , y\right)+F_{31}\! \left(x , y , z\right)\\
F_{29}\! \left(x , y\right) &= F_{30}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{26}\! \left(x , y\right)\\
F_{31}\! \left(x , y , z\right) &= F_{32}\! \left(x , y , z\right)+F_{35}\! \left(x , y , z\right)\\
F_{32}\! \left(x , y , z\right) &= F_{33}\! \left(x , y , z\right)\\
F_{33}\! \left(x , y , z\right) &= F_{19}\! \left(x , y , z\right) F_{26}\! \left(x , y\right) F_{34}\! \left(x , z\right)\\
F_{34}\! \left(x , y\right) &= y x\\
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_{47}\! \left(x \right)\\
F_{37}\! \left(x , y , z\right) &= F_{38}\! \left(x , y , z\right)+F_{40}\! \left(x , y , z\right)\\
F_{38}\! \left(x , y , z\right) &= F_{26}\! \left(x , y\right) F_{39}\! \left(x , z\right)\\
F_{39}\! \left(x , y\right) &= -\frac{y \left(F_{6}\! \left(x , 1\right)-F_{6}\! \left(x , y\right)\right)}{-1+y}\\
F_{40}\! \left(x , y , z\right) &= F_{41}\! \left(x , y , z\right)\\
F_{41}\! \left(x , y , z\right) &= F_{34}\! \left(x , z\right) F_{42}\! \left(x , y , z\right) F_{44}\! \left(x , z\right)\\
F_{43}\! \left(x , y , z\right) &= F_{34}\! \left(x , z\right) F_{42}\! \left(x , y , z\right)\\
F_{43}\! \left(x , y , z\right) &= F_{32}\! \left(x , y , z\right)\\
F_{44}\! \left(x , y\right) &= F_{45}\! \left(x , y , 1\right)\\
F_{45}\! \left(x , y , z\right) &= F_{46}\! \left(x , y , y z \right)\\
F_{46}\! \left(x , y , z\right) &= -\frac{-z F_{28}\! \left(x , y , z\right)+F_{28}\! \left(x , y , 1\right)}{-1+z}\\
F_{47}\! \left(x \right) &= x\\
F_{48}\! \left(x , y , z\right) &= F_{49}\! \left(x , y , z\right)\\
F_{49}\! \left(x , y , z\right) &= F_{47}\! \left(x \right) F_{50}\! \left(x , y , z\right)\\
F_{50}\! \left(x , y , z\right) &= F_{40}\! \left(x , y , z\right)+F_{51}\! \left(x , y , z\right)\\
F_{51}\! \left(x , y , z\right) &= F_{26}\! \left(x , y\right) F_{52}\! \left(x , y , z\right)\\
F_{52}\! \left(x , y , z\right) &= -\frac{z \left(F_{31}\! \left(x , y , 1\right)-F_{31}\! \left(x , y , z\right)\right)}{-1+z}\\
F_{54}\! \left(x , y , z\right) &= F_{53}\! \left(x , y , y z \right)\\
F_{54}\! \left(x , y , z\right) &= F_{13}\! \left(y x , z\right)\\
F_{55}\! \left(x , y\right) &= F_{34}\! \left(x , y\right) F_{56}\! \left(x , y\right)\\
F_{56}\! \left(x , y\right) &= F_{15}\! \left(x , y , 1\right)\\
F_{57}\! \left(x , y , z\right) &= F_{23}\! \left(x , y , y z \right)\\
F_{58}\! \left(x , y\right) &= F_{39}\! \left(x , y\right) F_{47}\! \left(x \right)\\
\end{align*}\)