Av(12354, 21354, 23154, 23514)
Counting Sequence
1, 1, 2, 6, 24, 116, 634, 3766, 23741, 156468, 1067369, 7483996, 53664321, 392040003, 2909452383, ...
This specification was found using the strategy pack "Row Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 103 rules.
Finding the specification took 4552 seconds.
This tree is too big to show here. Click to view tree on new page.
Copy 103 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_{11}\! \left(x \right) F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{88}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{11}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x \right)+F_{85}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x , 1\right)\\
F_{7}\! \left(x , y_{0}\right) &= F_{11}\! \left(x \right) F_{8}\! \left(x , y_{0}\right)\\
F_{8}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y_{0}\right)+F_{79}\! \left(x , y_{0}\right)+F_{81}\! \left(x , y_{0}\right)+F_{9}\! \left(x , y_{0}\right)\\
F_{9}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{11}\! \left(x \right)\\
F_{10}\! \left(x , y_{0}\right) &= -\frac{-F_{8}\! \left(x , y_{0}\right) y_{0}+F_{8}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{11}\! \left(x \right) &= x\\
F_{12}\! \left(x , y_{0}\right) &= F_{11}\! \left(x \right) F_{13}\! \left(x , y_{0}\right)\\
F_{13}\! \left(x , y_{0}\right) &= -\frac{-F_{14}\! \left(x , y_{0}\right) y_{0}+F_{14}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{14}\! \left(x , y_{0}\right) &= F_{15}\! \left(x , 1, y_{0}\right)\\
F_{15}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{16}\! \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_{74}\! \left(x , y_{1}\right)\\
F_{16}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x \right) F_{17}\! \left(x , y_{0}, y_{1}\right)\\
F_{17}\! \left(x , y_{0}, y_{1}\right) &= F_{18}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{19}\! \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}, y_{1}, y_{2}\right)+F_{35}\! \left(x , y_{0}, y_{2}\right)+F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{19}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{11}\! \left(x \right) F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{20}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{18}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{18}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{21}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{11}\! \left(x \right) F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{22}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{23}\! \left(x , y_{0}, y_{2}\right) y_{0}-F_{23}\! \left(x , y_{1}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{23}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{14}\! \left(x , y_{0}\right) y_{0}-F_{14}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{24}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) F_{34}\! \left(x , y_{0}\right)\\
F_{25}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{26}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{26}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{26}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{27}\! \left(x , y_{0}, y_{1}\right) y_{0} y_{1}-F_{27}\! \left(x , y_{0}, \frac{y_{2}}{y_{0}}\right) y_{2}}{y_{0} y_{1}-y_{2}}\\
F_{27}\! \left(x , y_{0}, y_{1}\right) &= F_{28}\! \left(x , y_{0}, y_{0} 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_{31}\! \left(x , y_{0}, y_{1}\right)+F_{32}\! \left(x , y_{0}, y_{1}\right)+F_{35}\! \left(x , y_{0}, y_{1}\right)\\
F_{29}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x \right) F_{30}\! \left(x , y_{0}, y_{1}\right)\\
F_{30}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{28}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{28}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{31}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x \right) F_{23}\! \left(x , y_{0}, y_{1}\right)\\
F_{32}\! \left(x , y_{0}, y_{1}\right) &= F_{33}\! \left(x , y_{0}, y_{1}\right) F_{34}\! \left(x , y_{0}\right)\\
F_{33}\! \left(x , y_{0}, y_{1}\right) &= \frac{F_{27}\! \left(x , y_{0}, 1\right) y_{0}-F_{27}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{34}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{35}\! \left(x , y_{0}, y_{1}\right) &= F_{28}\! \left(x , y_{0}, y_{1}\right) F_{34}\! \left(x , y_{1}\right)\\
F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{34}\! \left(x , y_{1}\right) F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{35}\! \left(x , y_{0}, y_{2}\right)+F_{36}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{38}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{11}\! \left(x \right) F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{39}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{37}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{37}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{40}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{41}\! \left(x , y_{0}, y_{1}, 1, y_{2}\right)\\
F_{41}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{42}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}, y_{3}\right)\\
F_{42}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{11}\! \left(x \right) F_{43}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)\\
F_{43}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= \frac{F_{22}\! \left(x , y_{0}, y_{2}, y_{3}\right) y_{0}-F_{22}\! \left(x , y_{1}, y_{2}, y_{3}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{44}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{45}\! \left(x , y_{0}, y_{1}, 1, y_{2}\right)\\
F_{45}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{46}\! \left(x , y_{0}, y_{1}, y_{1} y_{2}, y_{3}\right)\\
F_{46}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{34}\! \left(x , y_{0}\right) F_{47}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)\\
F_{47}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= \frac{F_{25}\! \left(x , y_{0}, y_{1}, y_{3}\right) y_{1}-F_{25}\! \left(x , y_{0}, y_{2}, y_{3}\right) y_{2}}{-y_{2}+y_{1}}\\
F_{48}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{34}\! \left(x , y_{1}\right) F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{49}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{50}\! \left(x , y_{0}, y_{1}, 1, y_{2}\right)\\
F_{50}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= -\frac{-F_{51}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) y_{2}+F_{51}\! \left(x , y_{0}, y_{1}, 1, y_{3}\right)}{-1+y_{2}}\\
F_{51}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{1}\! \left(x \right)+F_{35}\! \left(x , y_{0}, y_{3}\right)+F_{41}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{45}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{52}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{54}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)+F_{56}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)\\
F_{52}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{11}\! \left(x \right) F_{53}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)\\
F_{53}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= -\frac{-F_{51}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) y_{0}+F_{51}\! \left(x , 1, y_{1}, y_{2}, y_{3}\right)}{-1+y_{0}}\\
F_{54}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{34}\! \left(x , y_{1}\right) F_{55}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)\\
F_{55}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= -\frac{-F_{51}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) y_{2}+F_{51}\! \left(x , y_{0}, y_{1}, 1, y_{3}\right)}{-1+y_{2}}\\
F_{56}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right) &= F_{34}\! \left(x , y_{2}\right) F_{51}\! \left(x , y_{0}, y_{1}, y_{2}, y_{3}\right)\\
F_{57}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x \right) F_{58}\! \left(x , y_{0}, y_{1}\right)\\
F_{58}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{15}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{15}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{59}\! \left(x , y_{0}, y_{1}\right) &= F_{34}\! \left(x , y_{0}\right) F_{60}\! \left(x , y_{0}, y_{1}\right)\\
F_{60}\! \left(x , y_{0}, y_{1}\right) &= F_{61}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{61}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{62}\! \left(x , y_{0} y_{1}, y_{1}, y_{2}\right)\\
F_{63}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{62}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)\\
F_{63}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{1}\! \left(x \right)+F_{64}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{69}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{72}\! \left(x , y_{0}, y_{1}, y_{2}\right)+F_{74}\! \left(x , y_{2}\right)\\
F_{64}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{11}\! \left(x \right) F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{65}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{51}\! \left(x , 1, y_{0}, y_{1}, y_{2}\right)\\
F_{66}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{67}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)\\
F_{67}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{11}\! \left(x \right) F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{68}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{62}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{0}+F_{62}\! \left(x , 1, y_{1}, y_{2}\right)}{-1+y_{0}}\\
F_{69}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{70}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)\\
F_{70}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{34}\! \left(x , y_{0}\right) F_{71}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{71}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= \frac{F_{63}\! \left(x , y_{0}, 1, y_{2}\right) y_{0}-F_{63}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}, y_{2}\right) y_{1}}{-y_{1}+y_{0}}\\
F_{72}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{73}\! \left(x , y_{0}, y_{0} y_{1}, y_{2}\right)\\
F_{73}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{34}\! \left(x , y_{1}\right) F_{62}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{74}\! \left(x , y_{0}\right) &= F_{34}\! \left(x , y_{0}\right) F_{75}\! \left(x , y_{0}\right)\\
F_{75}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{74}\! \left(x , y_{0}\right)+F_{76}\! \left(x , y_{0}\right)+F_{78}\! \left(x , y_{0}\right)\\
F_{76}\! \left(x , y_{0}\right) &= F_{11}\! \left(x \right) F_{77}\! \left(x , y_{0}\right)\\
F_{77}\! \left(x , y_{0}\right) &= F_{28}\! \left(x , 1, y_{0}\right)\\
F_{78}\! \left(x , y_{0}\right) &= F_{11}\! \left(x \right) F_{14}\! \left(x , y_{0}\right)\\
F_{79}\! \left(x , y_{0}\right) &= F_{11}\! \left(x \right) F_{80}\! \left(x , y_{0}\right)\\
F_{80}\! \left(x , y_{0}\right) &= -\frac{-F_{77}\! \left(x , y_{0}\right) y_{0}+F_{77}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{81}\! \left(x , y_{0}\right) &= F_{34}\! \left(x , y_{0}\right) F_{82}\! \left(x , y_{0}\right)\\
F_{82}\! \left(x , y_{0}\right) &= F_{83}\! \left(x , 1, y_{0}\right)\\
F_{83}\! \left(x , y_{0}, y_{1}\right) &= -\frac{F_{84}\! \left(x , 1, y_{1}\right) y_{1}-F_{84}\! \left(x , \frac{y_{0}}{y_{1}}, y_{1}\right) y_{0}}{-y_{1}+y_{0}}\\
F_{84}\! \left(x , y_{0}, y_{1}\right) &= F_{28}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{85}\! \left(x \right) &= F_{78}\! \left(x , 1\right)\\
F_{86}\! \left(x \right) &= F_{11}\! \left(x \right) F_{87}\! \left(x \right)\\
F_{87}\! \left(x \right) &= F_{77}\! \left(x , 1\right)\\
F_{88}\! \left(x \right) &= F_{11}\! \left(x \right) F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x , 1\right)\\
F_{90}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{7}\! \left(x , y_{0}\right)+F_{91}\! \left(x , y_{0}\right)+F_{93}\! \left(x , y_{0}\right)\\
F_{91}\! \left(x , y_{0}\right) &= F_{11}\! \left(x \right) F_{92}\! \left(x , y_{0}\right)\\
F_{92}\! \left(x , y_{0}\right) &= -\frac{-F_{90}\! \left(x , y_{0}\right) y_{0}+F_{90}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{93}\! \left(x , y_{0}\right) &= F_{34}\! \left(x , y_{0}\right) F_{94}\! \left(x , y_{0}\right)\\
F_{94}\! \left(x , y_{0}\right) &= F_{95}\! \left(x , 1, y_{0}\right)\\
F_{95}\! \left(x , y_{0}, y_{1}\right) &= F_{96}\! \left(x , y_{0} y_{1}, y_{1}\right)\\
F_{96}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{102}\! \left(x , y_{0}, y_{1}\right)+F_{29}\! \left(x , y_{0}, y_{1}\right)+F_{97}\! \left(x , y_{0}, y_{1}\right)+F_{99}\! \left(x , y_{0}, y_{1}\right)\\
F_{97}\! \left(x , y_{0}, y_{1}\right) &= F_{11}\! \left(x \right) F_{98}\! \left(x , y_{0}, y_{1}\right)\\
F_{98}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{96}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{96}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{99}\! \left(x , y_{0}, y_{1}\right) &= F_{100}\! \left(x , y_{0}, y_{1}\right) F_{34}\! \left(x , y_{0}\right)\\
F_{100}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} F_{101}\! \left(x , y_{0}, 1\right)-y_{1} F_{101}\! \left(x , y_{0}, \frac{y_{1}}{y_{0}}\right)}{-y_{1}+y_{0}}\\
F_{101}\! \left(x , y_{0}, y_{1}\right) &= F_{96}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{102}\! \left(x , y_{0}, y_{1}\right) &= F_{34}\! \left(x , y_{1}\right) F_{96}\! \left(x , y_{0}, y_{1}\right)\\
\end{align*}\)