Av(2143)
Counting Sequence
1, 1, 2, 6, 23, 103, 513, 2761, 15767, 94359, 586590, 3763290, 24792705, 167078577, 1148208090, ...
This specification was found using the strategy pack "Requirement Placements Tracked Fusion Symmetries Expand Verified Short Obs 3" and has 105 rules.
Found on February 11, 2022.Finding the specification took 90918 seconds.
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\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{1}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{3}\! \left(x \right)\\
F_{2}\! \left(x \right) &= 1\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{1}\! \left(x \right) F_{5}\! \left(x \right)\\
F_{5}\! \left(x \right) &= x\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{5}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x , 1\right)\\
F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right)\\
F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{24}\! \left(x , y\right)\\
F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)+F_{90}\! \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_{21}\! \left(x , y\right)\\
F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)+F_{89}\! \left(x , y\right)\\
F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)+F_{30}\! \left(x , y\right)\\
F_{17}\! \left(x , y\right) &= F_{18}\! \left(x \right)+F_{28}\! \left(x , y\right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right)\\
F_{19}\! \left(x \right) &= F_{20}\! \left(x , 1\right)\\
F_{20}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)+F_{25}\! \left(x , y\right)\\
F_{21}\! \left(x , y\right) &= F_{2}\! \left(x \right)+F_{22}\! \left(x , y\right)\\
F_{22}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)\\
F_{23}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{24}\! \left(x , y\right)\\
F_{24}\! \left(x , y\right) &= y x\\
F_{25}\! \left(x , y\right) &= F_{26}\! \left(x , y\right)\\
F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{27}\! \left(x , y\right) &= F_{10}\! \left(x , y\right)+F_{16}\! \left(x , y\right)\\
F_{28}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)\\
F_{29}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{24}\! \left(x , y\right)\\
F_{30}\! \left(x , y\right) &= F_{31}\! \left(x , y\right)\\
F_{31}\! \left(x , y\right) &= F_{32}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{32}\! \left(x , y\right) &= F_{33}\! \left(x , y\right)\\
F_{33}\! \left(x , y\right) &= F_{34}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{34}\! \left(x , y\right) &= F_{35}\! \left(x , y , 1\right)\\
F_{35}\! \left(x , y , z\right) &= F_{36}\! \left(x , y , z\right)+F_{86}\! \left(x , y , z\right)\\
F_{37}\! \left(x , y , z\right) &= F_{24}\! \left(x , y\right) F_{36}\! \left(x , y , z\right)\\
F_{37}\! \left(x , y , z\right) &= F_{38}\! \left(x , y , z\right)\\
F_{38}\! \left(x , y , z\right) &= \frac{y \left(F_{39}\! \left(x , y\right)-F_{39}\! \left(x , z\right)\right)}{-z +y}\\
F_{39}\! \left(x , y\right) &= F_{40}\! \left(x , y\right)\\
F_{40}\! \left(x , y\right) &= F_{41}\! \left(x , 1, y\right)\\
F_{41}\! \left(x , y , z\right) &= F_{42}\! \left(x , y , z\right)\\
F_{42}\! \left(x , y , z\right) &= F_{24}\! \left(x , z\right) F_{43}\! \left(x , y , z\right)\\
F_{43}\! \left(x , y , z\right) &= F_{44}\! \left(x , y , z\right)+F_{66}\! \left(x , y , z\right)\\
F_{44}\! \left(x , y , z\right) &= F_{45}\! \left(x , y , z\right)+F_{58}\! \left(x , y , z\right)\\
F_{45}\! \left(x , y , z\right) &= F_{46}\! \left(x , y\right)+F_{52}\! \left(x , y , z\right)\\
F_{47}\! \left(x , y\right) &= F_{46}\! \left(x , y\right)+F_{51}\! \left(x , y\right)\\
F_{47}\! \left(x , y\right) &= F_{48}\! \left(x , y\right)+F_{49}\! \left(x , y\right)\\
F_{48}\! \left(x , y\right) &= F_{1}\! \left(x \right) F_{17}\! \left(x , y\right)\\
F_{49}\! \left(x , y\right) &= F_{50}\! \left(x , y\right)\\
F_{50}\! \left(x , y\right) &= F_{1}\! \left(x \right) F_{34}\! \left(x , y\right) F_{5}\! \left(x \right)\\
F_{51}\! \left(x , y\right) &= F_{52}\! \left(x , y , 1\right)\\
F_{52}\! \left(x , y , z\right) &= F_{53}\! \left(x , y , z\right)\\
F_{53}\! \left(x , y , z\right) &= F_{24}\! \left(x , z\right) F_{54}\! \left(x , y , z\right)\\
F_{54}\! \left(x , y , z\right) &= F_{55}\! \left(x , z , y\right)\\
F_{56}\! \left(x , y , z\right) &= F_{24}\! \left(x , z\right) F_{55}\! \left(x , y , z\right)\\
F_{56}\! \left(x , y , z\right) &= F_{57}\! \left(x , y , z\right)\\
F_{57}\! \left(x , y , z\right) &= -\frac{z \left(F_{41}\! \left(x , y , 1\right)-F_{41}\! \left(x , y , z\right)\right)}{-1+z}\\
F_{58}\! \left(x , y , z\right) &= F_{59}\! \left(x , z , y\right)\\
F_{45}\! \left(x , y , z\right) &= F_{59}\! \left(x , y , z\right)+F_{60}\! \left(x , y , z\right)\\
F_{60}\! \left(x , y , z\right) &= F_{1}\! \left(x \right) F_{61}\! \left(x , y , z\right)\\
F_{61}\! \left(x , y , z\right) &= F_{62}\! \left(x , z\right)+F_{63}\! \left(x , y , z\right)\\
F_{62}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)\\
F_{63}\! \left(x , y , z\right) &= F_{64}\! \left(x , y , z\right)\\
F_{64}\! \left(x , y , z\right) &= F_{24}\! \left(x , y\right) F_{65}\! \left(x , y , z\right)\\
F_{65}\! \left(x , y , z\right) &= F_{16}\! \left(x , y\right)+F_{41}\! \left(x , y , z\right)\\
F_{66}\! \left(x , y , z\right) &= F_{67}\! \left(x , y , z\right)\\
F_{67}\! \left(x , y , z\right) &= F_{5}\! \left(x \right) F_{68}\! \left(x , y , z\right)\\
F_{68}\! \left(x , y , z\right) &= F_{69}\! \left(x , z , y\right)\\
F_{70}\! \left(x , y , z\right) &= F_{1}\! \left(x \right) F_{5}\! \left(x \right) F_{69}\! \left(x , y , z\right)\\
F_{70}\! \left(x , y , z\right) &= F_{71}\! \left(x , y , z\right)\\
F_{71}\! \left(x , y , z\right) &= F_{72}\! \left(x , y , z\right)\\
F_{72}\! \left(x , y , z\right) &= F_{5}\! \left(x \right) F_{73}\! \left(x , y , z\right)\\
F_{73}\! \left(x , y , z\right) &= F_{71}\! \left(x , y , z\right)+F_{74}\! \left(x , y , z\right)\\
F_{74}\! \left(x , y , z\right) &= F_{75}\! \left(x , z , y\right)\\
F_{75}\! \left(x , y , z\right) &= -\frac{F_{76}\! \left(x , 1, z\right)-F_{76}\! \left(x , y , z\right)}{-1+y}\\
F_{76}\! \left(x , y , z\right) &= F_{77}\! \left(x , z , y\right)\\
F_{78}\! \left(x , y , z\right) &= F_{21}\! \left(x , z\right) F_{5}\! \left(x \right) F_{77}\! \left(x , y , z\right)\\
F_{78}\! \left(x , y , z\right) &= F_{79}\! \left(x , y , z\right)\\
F_{79}\! \left(x , y , z\right) &= F_{80}\! \left(x , y , z\right)\\
F_{80}\! \left(x , y , z\right) &= F_{24}\! \left(x , z\right) F_{81}\! \left(x , y , z\right)\\
F_{81}\! \left(x , y , z\right) &= F_{79}\! \left(x , y , z\right)+F_{82}\! \left(x , y , z\right)\\
F_{82}\! \left(x , y , z\right) &= F_{83}\! \left(x , z , y\right)\\
F_{55}\! \left(x , y , z\right) &= F_{83}\! \left(x , y , z\right)+F_{84}\! \left(x , y , z\right)\\
F_{84}\! \left(x , y , z\right) &= F_{58}\! \left(x , y , z\right)+F_{85}\! \left(x , y , z\right)\\
F_{85}\! \left(x , y , z\right) &= F_{1}\! \left(x \right) F_{65}\! \left(x , y , z\right)\\
F_{86}\! \left(x , y , z\right) &= F_{87}\! \left(x , y , z\right)\\
F_{87}\! \left(x , y , z\right) &= F_{5}\! \left(x \right) F_{88}\! \left(x , y , z\right)\\
F_{88}\! \left(x , y , z\right) &= -\frac{-z F_{35}\! \left(x , y , z\right)+F_{35}\! \left(x , y , 1\right)}{-1+z}\\
F_{89}\! \left(x , y\right) &= F_{41}\! \left(x , y , 1\right)\\
F_{90}\! \left(x , y\right) &= F_{91}\! \left(x , y\right)\\
F_{91}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{92}\! \left(x , y\right)\\
F_{92}\! \left(x , y\right) &= F_{93}\! \left(x , y\right)+F_{97}\! \left(x , y\right)\\
F_{93}\! \left(x , y\right) &= F_{94}\! \left(x , y\right)\\
F_{94}\! \left(x , y\right) &= F_{21}\! \left(x , y\right) F_{95}\! \left(x , y\right)\\
F_{95}\! \left(x , y\right) &= F_{96}\! \left(x , y , 1\right)\\
F_{96}\! \left(x , y , z\right) &= -\frac{z \left(F_{41}\! \left(x , y , 1\right)-F_{41}\! \left(x , y , z\right)\right)}{-1+z}\\
F_{97}\! \left(x , y\right) &= F_{98}\! \left(x , y , 1\right)\\
F_{98}\! \left(x , y , z\right) &= F_{99}\! \left(x , y , z\right)\\
F_{99}\! \left(x , y , z\right) &= F_{100}\! \left(x , y , z\right) F_{24}\! \left(x , y\right)\\
F_{100}\! \left(x , y , z\right) &= F_{101}\! \left(x , y , z\right)+F_{104}\! \left(x , y , z\right)\\
F_{101}\! \left(x , y , z\right) &= F_{102}\! \left(x , y , z\right)\\
F_{102}\! \left(x , y , z\right) &= F_{103}\! \left(x , y , z\right) F_{21}\! \left(x , y\right)\\
F_{103}\! \left(x , y , z\right) &= -\frac{F_{96}\! \left(x , y , 1\right)-F_{96}\! \left(x , y , z\right)}{-1+z}\\
F_{104}\! \left(x , y , z\right) &= -\frac{-z F_{98}\! \left(x , y , z\right)+F_{98}\! \left(x , y , 1\right)}{-1+z}\\
\end{align*}\)