Av(13254, 13524, 31254, 31524, 35124)
Counting Sequence
1, 1, 2, 6, 24, 115, 614, 3509, 21006, 130090, 826970, 5367586, 35437376, 237304847, 1608306876, ...
This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Req Corrob Symmetries" and has 128 rules.
Finding the specification took 45054 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_{24}\! \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_{2}\! \left(x \right)+F_{6}\! \left(x \right)\\
F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\
F_{7}\! \left(x \right) &= F_{24}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{2}\! \left(x \right) F_{4}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{117}\! \left(x \right) F_{12}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x , 1\right)\\
F_{14}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right)\\
F_{14}\! \left(x , y_{0}\right) &= F_{15}\! \left(x , y_{0}\right)\\
F_{15}\! \left(x , y_{0}\right) &= F_{16}\! \left(x , y_{0}\right)+F_{26}\! \left(x , y_{0}\right)\\
F_{16}\! \left(x , y_{0}\right) &= F_{17}\! \left(x , y_{0}\right)\\
F_{17}\! \left(x , y_{0}\right) &= F_{18}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right)\\
F_{18}\! \left(x , y_{0}\right) &= F_{19}\! \left(x , y_{0}\right)+F_{22}\! \left(x , y_{0}\right)\\
F_{19}\! \left(x , y_{0}\right) &= F_{20}\! \left(x , y_{0}\right)+F_{21}\! \left(x , y_{0}\right)\\
F_{20}\! \left(x , y_{0}\right) &= F_{0}\! \left(x \right)+F_{16}\! \left(x , y_{0}\right)\\
F_{21}\! \left(x , y_{0}\right) &= F_{16}\! \left(x , y_{0}\right)\\
F_{22}\! \left(x , y_{0}\right) &= F_{23}\! \left(x , y_{0}\right)\\
F_{23}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= x\\
F_{25}\! \left(x , y_{0}\right) &= y_{0} x\\
F_{26}\! \left(x , y_{0}\right) &= F_{27}\! \left(x , y_{0}\right)\\
F_{27}\! \left(x , y_{0}\right) &= F_{24}\! \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_{47}\! \left(x , y_{0}\right)\\
F_{29}\! \left(x , y_{0}\right) &= F_{30}\! \left(x , y_{0}\right)+F_{31}\! \left(x , y_{0}\right)\\
F_{30}\! \left(x , y_{0}\right) &= F_{16}\! \left(x , y_{0}\right) F_{4}\! \left(x \right)\\
F_{31}\! \left(x , y_{0}\right) &= F_{32}\! \left(x , y_{0}\right)\\
F_{32}\! \left(x , y_{0}\right) &= F_{12}\! \left(x \right) F_{24}\! \left(x \right) F_{33}\! \left(x , y_{0}\right)\\
F_{33}\! \left(x , y_{0}\right) &= -\frac{y_{0} \left(F_{34}\! \left(x , 1\right)-F_{34}\! \left(x , y_{0}\right)\right)}{-1+y_{0}}\\
F_{34}\! \left(x , y_{0}\right) &= F_{35}\! \left(x , y_{0}\right)\\
F_{35}\! \left(x , y_{0}\right) &= F_{25}\! \left(x , y_{0}\right) F_{36}\! \left(x , y_{0}\right)\\
F_{36}\! \left(x , y_{0}\right) &= F_{37}\! \left(x \right)+F_{40}\! \left(x , y_{0}\right)\\
F_{37}\! \left(x \right) &= F_{38}\! \left(x , 1\right)\\
F_{38}\! \left(x , y_{0}\right) &= -\frac{-F_{39}\! \left(x , y_{0}\right) y_{0}+F_{39}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{39}\! \left(x , y_{0}\right) &= y_{0}^{4} x^{4} F_{39}\! \left(x , y_{0}\right)^{3}+5 x^{3} F_{39}\! \left(x , y_{0}\right)^{2} y_{0}^{3}-11 y_{0}^{2} x^{2} F_{39}\! \left(x , y_{0}\right)^{2}+3 x^{2} F_{39}\! \left(x , y_{0}\right) y_{0}^{2}+10 x F_{39}\! \left(x , y_{0}\right) y_{0}-9 y_{0} x +1\\
F_{40}\! \left(x , y_{0}\right) &= F_{41}\! \left(x , y_{0}\right)\\
F_{41}\! \left(x , y_{0}\right) &= F_{25}\! \left(x , y_{0}\right) F_{42}\! \left(x , y_{0}\right)\\
F_{42}\! \left(x , y_{0}\right) &= F_{43}\! \left(x , 1, y_{0}\right)\\
F_{43}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{44}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{44}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\
F_{44}\! \left(x , y_{0}, y_{1}\right) &= F_{38}\! \left(x , y_{0}\right)+F_{45}\! \left(x , y_{0}, y_{1}\right)\\
F_{45}\! \left(x , y_{0}, y_{1}\right) &= F_{46}\! \left(x , y_{0}, y_{1}\right)\\
F_{46}\! \left(x , y_{0}, y_{1}\right) &= F_{25}\! \left(x , y_{1}\right) F_{43}\! \left(x , y_{0}, y_{1}\right)\\
F_{47}\! \left(x , y_{0}\right) &= F_{101}\! \left(x , y_{0}\right)+F_{48}\! \left(x , y_{0}\right)\\
F_{48}\! \left(x , y_{0}\right) &= F_{49}\! \left(x , y_{0}\right)\\
F_{49}\! \left(x , y_{0}\right) &= F_{13}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right) F_{50}\! \left(x , y_{0}\right)\\
F_{50}\! \left(x , y_{0}\right) &= F_{51}\! \left(x , y_{0}\right)+F_{53}\! \left(x , y_{0}\right)\\
F_{51}\! \left(x , y_{0}\right) &= F_{34}\! \left(x , y_{0}\right)+F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= x^{4} F_{52} \left(x \right)^{3}+5 x^{3} F_{52} \left(x \right)^{2}-11 x^{2} F_{52} \left(x \right)^{2}+3 x^{2} F_{52}\! \left(x \right)+10 x F_{52}\! \left(x \right)-9 x +1\\
F_{53}\! \left(x , y_{0}\right) &= F_{54}\! \left(x , y_{0}, 1\right)\\
F_{54}\! \left(x , y_{0}, y_{1}\right) &= F_{55}\! \left(x , y_{0}, y_{0} y_{1}\right)\\
F_{56}\! \left(x , y_{0}, y_{1}\right) &= F_{51}\! \left(x , y_{0}\right)+F_{55}\! \left(x , y_{0}, y_{1}\right)\\
F_{56}\! \left(x , y_{0}, y_{1}\right) &= F_{57}\! \left(x , y_{0}, y_{1}\right)+F_{68}\! \left(x , y_{0}, y_{1}\right)\\
F_{57}\! \left(x , y_{0}, y_{1}\right) &= F_{58}\! \left(x , y_{1}\right)+F_{61}\! \left(x , y_{0}, y_{1}\right)\\
F_{58}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{59}\! \left(x , y_{0}\right)\\
F_{59}\! \left(x , y_{0}\right) &= F_{60}\! \left(x , y_{0}\right)\\
F_{60}\! \left(x , y_{0}\right) &= F_{25}\! \left(x , y_{0}\right) F_{58}\! \left(x , y_{0}\right)\\
F_{61}\! \left(x , y_{0}, y_{1}\right) &= F_{62}\! \left(x , y_{0}\right)+F_{63}\! \left(x , y_{0}, y_{1}\right)\\
F_{62}\! \left(x , y_{0}\right) &= F_{59}\! \left(x , y_{0}\right)\\
F_{63}\! \left(x , y_{0}, y_{1}\right) &= F_{64}\! \left(x \right)+F_{65}\! \left(x , y_{0}, y_{1}\right)+F_{67}\! \left(x , y_{1}, y_{0}\right)\\
F_{64}\! \left(x \right) &= 0\\
F_{65}\! \left(x , y_{0}, y_{1}\right) &= F_{25}\! \left(x , y_{0}\right) F_{66}\! \left(x , y_{0}, y_{1}\right)\\
F_{66}\! \left(x , y_{0}, y_{1}\right) &= F_{59}\! \left(x , y_{1}\right)+F_{63}\! \left(x , y_{0}, y_{1}\right)\\
F_{67}\! \left(x , y_{0}, y_{1}\right) &= F_{25}\! \left(x , y_{0}\right) F_{61}\! \left(x , y_{1}, y_{0}\right)\\
F_{68}\! \left(x , y_{0}, y_{1}\right) &= F_{69}\! \left(x , y_{0}, y_{1}\right)\\
F_{69}\! \left(x , y_{0}, y_{1}\right) &= F_{24}\! \left(x \right) F_{57}\! \left(x , y_{0}, y_{1}\right) F_{70}\! \left(x , y_{0}, y_{1}\right)\\
F_{70}\! \left(x , y_{0}, y_{1}\right) &= F_{56}\! \left(x , y_{0}, y_{1}\right)+F_{71}\! \left(x , y_{0}, y_{1}\right)\\
F_{71}\! \left(x , y_{0}, y_{1}\right) &= F_{72}\! \left(x , y_{0}, y_{1}\right)\\
F_{72}\! \left(x , y_{0}, y_{1}\right) &= F_{24}\! \left(x \right) F_{73}\! \left(x , y_{0}, y_{1}\right)\\
F_{73}\! \left(x , y_{0}, y_{1}\right) &= F_{100}\! \left(x , y_{0}, y_{1}\right)+F_{74}\! \left(x , y_{0}, y_{1}\right)\\
F_{74}\! \left(x , y_{0}, y_{1}\right) &= F_{75}\! \left(x , 1, y_{0}, y_{1}\right)\\
F_{75}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right) y_{2}+F_{76}\! \left(x , y_{0}, y_{1}, 1\right)}{-1+y_{2}}\\
F_{76}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{77}\! \left(x , y_{0}, y_{2}, y_{1}\right)+F_{97}\! \left(x , y_{0}, y_{1}, y_{2}\right)\\
F_{77}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= F_{78}\! \left(x , y_{1}\right) F_{95}\! \left(x , y_{0}, y_{2}\right)\\
F_{78}\! \left(x , y_{0}\right) &= F_{79}\! \left(x , y_{0}\right)+F_{82}\! \left(x , y_{0}\right)\\
F_{79}\! \left(x , y_{0}\right) &= F_{58}\! \left(x , y_{0}\right)+F_{80}\! \left(x , y_{0}\right)\\
F_{80}\! \left(x , y_{0}\right) &= F_{81}\! \left(x , y_{0}\right)\\
F_{81}\! \left(x , y_{0}\right) &= F_{24}\! \left(x \right) F_{58}\! \left(x , y_{0}\right) F_{78}\! \left(x , y_{0}\right)\\
F_{82}\! \left(x , y_{0}\right) &= F_{83}\! \left(x , y_{0}\right)\\
F_{83}\! \left(x , y_{0}\right) &= F_{24}\! \left(x \right) F_{84}\! \left(x , y_{0}\right)\\
F_{84}\! \left(x , y_{0}\right) &= F_{85}\! \left(x , y_{0}\right)+F_{86}\! \left(x , y_{0}\right)\\
F_{85}\! \left(x , y_{0}\right) &= F_{78}\! \left(x , y_{0}\right) F_{79}\! \left(x , y_{0}\right)\\
F_{86}\! \left(x , y_{0}\right) &= F_{52}\! \left(x \right) F_{87}\! \left(x , y_{0}\right)\\
F_{87}\! \left(x , y_{0}\right) &= -\frac{-F_{88}\! \left(x , y_{0}\right)+F_{88}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{78}\! \left(x , y_{0}\right) &= F_{88}\! \left(x , y_{0}\right)+F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= F_{90}\! \left(x \right)\\
F_{90}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{24}\! \left(x \right) F_{52}\! \left(x \right) F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{78}\! \left(x , 1\right)\\
F_{95}\! \left(x , y_{0}, y_{1}\right) &= F_{52}\! \left(x \right)+F_{96}\! \left(x , y_{0}, y_{1}\right)\\
F_{96}\! \left(x , y_{0}, y_{1}\right) &= y_{0} F_{34}\! \left(x , y_{1}\right)\\
F_{97}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= y_{0} F_{98}\! \left(x , y_{2}, y_{2}\right)\\
F_{98}\! \left(x , y_{0}, y_{1}\right) &= F_{51}\! \left(x , y_{0}\right) F_{99}\! \left(x , y_{0}, y_{1}\right)\\
F_{70}\! \left(x , y_{0}, y_{1}\right) &= F_{78}\! \left(x , y_{1}\right)+F_{99}\! \left(x , y_{0}, y_{1}\right)\\
F_{100}\! \left(x , y_{0}, y_{1}\right) &= F_{55}\! \left(x , y_{0}, y_{1}\right) F_{70}\! \left(x , y_{0}, y_{1}\right)\\
F_{101}\! \left(x , y_{0}\right) &= F_{102}\! \left(x , y_{0}\right)\\
F_{102}\! \left(x , y_{0}\right) &= F_{103}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right) F_{51}\! \left(x , y_{0}\right)\\
F_{104}\! \left(x , y_{0}\right) &= F_{103}\! \left(x , y_{0}\right) F_{116}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right)\\
F_{104}\! \left(x , y_{0}\right) &= F_{105}\! \left(x , y_{0}\right)\\
F_{106}\! \left(x , y_{0}\right) &= F_{105}\! \left(x , y_{0}\right)+F_{110}\! \left(x , y_{0}\right)\\
F_{106}\! \left(x , y_{0}\right) &= F_{107}\! \left(x , y_{0}\right)+F_{108}\! \left(x , y_{0}\right)\\
F_{107}\! \left(x , y_{0}\right) &= -\frac{-F_{15}\! \left(x , y_{0}\right)+F_{15}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{108}\! \left(x , y_{0}\right) &= F_{109}\! \left(x , y_{0}\right)\\
F_{109}\! \left(x , y_{0}\right) &= F_{106}\! \left(x , y_{0}\right) F_{25}\! \left(x , y_{0}\right)\\
F_{110}\! \left(x , y_{0}\right) &= F_{111}\! \left(x , 1, y_{0}\right)\\
F_{111}\! \left(x , y_{0}, y_{1}\right) &= F_{112}\! \left(x \right) F_{114}\! \left(x , y_{0}, y_{1}\right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{12}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{114}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{115}\! \left(x , y_{0}, y_{1}\right)\\
F_{115}\! \left(x , y_{0}, y_{1}\right) &= y_{0} F_{62}\! \left(x , y_{1}\right)\\
F_{116}\! \left(x , y_{0}\right) &= F_{58}\! \left(x , y_{0}\right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{120}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{121}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{123}\! \left(x \right) F_{24}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{124}\! \left(x , 1\right)\\
F_{124}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{125}\! \left(x , y_{0}\right)+F_{125}\! \left(x , 1\right)}{-1+y_{0}}\\
F_{125}\! \left(x , y_{0}\right) &= F_{126}\! \left(x , y_{0}\right)+F_{38}\! \left(x , y_{0}\right)\\
F_{126}\! \left(x , y_{0}\right) &= F_{127}\! \left(x , y_{0}\right)\\
F_{127}\! \left(x , y_{0}\right) &= F_{124}\! \left(x , y_{0}\right) F_{24}\! \left(x \right)\\
\end{align*}\)