Av(12354, 13254, 21354, 23154, 23514, 23541, 31254, 32154, 32514, 32541)
Counting Sequence
1, 1, 2, 6, 24, 110, 540, 2758, 14448, 77022, 415860, 2267078, 12452616, 68814798, 382168332, ...
This specification was found using the strategy pack "Point Placements Tracked Fusion" and has 8 rules.
Finding the specification took 0 seconds.
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\(\begin{align*}
F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\
F_{1}\! \left(x \right) &= 1\\
F_{2}\! \left(x \right) &= F_{3}\! \left(x \right)\\
F_{3}\! \left(x \right) &= F_{4}\! \left(x \right) F_{7}\! \left(x \right)\\
F_{4}\! \left(x \right) &= F_{5}\! \left(x , 1\right)\\
F_{5}\! \left(x , y\right) &= -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}\\
F_{6}\! \left(x , y\right) &= x F_{6}\! \left(x , y\right) y +F_{6}\! \left(x , y\right)^{2}-2 F_{6}\! \left(x , y\right)+2\\
F_{7}\! \left(x \right) &= x\\
\end{align*}\)
This specification was found using the strategy pack "Point Placements Req Corrob" and has 141 rules.
Finding the specification took 2513 seconds.
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Copy 141 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_{19}\! \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_{19}\! \left(x \right) F_{8}\! \left(x \right)\\
F_{8}\! \left(x \right) &= F_{139}\! \left(x \right)+F_{9}\! \left(x \right)\\
F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)\\
F_{10}\! \left(x \right) &= F_{11}\! \left(x \right) F_{19}\! \left(x \right)\\
F_{11}\! \left(x \right) &= F_{12}\! \left(x \right)+F_{135}\! \left(x \right)\\
F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{131}\! \left(x \right)\\
F_{13}\! \left(x \right) &= F_{14}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{14}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{16}\! \left(x \right)\\
F_{15}\! \left(x \right) &= F_{15}\! \left(x \right) x +F_{15} \left(x \right)^{2}-2 F_{15}\! \left(x \right)+2\\
F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{17}\! \left(x \right) &= F_{18}\! \left(x \right)\\
F_{18}\! \left(x \right) &= F_{19}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{19}\! \left(x \right) &= x\\
F_{20}\! \left(x \right) &= \frac{F_{21}\! \left(x \right)}{F_{19}\! \left(x \right)}\\
F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)\\
F_{22}\! \left(x \right) &= F_{2}\! \left(x \right)+F_{23}\! \left(x \right)\\
F_{23}\! \left(x \right) &= -F_{27}\! \left(x \right)+F_{24}\! \left(x \right)\\
F_{24}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{25}\! \left(x \right)\\
F_{25}\! \left(x \right) &= \frac{F_{26}\! \left(x \right)}{F_{19}\! \left(x \right)}\\
F_{26}\! \left(x \right) &= F_{2}\! \left(x \right)\\
F_{27}\! \left(x \right) &= F_{27}\! \left(x \right) x +F_{27} \left(x \right)^{2}+x\\
F_{28}\! \left(x \right) &= \frac{F_{29}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{29}\! \left(x \right) &= -F_{32}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{30}\! \left(x \right) &= \frac{F_{31}\! \left(x \right)}{F_{19}\! \left(x \right)}\\
F_{31}\! \left(x \right) &= F_{16}\! \left(x \right)\\
F_{32}\! \left(x \right) &= -F_{130}\! \left(x \right)+F_{33}\! \left(x \right)\\
F_{33}\! \left(x \right) &= \frac{F_{34}\! \left(x \right)}{F_{19}\! \left(x \right)}\\
F_{34}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{35}\! \left(x \right) &= F_{19}\! \left(x \right) F_{36}\! \left(x \right)\\
F_{36}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{37}\! \left(x \right)\\
F_{37}\! \left(x \right) &= F_{17}\! \left(x \right)+F_{38}\! \left(x \right)\\
F_{38}\! \left(x \right) &= F_{39}\! \left(x \right)\\
F_{39}\! \left(x \right) &= F_{107}\! \left(x \right) F_{19}\! \left(x \right) F_{40}\! \left(x \right)\\
F_{40}\! \left(x \right) &= -F_{43}\! \left(x \right)+F_{41}\! \left(x \right)\\
F_{41}\! \left(x \right) &= \frac{F_{42}\! \left(x \right)}{F_{19}\! \left(x \right)}\\
F_{42}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)\\
F_{44}\! \left(x \right) &= \frac{F_{45}\! \left(x \right)}{F_{19}\! \left(x \right)}\\
F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)\\
F_{46}\! \left(x \right) &= F_{19}\! \left(x \right) F_{47}\! \left(x \right)\\
F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)\\
F_{48}\! \left(x \right) &= F_{119}\! \left(x \right) F_{19}\! \left(x \right) F_{49}\! \left(x \right)\\
F_{49}\! \left(x \right) &= \frac{F_{50}\! \left(x \right)}{F_{19}\! \left(x \right) F_{77}\! \left(x \right)}\\
F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)\\
F_{51}\! \left(x \right) &= -F_{67}\! \left(x \right)+F_{52}\! \left(x \right)\\
F_{52}\! \left(x \right) &= \frac{F_{53}\! \left(x \right)}{F_{19}\! \left(x \right)}\\
F_{53}\! \left(x \right) &= F_{54}\! \left(x \right)\\
F_{54}\! \left(x \right) &= -F_{55}\! \left(x \right)+F_{30}\! \left(x \right)\\
F_{55}\! \left(x \right) &= F_{56}\! \left(x \right)+F_{57}\! \left(x \right)\\
F_{56}\! \left(x \right) &= F_{15} \left(x \right)^{2}\\
F_{57}\! \left(x \right) &= F_{58}\! \left(x \right)\\
F_{58}\! \left(x \right) &= F_{19}\! \left(x \right) F_{20}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{59}\! \left(x \right) &= \frac{F_{60}\! \left(x \right)}{F_{15}\! \left(x \right)}\\
F_{60}\! \left(x \right) &= -F_{63}\! \left(x \right)+F_{61}\! \left(x \right)\\
F_{61}\! \left(x \right) &= \frac{F_{62}\! \left(x \right)}{F_{19}\! \left(x \right)}\\
F_{62}\! \left(x \right) &= F_{17}\! \left(x \right)\\
F_{63}\! \left(x \right) &= -F_{66}\! \left(x \right)+F_{64}\! \left(x \right)\\
F_{64}\! \left(x \right) &= \frac{F_{65}\! \left(x \right)}{F_{19}\! \left(x \right)}\\
F_{65}\! \left(x \right) &= F_{35}\! \left(x \right)\\
F_{66}\! \left(x \right) &= F_{27}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)+F_{69}\! \left(x \right)\\
F_{68}\! \left(x \right) &= F_{28}\! \left(x \right) F_{55}\! \left(x \right)\\
F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)\\
F_{70}\! \left(x \right) &= F_{19}\! \left(x \right) F_{71}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{71}\! \left(x \right) &= F_{72}\! \left(x \right)+F_{73}\! \left(x \right)\\
F_{72}\! \left(x \right) &= F_{15}\! \left(x \right) F_{59}\! \left(x \right)\\
F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)\\
F_{74}\! \left(x \right) &= F_{19}\! \left(x \right) F_{59}\! \left(x \right) F_{75}\! \left(x \right)\\
F_{75}\! \left(x \right) &= \frac{F_{76}\! \left(x \right)}{F_{19}\! \left(x \right)}\\
F_{76}\! \left(x \right) &= F_{40}\! \left(x \right)\\
F_{77}\! \left(x \right) &= F_{129}\! \left(x \right)+F_{78}\! \left(x \right)\\
F_{78}\! \left(x \right) &= \frac{F_{79}\! \left(x \right)}{F_{119}\! \left(x \right) F_{19} \left(x \right)^{2}}\\
F_{79}\! \left(x \right) &= F_{80}\! \left(x \right)\\
F_{80}\! \left(x \right) &= F_{19}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{81}\! \left(x \right) &= -F_{124}\! \left(x \right)+F_{82}\! \left(x \right)\\
F_{82}\! \left(x \right) &= -F_{85}\! \left(x \right)+F_{83}\! \left(x \right)\\
F_{83}\! \left(x \right) &= \frac{F_{84}\! \left(x \right)}{F_{19}\! \left(x \right)}\\
F_{84}\! \left(x \right) &= F_{23}\! \left(x \right)\\
F_{85}\! \left(x \right) &= -F_{88}\! \left(x \right)+F_{86}\! \left(x \right)\\
F_{86}\! \left(x \right) &= \frac{F_{87}\! \left(x \right)}{F_{19}\! \left(x \right)}\\
F_{87}\! \left(x \right) &= F_{22}\! \left(x \right)\\
F_{88}\! \left(x \right) &= -F_{108}\! \left(x \right)+F_{89}\! \left(x \right)\\
F_{89}\! \left(x \right) &= \frac{F_{90}\! \left(x \right)}{F_{19}\! \left(x \right)}\\
F_{90}\! \left(x \right) &= F_{91}\! \left(x \right)\\
F_{91}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{92}\! \left(x \right)\\
F_{92}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{93}\! \left(x \right)\\
F_{93}\! \left(x \right) &= F_{94}\! \left(x \right)\\
F_{94}\! \left(x \right) &= F_{19}\! \left(x \right) F_{95}\! \left(x \right)\\
F_{95}\! \left(x \right) &= F_{104}\! \left(x \right)+F_{96}\! \left(x \right)\\
F_{96}\! \left(x \right) &= F_{37}\! \left(x \right)+F_{97}\! \left(x \right)\\
F_{97}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{98}\! \left(x \right) &= F_{99}\! \left(x \right)\\
F_{99}\! \left(x \right) &= F_{100}\! \left(x \right) F_{19}\! \left(x \right)\\
F_{100}\! \left(x \right) &= F_{101}\! \left(x \right)+F_{102}\! \left(x \right)\\
F_{101}\! \left(x \right) &= F_{15}\! \left(x \right) F_{97}\! \left(x \right)\\
F_{102}\! \left(x \right) &= F_{103}\! \left(x \right)\\
F_{103}\! \left(x \right) &= F_{19}\! \left(x \right) F_{59}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{104}\! \left(x \right) &= F_{105}\! \left(x \right)+F_{57}\! \left(x \right)\\
F_{105}\! \left(x \right) &= F_{106}\! \left(x \right)\\
F_{106}\! \left(x \right) &= F_{107}\! \left(x \right) F_{19}\! \left(x \right) F_{47}\! \left(x \right)\\
F_{107}\! \left(x \right) &= F_{15}\! \left(x \right)+F_{81}\! \left(x \right)\\
F_{108}\! \left(x \right) &= F_{109}\! \left(x \right)\\
F_{109}\! \left(x \right) &= F_{110}\! \left(x \right) F_{19}\! \left(x \right)\\
F_{110}\! \left(x \right) &= \frac{F_{111}\! \left(x \right)}{F_{19}\! \left(x \right)}\\
F_{111}\! \left(x \right) &= F_{112}\! \left(x \right)\\
F_{112}\! \left(x \right) &= F_{113}\! \left(x \right)+F_{98}\! \left(x \right)\\
F_{113}\! \left(x \right) &= F_{114}\! \left(x \right)\\
F_{114}\! \left(x \right) &= F_{115}\! \left(x \right) F_{19}\! \left(x \right)\\
F_{115}\! \left(x \right) &= F_{116}\! \left(x \right)+F_{120}\! \left(x \right)\\
F_{116}\! \left(x \right) &= F_{117}\! \left(x \right) F_{20}\! \left(x \right)\\
F_{117}\! \left(x \right) &= F_{118}\! \left(x \right)\\
F_{118}\! \left(x \right) &= F_{119} \left(x \right)^{2} F_{19}\! \left(x \right)\\
F_{119}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{117}\! \left(x \right)\\
F_{120}\! \left(x \right) &= F_{107}\! \left(x \right) F_{121}\! \left(x \right)\\
F_{121}\! \left(x \right) &= F_{122}\! \left(x \right)\\
F_{122}\! \left(x \right) &= F_{119} \left(x \right)^{2} F_{123}\! \left(x \right) F_{19}\! \left(x \right)\\
F_{123}\! \left(x \right) &= F_{119}\! \left(x \right)+F_{121}\! \left(x \right)\\
F_{124}\! \left(x \right) &= -F_{93}\! \left(x \right)+F_{125}\! \left(x \right)\\
F_{125}\! \left(x \right) &= -F_{108}\! \left(x \right)+F_{126}\! \left(x \right)\\
F_{126}\! \left(x \right) &= \frac{F_{127}\! \left(x \right)}{F_{19}\! \left(x \right)}\\
F_{127}\! \left(x \right) &= F_{128}\! \left(x \right)\\
F_{128}\! \left(x \right) &= -F_{27}\! \left(x \right)+F_{91}\! \left(x \right)\\
F_{129}\! \left(x \right) &= F_{119}\! \left(x \right) F_{81}\! \left(x \right)\\
F_{130}\! \left(x \right) &= F_{27}\! \left(x \right) F_{28}\! \left(x \right)\\
F_{131}\! \left(x \right) &= F_{132}\! \left(x \right)\\
F_{132}\! \left(x \right) &= F_{133}\! \left(x \right) F_{19}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{133}\! \left(x \right) &= F_{134}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{134}\! \left(x \right) &= F_{47}\! \left(x \right)\\
F_{135}\! \left(x \right) &= F_{136}\! \left(x \right)\\
F_{136}\! \left(x \right) &= F_{137}\! \left(x \right) F_{19}\! \left(x \right) F_{77}\! \left(x \right)\\
F_{137}\! \left(x \right) &= F_{138}\! \left(x \right)+F_{59}\! \left(x \right)\\
F_{138}\! \left(x \right) &= F_{40}\! \left(x \right)\\
F_{139}\! \left(x \right) &= F_{140}\! \left(x \right)\\
F_{140}\! \left(x \right) &= F_{19}\! \left(x \right) F_{59}\! \left(x \right) F_{86}\! \left(x \right)\\
\end{align*}\)