Av(12435, 12453, 12543, 15243, 21435, 21453, 21543, 25143, 51243, 52143)
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Counting Sequence
1, 1, 2, 6, 24, 110, 540, 2758, 14448, 77022, 415860, 2267078, 12452616, 68814798, 382168332, ...
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This specification was found using the strategy pack "Point Placements Req Corrob" and has 95 rules.

Finding the specification took 692 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_{30}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2\\ F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{30}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{30}\! \left(x \right) F_{64}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{15}\! \left(x \right) F_{30}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{15}\! \left(x \right) &= \frac{F_{16}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= -F_{73}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{18}\! \left(x \right) &= \frac{F_{19}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{22}\! \left(x \right) F_{30}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{26}\! \left(x \right) F_{30}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{26}\! \left(x \right) &= \frac{F_{27}\! \left(x \right)}{F_{5}\! \left(x \right)}\\ F_{27}\! \left(x \right) &= -F_{31}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= \frac{F_{29}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{29}\! \left(x \right) &= F_{6}\! \left(x \right)\\ F_{30}\! \left(x \right) &= x\\ F_{31}\! \left(x \right) &= -F_{36}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= \frac{F_{33}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= -F_{35}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{35}\! \left(x \right) x +F_{35} \left(x \right)^{2}+x\\ F_{36}\! \left(x \right) &= F_{26}\! \left(x \right) F_{35}\! \left(x \right)\\ F_{37}\! \left(x \right) &= \frac{F_{38}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{38}\! \left(x \right) &= F_{6}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{30}\! \left(x \right) F_{41}\! \left(x \right)\\ F_{41}\! \left(x \right) &= F_{42}\! \left(x \right)\\ F_{42}\! \left(x \right) &= F_{30}\! \left(x \right) F_{43}\! \left(x \right) F_{64}\! \left(x \right)\\ F_{43}\! \left(x \right) &= \frac{F_{44}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= -F_{46}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{46}\! \left(x \right) &= -F_{47}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{48}\! \left(x \right)+F_{54}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{52}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{49} \left(x \right)^{2} F_{30}\! \left(x \right)\\ F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= F_{49} \left(x \right)^{2} F_{30}\! \left(x \right) F_{48}\! \left(x \right)\\ F_{54}\! \left(x \right) &= -F_{62}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= \frac{F_{56}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{56}\! \left(x \right) &= F_{57}\! \left(x \right)\\ F_{57}\! \left(x \right) &= -F_{61}\! \left(x \right)+F_{58}\! \left(x \right)\\ F_{58}\! \left(x \right) &= -F_{0}\! \left(x \right)+F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= \frac{F_{60}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{60}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{61}\! \left(x \right) &= 4 x F_{61} \left(x \right)^{2}+x^{2}-F_{61} \left(x \right)^{2}+F_{61}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{15}\! \left(x \right) F_{30}\! \left(x \right) F_{49}\! \left(x \right)\\ F_{64}\! \left(x \right) &= \frac{F_{65}\! \left(x \right)}{F_{0}\! \left(x \right)}\\ F_{65}\! \left(x \right) &= -F_{69}\! \left(x \right)+F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= \frac{F_{67}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{69}\! \left(x \right) &= -F_{72}\! \left(x \right)+F_{70}\! \left(x \right)\\ F_{70}\! \left(x \right) &= \frac{F_{71}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{71}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{2}\! \left(x \right) F_{64}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{74}\! \left(x \right)+F_{91}\! \left(x \right)\\ F_{74}\! \left(x \right) &= F_{75}\! \left(x \right)+F_{84}\! \left(x \right)\\ F_{75}\! \left(x \right) &= -F_{82}\! \left(x \right)+F_{76}\! \left(x \right)\\ F_{76}\! \left(x \right) &= -F_{77}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{77}\! \left(x \right) &= -F_{80}\! \left(x \right)+F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= \frac{F_{79}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{79}\! \left(x \right) &= F_{57}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)+F_{82}\! \left(x \right)\\ F_{81}\! \left(x \right) &= -F_{49}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{30}\! \left(x \right) F_{54}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{85}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{30}\! \left(x \right) F_{86}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{87}\! \left(x \right)+F_{90}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)+F_{89}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{48}\! \left(x \right) F_{81}\! \left(x \right)\\ F_{89}\! \left(x \right) &= F_{49}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{90}\! \left(x \right) &= F_{49}\! \left(x \right) F_{77}\! \left(x \right)\\ F_{91}\! \left(x \right) &= F_{92}\! \left(x \right)\\ F_{92}\! \left(x \right) &= F_{26}\! \left(x \right) F_{30}\! \left(x \right) F_{93}\! \left(x \right)\\ F_{93}\! \left(x \right) &= \frac{F_{94}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{94}\! \left(x \right) &= F_{82}\! \left(x \right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Tracked Fusion" and has 8 rules.

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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 91 rules.

Finding the specification took 449 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_{30}\! \left(x \right) F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{5}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{5}\! \left(x \right) x +F_{5} \left(x \right)^{2}-2 F_{5}\! \left(x \right)+2\\ F_{6}\! \left(x \right) &= F_{7}\! \left(x \right)\\ F_{7}\! \left(x \right) &= F_{30}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{23}\! \left(x \right)+F_{9}\! \left(x \right)\\ F_{9}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{10}\! \left(x \right) &= F_{11}\! \left(x \right)\\ F_{11}\! \left(x \right) &= F_{12}\! \left(x \right) F_{30}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{13}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{13}\! \left(x \right) &= F_{14}\! \left(x \right)\\ F_{14}\! \left(x \right) &= F_{15}\! \left(x \right) F_{30}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{15}\! \left(x \right) &= \frac{F_{16}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{16}\! \left(x \right) &= F_{17}\! \left(x \right)\\ F_{17}\! \left(x \right) &= -F_{69}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{18}\! \left(x \right) &= \frac{F_{19}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{19}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{20}\! \left(x \right) &= F_{21}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{22}\! \left(x \right) F_{30}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{10}\! \left(x \right)+F_{23}\! \left(x \right)\\ F_{23}\! \left(x \right) &= F_{24}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{24}\! \left(x \right) &= F_{25}\! \left(x \right)\\ F_{25}\! \left(x \right) &= F_{26}\! \left(x \right) F_{30}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{26}\! \left(x \right) &= \frac{F_{27}\! \left(x \right)}{F_{5}\! \left(x \right)}\\ F_{27}\! \left(x \right) &= -F_{31}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{28}\! \left(x \right) &= \frac{F_{29}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{29}\! \left(x \right) &= F_{6}\! \left(x \right)\\ F_{30}\! \left(x \right) &= x\\ F_{31}\! \left(x \right) &= -F_{36}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{32}\! \left(x \right) &= \frac{F_{33}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{33}\! \left(x \right) &= F_{34}\! \left(x \right)\\ F_{34}\! \left(x \right) &= -F_{35}\! \left(x \right)+F_{6}\! \left(x \right)\\ F_{35}\! \left(x \right) &= F_{35}\! \left(x \right) x +F_{35} \left(x \right)^{2}+x\\ F_{36}\! \left(x \right) &= F_{26}\! \left(x \right) F_{35}\! \left(x \right)\\ F_{37}\! \left(x \right) &= \frac{F_{38}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{38}\! \left(x \right) &= F_{6}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{30}\! \left(x \right) F_{41}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{41}\! \left(x \right) &= -F_{42}\! \left(x \right)+F_{32}\! \left(x \right)\\ F_{42}\! \left(x \right) &= -F_{43}\! \left(x \right)+F_{28}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{45}\! \left(x \right)+F_{48}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{46}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{47}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{45} \left(x \right)^{2} F_{30}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{45} \left(x \right)^{2} F_{30}\! \left(x \right) F_{44}\! \left(x \right)\\ F_{50}\! \left(x \right) &= -F_{58}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= \frac{F_{52}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{52}\! \left(x \right) &= F_{53}\! \left(x \right)\\ F_{53}\! \left(x \right) &= -F_{2}\! \left(x \right)+F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= -F_{57}\! \left(x \right)+F_{55}\! \left(x \right)\\ F_{55}\! \left(x \right) &= \frac{F_{56}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{56}\! \left(x \right) &= F_{2}\! \left(x \right)\\ F_{57}\! \left(x \right) &= 4 F_{57} \left(x \right)^{2} x +x^{2}-8 F_{57}\! \left(x \right) x -F_{57} \left(x \right)^{2}+4 x +3 F_{57}\! \left(x \right)-1\\ F_{58}\! \left(x \right) &= F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{15}\! \left(x \right) F_{30}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{60}\! \left(x \right) &= \frac{F_{61}\! \left(x \right)}{F_{0}\! \left(x \right)}\\ F_{61}\! \left(x \right) &= -F_{65}\! \left(x \right)+F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= \frac{F_{63}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{63}\! \left(x \right) &= F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{20}\! \left(x \right)+F_{35}\! \left(x \right)\\ F_{65}\! \left(x \right) &= -F_{68}\! \left(x \right)+F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= \frac{F_{67}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{67}\! \left(x \right) &= F_{20}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{2}\! \left(x \right) F_{60}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{70}\! \left(x \right)+F_{87}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)+F_{80}\! \left(x \right)\\ F_{71}\! \left(x \right) &= -F_{78}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{72}\! \left(x \right) &= -F_{73}\! \left(x \right)+F_{18}\! \left(x \right)\\ F_{73}\! \left(x \right) &= -F_{76}\! \left(x \right)+F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= \frac{F_{75}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{75}\! \left(x \right) &= F_{53}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)+F_{78}\! \left(x \right)\\ F_{77}\! \left(x \right) &= -F_{45}\! \left(x \right)+F_{26}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{30}\! \left(x \right) F_{50}\! \left(x \right)\\ F_{80}\! \left(x \right) &= F_{81}\! \left(x \right)\\ F_{81}\! \left(x \right) &= F_{30}\! \left(x \right) F_{82}\! \left(x \right)\\ F_{82}\! \left(x \right) &= F_{83}\! \left(x \right)+F_{86}\! \left(x \right)\\ F_{83}\! \left(x \right) &= F_{84}\! \left(x \right)+F_{85}\! \left(x \right)\\ F_{84}\! \left(x \right) &= F_{44}\! \left(x \right) F_{77}\! \left(x \right)\\ F_{85}\! \left(x \right) &= F_{45}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{86}\! \left(x \right) &= F_{45}\! \left(x \right) F_{73}\! \left(x \right)\\ F_{87}\! \left(x \right) &= F_{88}\! \left(x \right)\\ F_{88}\! \left(x \right) &= F_{26}\! \left(x \right) F_{30}\! \left(x \right) F_{89}\! \left(x \right)\\ F_{89}\! \left(x \right) &= \frac{F_{90}\! \left(x \right)}{F_{30}\! \left(x \right)}\\ F_{90}\! \left(x \right) &= F_{78}\! \left(x \right)\\ \end{align*}\)