Av(12453, 13452, 14352, 15342, 23451, 24351, 25341)
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Counting Sequence
1, 1, 2, 6, 24, 113, 580, 3129, 17442, 99574, 579108, 3419056, 20440024, 123494294, 752913720, ...
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This specification was found using the strategy pack "Col Placements Tracked Fusion" and has 38 rules.

Finding the specification took 17 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_{4}\! \left(x \right)\\ F_{3}\! \left(x \right) &= x\\ F_{4}\! \left(x \right) &= F_{5}\! \left(x , 1\right)\\ F_{5}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x , y_{0}\right)+F_{8}\! \left(x , y_{0}\right)\\ F_{6}\! \left(x , y_{0}\right) &= F_{3}\! \left(x \right) F_{7}\! \left(x , y_{0}\right)\\ F_{7}\! \left(x , y_{0}\right) &= -\frac{-F_{5}\! \left(x , y_{0}\right) y_{0}+F_{5}\! \left(x , 1\right)}{-1+y_{0}}\\ F_{8}\! \left(x , y_{0}\right) &= F_{10}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\ F_{9}\! \left(x , y_{0}\right) &= y_{0} x\\ F_{10}\! \left(x , y_{0}\right) &= F_{11}\! \left(x , 1, y_{0}\right)\\ F_{11}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{12}\! \left(x , y_{0} y_{1}\right) y_{0}+F_{12}\! \left(x , y_{1}\right)}{-1+y_{0}}\\ F_{12}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y_{0}\right)+F_{36}\! \left(x , y_{0}\right)\\ F_{13}\! \left(x , y_{0}\right) &= F_{14}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)\\ F_{14}\! \left(x , y_{0}\right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x , y_{0}\right)+F_{30}\! \left(x , y_{0}\right)+F_{33}\! \left(x , y_{0}\right)\\ F_{15}\! \left(x , y_{0}\right) &= F_{16}\! \left(x , y_{0}\right) F_{3}\! \left(x \right)\\ F_{16}\! \left(x , y_{0}\right) &= F_{17}\! \left(x , 1, y_{0}\right)\\ F_{17}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{18}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{18}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\ F_{18}\! \left(x , y_{0}, y_{1}\right) &= F_{1}\! \left(x \right)+F_{19}\! \left(x , y_{0}, y_{1}\right)+F_{21}\! \left(x , y_{0}, y_{1}\right)+F_{25}\! \left(x , y_{1}, y_{0}\right)\\ F_{19}\! \left(x , y_{0}, y_{1}\right) &= F_{20}\! \left(x , y_{0}, y_{1}\right) F_{3}\! \left(x \right)\\ F_{20}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-F_{18}\! \left(x , y_{0}, y_{1}\right) y_{0}+F_{18}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\ F_{21}\! \left(x , y_{0}, y_{1}\right) &= F_{22}\! \left(x , y_{0}, y_{1}\right) F_{9}\! \left(x , y_{0}\right)\\ F_{22}\! \left(x , y_{0}, y_{1}\right) &= F_{23}\! \left(x , 1, y_{0}, y_{1}\right)\\ F_{23}\! \left(x , y_{0}, y_{1}, y_{2}\right) &= -\frac{-F_{24}\! \left(x , y_{0} y_{1}, y_{2}\right) y_{0}+F_{24}\! \left(x , y_{1}, y_{2}\right)}{-1+y_{0}}\\ F_{24}\! \left(x , y_{0}, y_{1}\right) &= \frac{y_{0} F_{12}\! \left(x , y_{0}\right)-F_{12}\! \left(x , y_{1}\right) y_{1}}{-y_{1}+y_{0}}\\ F_{25}\! \left(x , y_{0}, y_{1}\right) &= F_{26}\! \left(x , y_{0}, y_{1}\right)\\ F_{26}\! \left(x , y_{0}, y_{1}\right) &= F_{24}\! \left(x , y_{1}, y_{0}\right) F_{27}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\ F_{27}\! \left(x , y_{0}\right) &= F_{1}\! \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_{29}\! \left(x , y_{0}\right) &= F_{27}\! \left(x , y_{0}\right)^{2} F_{9}\! \left(x , y_{0}\right)\\ F_{30}\! \left(x , y_{0}\right) &= F_{3}\! \left(x \right) F_{31}\! \left(x , y_{0}\right)\\ F_{31}\! \left(x , y_{0}\right) &= F_{32}\! \left(x , 1, y_{0}\right)\\ F_{32}\! \left(x , y_{0}, y_{1}\right) &= -\frac{-y_{0} F_{24}\! \left(x , y_{0}, y_{1}\right)+F_{24}\! \left(x , 1, y_{1}\right)}{-1+y_{0}}\\ F_{33}\! \left(x , y_{0}\right) &= F_{34}\! \left(x , y_{0}\right)\\ F_{34}\! \left(x , y_{0}\right) &= F_{27}\! \left(x , y_{0}\right) F_{35}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\ F_{35}\! \left(x , y_{0}\right) &= -\frac{-y_{0} F_{12}\! \left(x , y_{0}\right)+F_{12}\! \left(x , 1\right)}{-1+y_{0}}\\ F_{36}\! \left(x , y_{0}\right) &= F_{37}\! \left(x , y_{0}\right)\\ F_{37}\! \left(x , y_{0}\right) &= F_{12}\! \left(x , y_{0}\right) F_{27}\! \left(x , y_{0}\right) F_{9}\! \left(x , y_{0}\right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Tracked Fusion" and has 48 rules.

Finding the specification took 1826 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_{0}\! \left(x \right)+F_{5}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{6}\! \left(x \right)\\ F_{6}\! \left(x \right) &= F_{7}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{7}\! \left(x \right) &= x\\ F_{8}\! \left(x \right) &= F_{45}\! \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_{18}\! \left(x , y\right)\\ F_{11}\! \left(x , y\right) &= F_{0}\! \left(x \right)+F_{12}\! \left(x , y\right)\\ F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right)\\ F_{13}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{14}\! \left(x , y\right) F_{15}\! \left(x , y\right)\\ F_{14}\! \left(x , y\right) &= y x\\ F_{15}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{16}\! \left(x , y\right)\\ F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right)\\ F_{17}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)^{2} F_{14}\! \left(x , y\right)\\ F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)\\ F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{7}\! \left(x \right)\\ F_{20}\! \left(x , y\right) &= -\frac{-F_{21}\! \left(x , y\right) y +F_{21}\! \left(x , 1\right)}{-1+y}\\ F_{21}\! \left(x , y\right) &= F_{10}\! \left(x , y\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_{24}\! \left(x , y\right) F_{7}\! \left(x \right)\\ F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)+F_{44}\! \left(x , y\right)\\ F_{26}\! \left(x , y\right) &= F_{14}\! \left(x , y\right) F_{15}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\ F_{26}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)\\ F_{28}\! \left(x , y\right) &= F_{27}\! \left(x , y\right)+F_{9}\! \left(x \right)\\ F_{28}\! \left(x , y\right) &= F_{29}\! \left(x , y\right)+F_{30}\! \left(x , y\right)\\ F_{29}\! \left(x , y\right) &= -\frac{-y F_{11}\! \left(x , y\right)+F_{11}\! \left(x , 1\right)}{-1+y}\\ 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_{7}\! \left(x \right)\\ F_{32}\! \left(x , y\right) &= F_{33}\! \left(x , 1, y\right)\\ F_{33}\! \left(x , y , z\right) &= -\frac{-y F_{34}\! \left(x , y , z\right)+F_{34}\! \left(x , 1, z\right)}{-1+y}\\ F_{34}\! \left(x , y , z\right) &= F_{35}\! \left(x , y , z\right)+F_{40}\! \left(x , y , z\right)\\ F_{35}\! \left(x , y , z\right) &= F_{36}\! \left(x , y , z\right)+F_{37}\! \left(x , y , z\right)\\ F_{36}\! \left(x , y , z\right) &= \frac{y F_{11}\! \left(x , y\right)-F_{11}\! \left(x , z\right) z}{-z +y}\\ F_{37}\! \left(x , y , z\right) &= F_{38}\! \left(x , y , z\right)\\ F_{38}\! \left(x , y , z\right) &= F_{39}\! \left(x , y , z\right) F_{7}\! \left(x \right)\\ F_{39}\! \left(x , y , z\right) &= -\frac{-y F_{34}\! \left(x , y , z\right)+F_{34}\! \left(x , 1, z\right)}{-1+y}\\ F_{40}\! \left(x , y , z\right) &= F_{41}\! \left(x , y , z\right)\\ F_{41}\! \left(x , y , z\right) &= F_{15}\! \left(x , z\right) F_{42}\! \left(x , y\right) F_{7}\! \left(x \right)\\ F_{43}\! \left(x , y\right) &= F_{42}\! \left(x , y\right) F_{7}\! \left(x \right)\\ F_{43}\! \left(x , y\right) &= F_{22}\! \left(x , y\right)\\ F_{44}\! \left(x , y\right) &= F_{15}\! \left(x , y\right) F_{45}\! \left(x \right)\\ F_{45}\! \left(x \right) &= F_{46}\! \left(x \right)\\ F_{46}\! \left(x \right) &= F_{47}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{47}\! \left(x \right) &= F_{24}\! \left(x , 1\right)\\ \end{align*}\)

This specification was found using the strategy pack "Point Placements Tracked Fusion Tracked Component Fusion Symmetries" and has 86 rules.

Finding the specification took 5782 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_{13}\! \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_{13}\! \left(x \right) F_{8}\! \left(x \right)\\ F_{8}\! \left(x \right) &= F_{14}\! \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)^{2} F_{13}\! \left(x \right)\\ F_{12}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{10}\! \left(x \right)\\ F_{13}\! \left(x \right) &= x\\ F_{14}\! \left(x \right) &= F_{15}\! \left(x , 1\right)\\ F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)+F_{33}\! \left(x , y\right)\\ F_{17}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)+F_{32}\! \left(x , y\right)\\ F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)+F_{27}\! \left(x , y\right)\\ F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)+F_{23}\! \left(x , y\right)\\ F_{19}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{20}\! \left(x , y\right)\\ F_{20}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)\\ F_{21}\! \left(x , y\right) &= F_{19}\! \left(x , y\right)^{2} F_{22}\! \left(x , y\right)\\ F_{22}\! \left(x , y\right) &= y x\\ F_{23}\! \left(x , y\right) &= F_{2}\! \left(x \right)+F_{24}\! \left(x , y\right)\\ F_{24}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)\\ F_{25}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{26}\! \left(x , y\right)\\ F_{26}\! \left(x , y\right) &= F_{23}\! \left(x , y\right)+F_{27}\! \left(x , y\right)\\ F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y\right)\\ F_{28}\! \left(x , y\right) &= F_{13}\! \left(x \right) F_{29}\! \left(x , y\right)\\ F_{29}\! \left(x , y\right) &= -\frac{-F_{30}\! \left(x , y\right) y +F_{30}\! \left(x , 1\right)}{-1+y}\\ F_{30}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)+F_{31}\! \left(x , y\right)\\ F_{31}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{4}\! \left(x \right)\\ F_{32}\! \left(x , y\right) &= F_{0}\! \left(x \right) F_{19}\! \left(x , y\right)\\ F_{33}\! \left(x , y\right) &= F_{34}\! \left(x , y\right)\\ F_{34}\! \left(x , y\right) &= F_{13}\! \left(x \right) F_{35}\! \left(x , y\right)\\ F_{35}\! \left(x , y\right) &= F_{36}\! \left(x , y\right)+F_{81}\! \left(x , y\right)\\ F_{36}\! \left(x , y\right) &= F_{37}\! \left(x \right) F_{80}\! \left(x , y\right)\\ F_{37}\! \left(x \right) &= F_{38}\! \left(x \right)+F_{41}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{0}\! \left(x \right)+F_{39}\! \left(x \right)\\ F_{39}\! \left(x \right) &= F_{40}\! \left(x \right)\\ F_{40}\! \left(x \right) &= F_{13}\! \left(x \right) F_{37}\! \left(x \right)\\ F_{41}\! \left(x \right) &= \frac{F_{42}\! \left(x \right)}{F_{45}\! \left(x \right)}\\ F_{42}\! \left(x \right) &= -F_{76}\! \left(x \right)+F_{43}\! \left(x \right)\\ F_{43}\! \left(x \right) &= F_{44}\! \left(x \right)+F_{60}\! \left(x \right)\\ F_{44}\! \left(x \right) &= F_{10}\! \left(x \right) F_{45}\! \left(x \right) F_{58}\! \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_{13}\! \left(x \right) F_{48}\! \left(x \right)\\ F_{48}\! \left(x \right) &= F_{49}\! \left(x \right)+F_{50}\! \left(x \right)\\ F_{49}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x \right)\\ F_{50}\! \left(x \right) &= F_{46}\! \left(x \right)+F_{51}\! \left(x \right)\\ F_{51}\! \left(x \right) &= F_{52}\! \left(x \right)+F_{53}\! \left(x \right)+F_{57}\! \left(x \right)\\ F_{52}\! \left(x \right) &= 0\\ F_{53}\! \left(x \right) &= F_{13}\! \left(x \right) F_{54}\! \left(x \right)\\ F_{54}\! \left(x \right) &= F_{55}\! \left(x \right)+F_{56}\! \left(x \right)\\ F_{55}\! \left(x \right) &= F_{13}\! \left(x \right)\\ F_{56}\! \left(x \right) &= F_{51}\! \left(x \right)\\ F_{57}\! \left(x \right) &= F_{13}\! \left(x \right) F_{46}\! \left(x \right)\\ F_{58}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{59}\! \left(x \right)\\ F_{59}\! \left(x \right) &= F_{13}\! \left(x \right) F_{58}\! \left(x \right)\\ F_{60}\! \left(x \right) &= F_{61}\! \left(x \right)\\ F_{61}\! \left(x \right) &= F_{45}\! \left(x \right) F_{62}\! \left(x \right)\\ F_{62}\! \left(x \right) &= F_{63}\! \left(x \right)\\ F_{63}\! \left(x \right) &= F_{13}\! \left(x \right) F_{64}\! \left(x \right)\\ F_{64}\! \left(x \right) &= F_{65}\! \left(x \right)+F_{72}\! \left(x \right)\\ F_{65}\! \left(x \right) &= F_{12}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{66}\! \left(x \right) &= \frac{F_{67}\! \left(x \right)}{F_{13}\! \left(x \right) F_{45}\! \left(x \right)}\\ F_{67}\! \left(x \right) &= F_{68}\! \left(x \right)\\ F_{68}\! \left(x \right) &= F_{69}\! \left(x \right)+F_{70}\! \left(x \right)\\ F_{69}\! \left(x \right) &= F_{2}\! \left(x \right) F_{45}\! \left(x \right)\\ F_{70}\! \left(x \right) &= F_{71}\! \left(x \right)\\ F_{71}\! \left(x \right) &= F_{13}\! \left(x \right) F_{43}\! \left(x \right)\\ F_{72}\! \left(x \right) &= F_{73}\! \left(x \right)\\ F_{73}\! \left(x \right) &= F_{12}\! \left(x \right) F_{13}\! \left(x \right) F_{74}\! \left(x \right)\\ F_{74}\! \left(x \right) &= \frac{F_{75}\! \left(x \right)}{F_{13}\! \left(x \right)}\\ F_{75}\! \left(x \right) &= F_{14}\! \left(x \right)\\ F_{76}\! \left(x \right) &= F_{77}\! \left(x \right)\\ F_{77}\! \left(x \right) &= F_{45}\! \left(x \right) F_{78}\! \left(x \right)\\ F_{78}\! \left(x \right) &= F_{79}\! \left(x \right)\\ F_{79}\! \left(x \right) &= F_{13}\! \left(x \right) F_{66}\! \left(x \right)\\ F_{80}\! \left(x , y\right) &= -\frac{-F_{20}\! \left(x , y\right)+F_{20}\! \left(x , 1\right)}{-1+y}\\ F_{81}\! \left(x , y\right) &= F_{82}\! \left(x , y\right)\\ F_{82}\! \left(x , y\right) &= F_{13}\! \left(x \right) F_{83}\! \left(x , y\right)\\ F_{83}\! \left(x , y\right) &= -\frac{-y F_{84}\! \left(x , y\right)+F_{84}\! \left(x , 1\right)}{-1+y}\\ F_{85}\! \left(x , y\right) &= F_{13}\! \left(x \right) F_{84}\! \left(x , y\right)\\ F_{85}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)\\ \end{align*}\)