Av(12345, 12354, 12435, 13245, 13254, 13524, 31245, 31254, 31524, 35124)
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Counting Sequence
1, 1, 2, 6, 24, 110, 532, 2629, 13135, 66133, 335163, 1708689, 8757982, 45108924, 233368559, ...

This specification was found using the strategy pack "Row And Col Placements Tracked Fusion" and has 36 rules.

Found on January 22, 2022.

Finding the specification took 260 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_{7}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{4}\! \left(x , 1\right)\\ F_{4}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{5}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\ F_{5}\! \left(x , y\right) &= F_{6}\! \left(x , y\right) F_{7}\! \left(x \right)\\ F_{6}\! \left(x , y\right) &= \frac{F_{4}\! \left(x , y\right) y -F_{4}\! \left(x , 1\right)}{-1+y}\\ F_{7}\! \left(x \right) &= x\\ F_{8}\! \left(x , y\right) &= F_{22}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\ F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , 1, y\right)\\ F_{10}\! \left(x , y , z\right) &= F_{11}\! \left(x , y z , z\right)\\ F_{11}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{24}\! \left(x , y , z\right)+F_{32}\! \left(x , y , z\right)\\ F_{12}\! \left(x , y , z\right) &= F_{13}\! \left(x , y , z\right) F_{7}\! \left(x \right)\\ F_{13}\! \left(x , y , z\right) &= \frac{F_{14}\! \left(x , y , z\right) y -F_{14}\! \left(x , 1, z\right)}{-1+y}\\ F_{14}\! \left(x , y , z\right) &= F_{15}\! \left(x , y , z\right)+F_{4}\! \left(x , y\right)\\ F_{15}\! \left(x , y , z\right) &= F_{16}\! \left(x , y , z\right)\\ F_{16}\! \left(x , y , z\right) &= F_{0}\! \left(x \right) F_{17}\! \left(x , y\right) F_{22}\! \left(x , z\right)\\ F_{17}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x , y\right)+F_{20}\! \left(x , y\right)\\ F_{18}\! \left(x , y\right) &= F_{19}\! \left(x , y\right) F_{7}\! \left(x \right)\\ F_{19}\! \left(x , y\right) &= \frac{F_{17}\! \left(x , y\right) y -F_{17}\! \left(x , 1\right)}{-1+y}\\ F_{20}\! \left(x , y\right) &= F_{21}\! \left(x , y\right)\\ F_{21}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{22}\! \left(x , y\right) F_{23}\! \left(x , y\right)\\ F_{22}\! \left(x , y\right) &= y x\\ F_{23}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{22}\! \left(x , y\right)\\ F_{24}\! \left(x , y , z\right) &= F_{22}\! \left(x , y\right) F_{25}\! \left(x , y , z\right)\\ F_{25}\! \left(x , y , z\right) &= F_{26}\! \left(x , y , z\right)+F_{9}\! \left(x , y\right)\\ F_{26}\! \left(x , y , z\right) &= F_{27}\! \left(x , y , z\right)\\ F_{27}\! \left(x , y , z\right) &= F_{22}\! \left(x , z\right) F_{23}\! \left(x , y\right) F_{28}\! \left(x , y\right)\\ F_{29}\! \left(x , y , z\right) &= F_{28}\! \left(x , y\right)+F_{31}\! \left(x , y , z\right)\\ F_{30}\! \left(x , y , z\right) &= F_{22}\! \left(x , z\right) F_{23}\! \left(x , z\right) F_{29}\! \left(x , y , z\right)\\ F_{30}\! \left(x , y , z\right) &= F_{31}\! \left(x , y , z\right)\\ F_{11}\! \left(x , y , z\right) &= F_{31}\! \left(x , y , z\right)+F_{4}\! \left(x , y\right)\\ F_{32}\! \left(x , y , z\right) &= F_{22}\! \left(x , z\right) F_{33}\! \left(x , y , z\right)\\ F_{33}\! \left(x , y , z\right) &= F_{11}\! \left(x , y , z\right)+F_{34}\! \left(x , y , z\right)\\ F_{34}\! \left(x , y , z\right) &= F_{35}\! \left(x , y , z\right)\\ F_{35}\! \left(x , y , z\right) &= F_{22}\! \left(x , z\right) F_{29}\! \left(x , y , z\right)\\ \end{align*}\)