Av(13254, 13524, 13542, 15324, 15342, 51324, 51342)
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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 "Row Placements Tracked Fusion" and has 20 rules.

Found on January 22, 2022.

Finding the specification took 6 seconds.

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\(\begin{align*} F_{0}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{2}\! \left(x \right)\\ F_{1}\! \left(x \right) &= 1\\ F_{2}\! \left(x \right) &= F_{3}\! \left(x \right) F_{7}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{4}\! \left(x , 1\right)\\ F_{4}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{5}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\ F_{5}\! \left(x , y\right) &= F_{6}\! \left(x , y\right) F_{7}\! \left(x \right)\\ F_{6}\! \left(x , y\right) &= \frac{y F_{4}\! \left(x , y\right)-F_{4}\! \left(x , 1\right)}{-1+y}\\ F_{7}\! \left(x \right) &= x\\ F_{8}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\ F_{9}\! \left(x , y\right) &= \frac{y F_{10}\! \left(x , 1, y\right)-F_{10}\! \left(x , \frac{1}{y}, y\right)}{-1+y}\\ F_{10}\! \left(x , y , z\right) &= F_{11}\! \left(x , y z , z\right)\\ F_{11}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y , z\right)+F_{18}\! \left(x , y , z\right)\\ F_{12}\! \left(x , y , z\right) &= F_{13}\! \left(x , y , z\right)\\ F_{13}\! \left(x , y , z\right) &= F_{11}\! \left(x , y , z\right) F_{14}\! \left(x , y\right) F_{17}\! \left(x , y\right)\\ F_{14}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)\\ F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right)\\ F_{16}\! \left(x , y\right) &= F_{14}\! \left(x , y\right)^{2} F_{17}\! \left(x , y\right)\\ F_{17}\! \left(x , y\right) &= y x\\ F_{18}\! \left(x , y , z\right) &= F_{17}\! \left(x , z\right) F_{19}\! \left(x , y , z\right)\\ F_{19}\! \left(x , y , z\right) &= \frac{-z F_{10}\! \left(x , 1, z\right)+y F_{10}\! \left(x , \frac{y}{z}, z\right)}{-z +y}\\ \end{align*}\)