Av(12453, 12543, 14253, 21453, 21543, 24153, 41253, 42153)
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Counting Sequence
1, 1, 2, 6, 24, 112, 568, 3032, 16768, 95200, 551616, 3248704, 19389824, 117021824, 712934784, ...
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This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 26 rules.

Found on January 22, 2022.

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