Av(12453, 14253, 41253)
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Counting Sequence
1, 1, 2, 6, 24, 117, 652, 3988, 26112, 180126, 1295090, 9631656, 73676572, 577180996, 4615090192, ...
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This specification was found using the strategy pack "Row And Col Placements Tracked Fusion" and has 25 rules.

Found on January 22, 2022.

Finding the specification took 129 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) &= 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_{14}\! \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_{7}\! \left(x \right)\\ F_{13}\! \left(x , y , z\right) &= \frac{F_{11}\! \left(x , y , z\right) y -F_{11}\! \left(x , 1, z\right)}{-1+y}\\ F_{14}\! \left(x , y , z\right) &= F_{15}\! \left(x , y , z\right) F_{17}\! \left(x , y\right)\\ F_{15}\! \left(x , y , z\right) &= \frac{F_{16}\! \left(x , y , 1\right) y -F_{16}\! \left(x , y , \frac{z}{y}\right) z}{-z +y}\\ F_{16}\! \left(x , y , z\right) &= F_{11}\! \left(x , y , y z \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) &= F_{11}\! \left(x , y , z\right)+F_{20}\! \left(x , y , z\right)\\ F_{20}\! \left(x , y , z\right) &= F_{21}\! \left(x , y , z\right)\\ F_{21}\! \left(x , y , z\right) &= F_{17}\! \left(x , z\right) F_{19}\! \left(x , y , z\right) F_{22}\! \left(x , z\right)\\ F_{22}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{23}\! \left(x , y\right)\\ F_{23}\! \left(x , y\right) &= F_{24}\! \left(x , y\right)\\ F_{24}\! \left(x , y\right) &= F_{22}\! \left(x , y\right)^{2} F_{17}\! \left(x , y\right)\\ \end{align*}\)