Av(12435, 12453)
Counting Sequence
1, 1, 2, 6, 24, 118, 672, 4256, 29176, 212586, 1625704, 12930160, 106242392, 897210996, 7756325952, ...

This specification was found using the strategy pack "Row And Col Placements Tracked Fusion" and has 21 rules.

Found on January 22, 2022.

Finding the specification took 208 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\right) &= F_{1}\! \left(x \right)+F_{6}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\ F_{6}\! \left(x , y\right) &= F_{3}\! \left(x \right) F_{7}\! \left(x , y\right)\\ F_{7}\! \left(x , y\right) &= \frac{y F_{5}\! \left(x , y\right)-F_{5}\! \left(x , 1\right)}{-1+y}\\ F_{8}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{9}\! \left(x , y\right)\\ F_{9}\! \left(x , y\right) &= y x\\ F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , 1, y\right)\\ F_{11}\! \left(x , y , z\right) &= F_{12}\! \left(x , y z , z\right)\\ F_{12}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{13}\! \left(x , y , z\right)+F_{15}\! \left(x , y , z\right)+F_{18}\! \left(x , z , y\right)\\ F_{13}\! \left(x , y , z\right) &= F_{14}\! \left(x , y , z\right) F_{3}\! \left(x \right)\\ F_{14}\! \left(x , y , z\right) &= \frac{y F_{12}\! \left(x , y , z\right)-F_{12}\! \left(x , 1, z\right)}{-1+y}\\ F_{15}\! \left(x , y , z\right) &= F_{16}\! \left(x , y , z\right) F_{9}\! \left(x , y\right)\\ F_{16}\! \left(x , y , z\right) &= \frac{y F_{17}\! \left(x , y , 1\right)-z F_{17}\! \left(x , y , \frac{z}{y}\right)}{-z +y}\\ F_{17}\! \left(x , y , z\right) &= F_{12}\! \left(x , y , y z \right)\\ F_{18}\! \left(x , y , z\right) &= F_{19}\! \left(x , z , y\right) F_{9}\! \left(x , y\right)\\ F_{19}\! \left(x , y , z\right) &= F_{12}\! \left(x , y , z\right)+F_{20}\! \left(x , y , z\right)\\ F_{12}\! \left(x , y , z\right) &= F_{20}\! \left(x , y , z\right)+F_{5}\! \left(x , y\right)\\ \end{align*}