###### Av(12453, 12543, 14253, 14523, 14532, 15243, 15423, 15432, 21453, 21543, 24153, 41253, 41523, 41532, 42153)
Counting Sequence
1, 1, 2, 6, 24, 105, 475, 2195, 10343, 49581, 241184, 1187790, 5911018, 29679420, 150172468, ...

### This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 40 rules.

Found on January 23, 2022.

Finding the specification took 49 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_{37}\! \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_{24}\! \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{F_{6}\! \left(x , y\right) y -F_{6}\! \left(x , 1\right)}{-1+y}\\ F_{9}\! \left(x \right) &= x\\ F_{10}\! \left(x , y\right) &= F_{11}\! \left(x , y\right) F_{9}\! \left(x \right)\\ F_{11}\! \left(x , y\right) &= \frac{F_{12}\! \left(x , y\right) y -F_{12}\! \left(x , 1\right)}{-1+y}\\ F_{12}\! \left(x , y\right) &= \frac{F_{13}\! \left(x , y\right) y -F_{13}\! \left(x , 1\right)}{-1+y}\\ F_{13}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{15}\! \left(x , y\right)\\ F_{14}\! \left(x , y\right) &= F_{6}\! \left(x , y\right) F_{9}\! \left(x \right)\\ F_{15}\! \left(x , y\right) &= F_{16}\! \left(x , y\right) F_{20}\! \left(x , y\right)\\ F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , 1, y\right)\\ F_{17}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , z\right)+F_{18}\! \left(x , y , z\right)+F_{21}\! \left(x , y , z\right)\\ F_{18}\! \left(x , y , z\right) &= F_{19}\! \left(x , y z , z\right)\\ F_{19}\! \left(x , y , z\right) &= F_{13}\! \left(x , z\right) F_{20}\! \left(x , y\right)\\ F_{20}\! \left(x , y\right) &= y x\\ F_{21}\! \left(x , y , z\right) &= F_{22}\! \left(x , y z , z\right)\\ F_{22}\! \left(x , y , z\right) &= F_{20}\! \left(x , z\right) F_{23}\! \left(x , y , z\right)\\ F_{23}\! \left(x , y , z\right) &= \frac{-F_{17}\! \left(x , 1, z\right) z +F_{17}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}\\ F_{24}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\ F_{25}\! \left(x , y\right) &= F_{26}\! \left(x , 1, y\right)\\ F_{26}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{27}\! \left(x , z\right)+F_{33}\! \left(x , y , z\right)+F_{35}\! \left(x , y , z\right)+F_{7}\! \left(x , z\right)\\ F_{27}\! \left(x , y\right) &= F_{28}\! \left(x , y\right) F_{9}\! \left(x \right)\\ F_{28}\! \left(x , y\right) &= \frac{F_{29}\! \left(x , y\right) y -F_{29}\! \left(x , 1\right)}{-1+y}\\ F_{29}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{30}\! \left(x , y\right)+F_{31}\! \left(x , y\right)\\ F_{30}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{9}\! \left(x \right)\\ F_{31}\! \left(x , y\right) &= F_{20}\! \left(x , y\right) F_{32}\! \left(x , y\right)\\ F_{32}\! \left(x , y\right) &= \frac{F_{17}\! \left(x , 1, y\right) y -F_{17}\! \left(x , \frac{1}{y}, y\right)}{-1+y}\\ F_{33}\! \left(x , y , z\right) &= F_{34}\! \left(x , y z , z\right)\\ F_{34}\! \left(x , y , z\right) &= F_{20}\! \left(x , y\right) F_{29}\! \left(x , z\right)\\ F_{36}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , z\right)+F_{18}\! \left(x , y , z\right)+F_{30}\! \left(x , z\right)+F_{35}\! \left(x , y , z\right)\\ F_{36}\! \left(x , y , z\right) &= \frac{F_{17}\! \left(x , y , z\right) y z -F_{17}\! \left(x , \frac{1}{z}, z\right)}{y z -1}\\ F_{37}\! \left(x \right) &= F_{38}\! \left(x \right) F_{9}\! \left(x \right)\\ F_{38}\! \left(x \right) &= F_{39}\! \left(x , 1\right)\\ F_{39}\! \left(x , y\right) &= \frac{F_{13}\! \left(x , y\right) y -F_{13}\! \left(x , 1\right)}{-1+y}\\ \end{align*}