###### Av(13452, 13524, 13542, 14352, 14532, 15324, 15342, 15432, 31452, 31524, 31542, 34152, 41352, 41532, 43152)
Counting Sequence
1, 1, 2, 6, 24, 105, 474, 2179, 10200, 48569, 234733, 1148712, 5680670, 28343816, 142513020, ...

### This specification was found using the strategy pack "Row Placements Tracked Fusion" and has 33 rules.

Found on January 22, 2022.

Finding the specification took 41 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{F_{4}\! \left(x , y\right) y -F_{4}\! \left(x , 1\right)}{-1+y}\\ F_{7}\! \left(x \right) &= x\\ F_{8}\! \left(x , y\right) &= F_{25}\! \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_{1}\! \left(x \right)+F_{11}\! \left(x , y , z\right)+F_{26}\! \left(x , y , z\right)+F_{30}\! \left(x , y , z\right)\\ F_{11}\! \left(x , y , z\right) &= F_{12}\! \left(x , y , z\right)\\ F_{12}\! \left(x , y , z\right) &= F_{13}\! \left(x , y z , z\right)\\ F_{13}\! \left(x , y , z\right) &= F_{14}\! \left(x , y , z\right) F_{7}\! \left(x \right)\\ F_{14}\! \left(x , y , z\right) &= F_{15}\! \left(x , y , z\right)+F_{6}\! \left(x , z\right)\\ F_{15}\! \left(x , y , z\right) &= F_{16}\! \left(x , z\right) F_{25}\! \left(x , y\right)\\ F_{16}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{17}\! \left(x , y\right)+F_{19}\! \left(x , y\right)+F_{23}\! \left(x , y\right)\\ F_{17}\! \left(x , y\right) &= F_{18}\! \left(x , y\right)\\ F_{18}\! \left(x , y\right) &= F_{13}\! \left(x , 1, y\right)\\ F_{19}\! \left(x , y\right) &= F_{20}\! \left(x , y\right)\\ F_{20}\! \left(x , y\right) &= F_{21}\! \left(x \right) F_{4}\! \left(x , y\right) F_{7}\! \left(x \right)\\ F_{21}\! \left(x \right) &= F_{22}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{22}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{7}\! \left(x \right)\\ F_{23}\! \left(x , y\right) &= F_{24}\! \left(x , y\right) F_{25}\! \left(x , y\right)\\ F_{24}\! \left(x , y\right) &= \frac{F_{10}\! \left(x , 1, y\right) y -F_{10}\! \left(x , \frac{1}{y}, y\right)}{-1+y}\\ F_{25}\! \left(x , y\right) &= y x\\ F_{26}\! \left(x , y , z\right) &= F_{27}\! \left(x , y , z\right)\\ F_{27}\! \left(x , y , z\right) &= F_{25}\! \left(x , z\right) F_{28}\! \left(x , z\right) F_{4}\! \left(x , z\right)\\ F_{28}\! \left(x , y\right) &= F_{25}\! \left(x , y\right)+F_{29}\! \left(x , y\right)\\ F_{29}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{25}\! \left(x , y\right)\\ F_{30}\! \left(x , y , z\right) &= F_{31}\! \left(x , y z , z\right)\\ F_{31}\! \left(x , y , z\right) &= F_{25}\! \left(x , z\right) F_{32}\! \left(x , y , z\right)\\ F_{32}\! \left(x , y , z\right) &= \frac{-F_{10}\! \left(x , 1, z\right) z +F_{10}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}\\ \end{align*}