###### Av(12354, 21354)
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 Placements Tracked Fusion Expand Verified" and has 28 rules.

Found on January 22, 2022.

Finding the specification took 12 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_{27}\! \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{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_{8}\! \left(x , y\right) F_{9}\! \left(x \right)\\ F_{11}\! \left(x , y\right) &= F_{12}\! \left(x , y\right) F_{25}\! \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_{1}\! \left(x \right)+F_{14}\! \left(x , y , z\right)+F_{16}\! \left(x , y , z\right)+F_{17}\! \left(x , y , z\right)+F_{26}\! \left(x , y , z\right)\\ F_{14}\! \left(x , y , z\right) &= F_{15}\! \left(x , y , z\right) F_{9}\! \left(x \right)\\ F_{15}\! \left(x , y , z\right) &= \frac{F_{13}\! \left(x , y , z\right) y z -F_{13}\! \left(x , \frac{1}{z}, z\right)}{y z -1}\\ F_{16}\! \left(x , y , z\right) &= F_{15}\! \left(x , y , z\right) F_{9}\! \left(x \right)\\ F_{17}\! \left(x , y , z\right) &= F_{18}\! \left(x , y z , z\right)\\ F_{19}\! \left(x , y , z\right) &= F_{1}\! \left(x \right)+F_{18}\! \left(x , y , z\right)+F_{20}\! \left(x , y , z\right)+F_{22}\! \left(x , y , z\right)+F_{23}\! \left(x , y , z\right)\\ F_{19}\! \left(x , y , z\right) &= \frac{F_{6}\! \left(x , y\right) y -F_{6}\! \left(x , z\right) z}{-z +y}\\ F_{20}\! \left(x , y , z\right) &= F_{21}\! \left(x , y , z\right) F_{9}\! \left(x \right)\\ F_{21}\! \left(x , y , z\right) &= \frac{F_{19}\! \left(x , y , z\right) y -F_{19}\! \left(x , 1, z\right)}{-1+y}\\ F_{22}\! \left(x , y , z\right) &= F_{21}\! \left(x , y , z\right) F_{9}\! \left(x \right)\\ F_{23}\! \left(x , y , z\right) &= F_{24}\! \left(x , y , z\right) F_{25}\! \left(x , z\right)\\ F_{24}\! \left(x , y , z\right) &= \frac{-F_{13}\! \left(x , 1, z\right) z +F_{13}\! \left(x , \frac{y}{z}, z\right) y}{-z +y}\\ F_{25}\! \left(x , y\right) &= y x\\ F_{26}\! \left(x , y , z\right) &= F_{13}\! \left(x , y , z\right) F_{25}\! \left(x , z\right)\\ F_{27}\! \left(x \right) &= F_{5}\! \left(x \right) F_{9}\! \left(x \right)\\ \end{align*}