###### Av(12345, 12354, 12435, 13245, 13254, 13425, 13452, 13524, 13542, 14235, 14325, 14352, 21345, 21354, 21435, 24135, 41235, 41325, 41352, 42135)
Counting Sequence
1, 1, 2, 6, 24, 100, 434, 1934, 8828, 41066, 194024, 928503, 4491346, 21924868, 107873194, ...

### This specification was found using the strategy pack "Row Placements Tracked Fusion Expand Verified" and has 22 rules.

Found on November 05, 2021.

Finding the specification took 11 seconds.

Copy to clipboard:

View tree on standalone page.

Copy 22 equations to clipboard:
\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_{18}\! \left(x \right) F_{3}\! \left(x \right)\\ F_{3}\! \left(x \right) &= F_{1}\! \left(x \right)+F_{21}\! \left(x \right)+F_{4}\! \left(x \right)\\ F_{4}\! \left(x \right) &= F_{18}\! \left(x \right) F_{5}\! \left(x \right)\\ F_{5}\! \left(x \right) &= F_{6}\! \left(x , 1\right)\\ F_{6}\! \left(x , y\right) &= -\frac{-y F_{7}\! \left(x , y\right)+F_{7}\! \left(x , 1\right)}{-1+y}\\ F_{7}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{8}\! \left(x , y\right)\\ F_{8}\! \left(x , y\right) &= F_{9}\! \left(x , y\right)\\ F_{9}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{11}\! \left(x , y\right) F_{7}\! \left(x , y\right)\\ F_{10}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)\\ F_{11}\! \left(x , y\right) &= y x\\ F_{12}\! \left(x , y\right) &= F_{13}\! \left(x , y\right) F_{18}\! \left(x \right)\\ F_{13}\! \left(x , y\right) &= F_{1}\! \left(x \right)+F_{14}\! \left(x , y\right)+F_{16}\! \left(x , y\right)+F_{19}\! \left(x , y\right)\\ F_{14}\! \left(x , y\right) &= F_{15}\! \left(x , y\right)\\ F_{15}\! \left(x , y\right) &= F_{10}\! \left(x , y\right) F_{11}\! \left(x , y\right) F_{6}\! \left(x , y\right)\\ F_{16}\! \left(x , y\right) &= F_{17}\! \left(x , y\right) F_{18}\! \left(x \right)\\ F_{17}\! \left(x , y\right) &= -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}\\ F_{18}\! \left(x \right) &= x\\ F_{19}\! \left(x , y\right) &= F_{18}\! \left(x \right) F_{20}\! \left(x , y\right)\\ F_{20}\! \left(x , y\right) &= -\frac{-y F_{13}\! \left(x , y\right)+F_{13}\! \left(x , 1\right)}{-1+y}\\ F_{21}\! \left(x \right) &= F_{12}\! \left(x , 1\right)\\ \end{align*}

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

Found on January 23, 2022.

Finding the specification took 8 seconds.

Copy to clipboard: