###### Av(1432)
Counting Sequence
1, 1, 2, 6, 23, 103, 513, 2761, 15767, 94359, 586590, 3763290, 24792705, 167078577, 1148208090, ...
Heatmap

To create this heatmap, we sampled 1,000,000 permutations of length 300 uniformly at random. The color of the point $$(i, j)$$ represents how many permutations have value $$j$$ at index $$i$$ (darker = more).

### This specification was found using the strategy pack "Col Placements Tracked Fusion" and has 20 rules.

Found on November 03, 2021.

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