How many points with integer coordinates lie on at least one of these paths? A bug travels in the coordinate plane, moving only along the lines that are parallel to the $x$-axis or $y$-axis. Let $A = (-3, 2)$ and $B = (3, -2)$. Consider all possible paths of the bug from $A$ to $B$ of length at most $20$. How many points with integer coordinates lie on at least one of these paths?


All coordinates on or within the outer border of points shown below, could be reached. I make it $195$ coordinates.

