How many points with integer coordinates lie on at least one of these paths?

contest-math combinatorics coordinate-systems

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.

enter image description here

Related

Let $ \Omega _1, \Omega _2$ be domains and let $f:\Omega _1\rightarrow \Omega _2$ be biholomorphism. Is this $f$ an open function?
Conditions for a linearly independent sequence with dense linear span to be a Schauder basis for a Banach space
Largest eigenvalue of entry-wise absolute value of a matrix w.r.t. original maximum eigenvalue [duplicate]
Saving and loading an image from localStorage
Authenticating the username, password by using filters in Java (contacting with database)
Justify text in an Android app using a WebView but presenting a TextView-like interface?
How does Keras 1d convolution layer work with word embeddings - text classification problem? (Filters, kernel size, and all hyperparameter)
UITableView with Multiple Sections using Realm and Swift
Auto Mobile Site Redirect
Correct naming structure for CodeIgniter
How to handle the pylint message: Warning: Method could be a function
Turn off sound in iPhone Simulator