Counting arrays with Euclidean distance at most 2 from a given binary array

Question

I have a binary array like this:

$$A = [0,1,0,0,1,0]\,.$$

I'm trying to find a way to calculate how many arrays of the same length exist that have a Euclidean distance of 2 or less from this array.

So, how many arrays of length 6 exist where

$$\sqrt{\Sigma(A_{_i} - B_{_i})^2}\leq 2\,?$$

I'm trying to find or create a formula that takes an array like above and outputs a count of how many possible binary arrays exist that fit the conditions of the above formula.

I've looked online for a formula without success.