This problem is looking for the number of vertices on the hexagonal grid inside the circle of radius r. The center of the hexagon is not counted as a point for this problem, and this is true for every hexagon inside the circle.

Welcome back, Richard. I have a question on the scoring - Would (()) count as one (Left 2 and Right 3) or two (L1 and R4, and L2 and R3)? I guess the more general question is can you have a balanced string inside of another balanced string?

For n=64, wouldn't the correct answer be 6, since 64 itself is also even? If you're not counting the number itself as a divisor, then the answers above for n=14 and n=68 would be incorrect.