Leetcode 2929. Distribute Candies Among Children II

Count the number of nonnegative integer triples (a,b,c) with a + b + c = n and 0 ≤ a,b,c ≤ limit. With n, limit up to 1e6, the task is to compute this count efficiently using combinatorics (stars-and-bars with inclusion–exclusion) rather than brute force.