I have been given a problem that at first seemed quite trivial but on further inspection seems to be quite hard. If n is a non-negative integer, in how many ways is it possible to write
for non-negative integers a, b, c.
clearly, if i fix some 0<c<floor(n/3), then i have n-3c choices for a and b, but i'm not sure how to proceed. I also thought it could be calculated using a recurrence relation, but I'm particularly rusty in that area of combinatorics. Any help would be greatly appreciated.