@MartinR Without those additional conditions, it would be a typical example of stars and bars, so I would go immediately with combinatorics. I am not sure whether it is suitable also for the modified question.

Somebody else has some idea on suitable tags for: Solving $a_1+...+a_n=2011$ , $a_1\leq |a_2-a_3|, \ldots a_n\leq|a_1-a_2|$ with non-negative integers?