Problem

Source: Argentina IMO TST 2006 problem 6

Tags: absolute value, combinatorics unsolved, combinatorics



Let $ n$ be a natural number, and we consider the sequence $ a_1, a_2 \ldots , a_{2n}$ where $ a_i \in (-1,0,1)$ If we make the sum of consecutive members of the sequence, starting from one with an odd index and finishing in one with and even index, the result is $ \le 2$ and $ \ge -2$ How many sequence are there satisfying this conditions?