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Find the number of sequences

Source: Argentina IMO TST 2006 problem 6

August 27, 2009
absolute valuecombinatorics unsolvedcombinatorics

Problem Statement

Let n n be a natural number, and we consider the sequence a1,a2…,a2n a_1, a_2 \ldots , a_{2n} where a_i \in (\minus{}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 ≤2 \le 2 and \ge \minus{}2 How many sequence are there satisfying this conditions?
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