IMO Shortlist 2001 problem C1


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2. travnja 2012.
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Let A = (a_1, a_2, \ldots, a_{2001}) be a sequence of positive integers. Let m be the number of 3-element subsequences (a_i,a_j,a_k) with 1 \leq i < j < k \leq 2001, such that a_j = a_i + 1 and a_k = a_j + 1. Considering all such sequences A, find the greatest value of m.
Izvor: Međunarodna matematička olimpijada, shortlist 2001