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balkan sequence

Source: Balkan Math Olympiad BkMO 2004, problem 1

May 7, 2004
inductionalgebra proposedalgebra

Problem Statement

The sequence {an}n≥0\{a_n\}_{n\geq 0} of real numbers satisfies the relation: am+n+am−n−m+n−1=12(a2m+a2n) a_{m+n} + a_{m-n} - m + n -1 = \frac12 (a_{2m} + a_{2n}) for all non-negative integers mm and nn, m≥nm \ge n. If a1=3a_1 = 3 find a2004a_{2004}.
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