BALKAN 2004 Problem 1

The sequence $\{a_n\}_{n\geq 0}$ of real numbers satisfies the relation: $$a_{m+n} + a_{m-n} - m + n -1 = \frac12 (a_{2m} + a_{2n})$$ for all non-negative integers $m$ and $n$ , $m \ge n$ . If $a_1 = 3$ find $a_{2004}$ .