AIMO 2015 Q9

A sequence is formed by the following rules:

\(s_1 = a, s_2 = b\) and \(s_{n+2} = s_{n+1} + (-1)^n s_n\) for all \(n \geq 1\).

If \(a=3\) and \(b < 1000\), what is the largest integral value of \(b\) for which 2015 is a member of the sequence?

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