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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