# End-of-the-year complex recurrence problem

Algebra Level 5

$2a_n=(1-\mathrm{i}\sqrt{3}-2\mathrm{i})a_{n-1}+(\sqrt{3}+\mathrm{i})a_{n-2}$

$a_0=0, a_1=1-\mathrm{i}\sqrt{3}+2\mathrm{i}$

$$|a_{2015}|^2$$ can be written as $$r - s\sqrt{t}$$, where $$r$$ and $$s$$ are positive integers and $$t$$ is a square-free positive integer. What is $$r + s + t$$?

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