# A Sidewinder Sequence

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Consider the recursive sequence defined by

$a_1=1;\; a_2=2;\; a_n=a_{n-1}\sqrt{3}-a_{n-2}\text{ for }n\ge 3.$

Then $$a_{2014}$$ can be expressed as $$m+n\sqrt{p}$$, where m, n, and p are integers, and p is positive and square-free. Find $$m+n+p$$.

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