A recurrence relation

Probability Level 3

Let a0,a1,a_0,a_1,\cdots be a sequence defined by a0=7a_0=7, a1=8a_1=8, and, for all n2n\ge 2, an=5an16an2a_n=5a_{n-1}-6a_{n-2} Find the remainder when a2014a_{2014} is divided by 1000.

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