Let a0, a1, a2, a3, . . . be a sequence of integers such that a0 = 3, a1 = 10, a2 = 38, and an+3 =30·an − 31·an+1 + 10·an+2, for all integers n≥0 Prove that for all integers n≥0,a =2n+3n+5n.

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