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Suppose that a sequence an (n = 0,1,2,...) is defined recursively by a0 = 1, a1...

  1. Suppose that a sequence an (n = 0,1,2,...) is defined recursively by a0 = 1, a1 = 7, an = 4an−1 − 4an−2 (n ≥ 2). Prove by induction that an = (5n + 2)2n−1 for all n ≥ 0.

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