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March 26, 2017

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Suppose a0, a1, a2 ,... is a sequence defined recursively as follows:

a1 = 1, a2 = 2, a3 = 3 and ak = ak-1 + ak-2 + ak-3 for all integers k > 3.

Use strong induction to show that an < 2n for all integers n ≥ 1.

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