Question: Define the integer sequence a0, < a1 > a2, a3, . . ., recursively by 1) a0 = 1 a1 = 1, a2 = 1;

Define the integer sequence a0, < a1 > a2, a3, . . ., recursively by
1) a0 = 1 a1 = 1, a2 = 1; and
2) For n > 3, an = an-1 + an-3.
Prove that an+2 > (√2)n for all n > 0.

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