Question: Recursively define the sequence an = 2an-1 - an-2 + 2, for n > 2, a0 = 1, a1 = 2. What is the order

Recursively define the sequence an = 2an-1 - an-2 + 2, for n > 2, a0 = 1, a1 = 2.

  1. What is the order of the given recurrence equation.
  2. Calculate the first 6 terms of the sequence
  3. Show that an = n2 + 1 for any n in {0, 1, 2 ...}
  4. Use induction to prove the formula in part (c)

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