Question: 1. The first two terms of the Fibonacci sequence are 1, 1. Find two other integers that, together with the recurrence an = an-1 + an-2, do not generate Fibonacci numbers. And, find two other integers that, together with the recurrence an = an-1 +an-2, do generate Fibonacci numbers. What kinds of integers do this?
2. Consider the sequence 0, 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176,... . Find both a recurrence and a closed form for this sequence.
3. Find a closed form for a0 = -1, a1 = 1, an = 2an-1 -an-2.