A bunny problem, or a bunny challenge

Depends on you.

This spring a student (her real name is not Nancy) posed a problem for herself:  Starting with one newborn pair of bunnies, after one month the pair matures, after the next month the pair produces a new pair, and continues doing so every subsequent month, until after six months the pair dies. Describe the number of living bunnies after n months.

Problem

If you are not sure how this is going to work, the problem is for you. See if you can figure out how many bunnies will be around for the first few months, and then see if you can describe the relationship mathematically.

Challenge

If this set up is not a problem for you (if you can write the recurrence relation directly from the problem set-up), then I have a challenge for you:  what interesting new problem can you create out of Nancy’s problem that would take someone who can already write the recurrence relation and make them think?