First, we start month 1 with one newly born pair, so

There is also 1 pair only during month 2 since they are not mature enough to have "babies" yet, so

Since we assume they mate at age 2 months then a new pair is born at
the start of month 3. So, after the second month, how many rabbits will
there be? i.e. What is f(n)?

All the rabbits from the previous month (there will be f(n-1) of them)
survive, so there are at least f(n-1) of them. How many new ones are
born? Any rabbit (pair) that was alive 2 months ago is now able to
produce a new pair, and we are assuming they always will and each
produces only 1 new pair per month.
Thus the number of newly born pairs is the same as the number of
pairs 2 alive 2 months ago: f(n-2). Since all the rabbit were alive last
month OR are newly born this month, we have:

© 1996-2006 Dr Ron Knott

updatedupdated 1 October 1999