Using mathematics to estimate pet populations has occurred for many years. The famous sequence of numbers, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …, in which each new number is the sum of the previous two, was given as the answer to the following problem, stated by Leonardo Pisano Fibonacci in his Liber Abaci:

What is the number of pairs of rabbits at the beginning of each month if a single pair of newly born rabbits is put into an enclosure at the beginning of January and if each pair breeds a new pair at the beginning of the second month following birth and an additional pair at the beginning of each month thereafter?

The first twelve numbers of the Fibonacci series give the answer for the first year. The sum of these first twelve is 376. At least in these theoretical circumstances, one pair of rabbits results in close to 400 rabbits after...