One of the most famous recursively defined sequences is the Fibonacci sequence. In 1202, the Italian mathematician Leonardo da Pisa, also called Fibonacci, proposed the following model for rabbit population growth. Suppose that every month each mature pair of rabbits in the population produces a new pair that begins reproducing after two months, and also suppose that no rabbits die. Beginning with one pair of newborn rabbits, the population can be modeled by the following recursively defined sequence:
a1 = 1, a2 = 1, an = an-1 + an-2, for n ‰¥ 3,
where an is the total number of pairs of rabbits in month n. Find the first 7 terms of the Fibonacci sequence.