Rabbit Problem

Classic Problem
Let there be a pair of rabbits.

For the purpose of this exercise, the following assumptions are made.

Rabbits take one month to reach an age at which they may give birth.

Every month thereafter, a breeding pair of rabbits produce one further pair of rabbits.

Rabbits never die and never stop being able to produce further rabbits.

How many pairs of rabbits will be produced from this single pair of rabbits after one year?

Also presented as
Some sources make the additional (often unspecified) assumption that at the start of the year the rabbits are newborn (that is, are not ready to breed).

Thus they only have their first pair of offspring in the $2$nd month.

In this case, it turns out that $R \left({n}\right) = F_{n + 1}$

Hence at the end of the year there are $233$ pairs of rabbits rather than $377$.