The first formula

The Fibonacci sequence
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...

The Fibonacci sequence can be obtained without the rabbit model. In order to present this method more clearly, I will introduce some notation.

Let Fn represent the nth term in the Fibonacci sequence.
**Important: Term number refers to the position of the term in the pattern.**
Example: The seventh term is 13 and will be represented as F7.

Any term in the Fibonacci sequence can be found by adding the two previous terms. Using the notation, we have Fn = Fn-1 + Fn-2.


The 3-month life-span sequence
1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, ...

The 3-month life-span sequence can also be obtained without the rabbit model.

Let Tn represent the nth term in the 3-month life-span sequence. Because the first three months are the same as the Fibonacci model, they can be found with the same formula.
For T1, T2, and T3: Tn = Tn-1 + Tn-2.

Any term after the first three can be found by adding the two terms previous to the previous term. Using the notation, we have Tn = Tn-2 + Tn-3.