Definition:Fibonacci String

Definition
Consider the alphabet $\left\{ {\text {a}, \text {b} }\right\}$.

For all $n \in \Z_{>0}$, let $S_n$ be the (finite) string formed as:


 * $S_n = \begin{cases} \text {a} & : n = 1 \\

\text {b} & : n = 2 \\ S_{n - 1} S_{n - 2} & : n > 2 \end{cases}$

where $S_{n - 1} S_{n - 2}$ denotes that $S_{n - 1}$ and $S_{n - 2}$ are concatenated.

The terms of the sequence $\left\langle{S_n}\right\rangle$ are Fibonacci strings.

Also defined as
The specific alphabet used is immaterial.

Different sources use different alphabets; $\left\{ {0, 1}\right\}$ is another common one.

Different starting values are also sometimes seen, for example:
 * $S_0 = 0, S_1 = 01$

uses $\left\{ {\text {a}, \text {b} }\right\}$ and the starting values given, by preference and for internal consistency.

Also known as
Some sources refer to a Fibonacci string as a Fibonacci word.