# Definition:Lucas Number/Definition 1

## Definition

The Lucas numbers are a sequence which is formally defined recursively as:

$L_n = \begin{cases} 2 & : n = 0 \\ 1 & : n = 1 \\ L_{n - 1} + L_{n - 2} & : \text{otherwise} \end{cases}$

### Sequence

The Lucas sequence begins:

$2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, \ldots$

## Also defined as

Some sources start the sequence at $1$:

$L_n = \begin{cases} 1 & : n = 1 \\ 3 & : n = 2 \\ L_{n - 1} + L_{n - 2} & : \text{otherwise} \end{cases}$

## Source of Name

This entry was named for François Édouard Anatole Lucas.