# Definition:Lucas Number/Definition 2

## Definition

The Lucas numbers are a sequence defined as:

$L_n = F_{n - 1} + F_{n + 1}$

where $F_k$ is the $k$th Fibonacci number.

### Sequence

The Lucas sequence begins:

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

## Source of Name

This entry was named for François Édouard Anatole Lucas.