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}$

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}$

Also see

 * Equivalence of Definitions of Lucas Numbers