Definition:Octagonal Number/Definition 1

Definition
Octagonal numbers are defined as:
 * $O_n = \begin{cases}

0 & : n = 0 \\ O_{n - 1} + 6 \left({n - 1}\right) + 1 & : n > 0 \end{cases}$ for $n = 1, 2, 3, \ldots$

Also see

 * Equivalence of Definitions of Octagonal Number