Definition:Octagonal Number/Definition 2

Definition
Octagonal numbers are defined as:
 * $\ds O_n = \sum_{i \mathop = 1}^n \paren {6 i - 5} = 1 + 7 + \cdots + \paren {6 \paren {n - 1} - 5} + \paren {6 n - 5}$

for $n = 1, 2, 3, \ldots$

Also see

 * Equivalence of Definitions of Octagonal Number