Definition:Octagonal Number/Definition 2

Definition
Octagonal numbers are defined as:
 * $\displaystyle O_n = \sum_{i \mathop = 1}^n \left({6 i - 5}\right) = 1 + 7 + \cdots + \left({6 \left({n - 1}\right) - 5}\right) + \left({6 n - 5}\right)$

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

Also see

 * Equivalence of Definitions of Octagonal Number