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

Examples of Octagonal Numbers

The first few octagonal numbers are as follows:

Sequence of Octagonal Numbers

The sequence of octagonal numbers, for $n \in \Z_{\ge 0}$, begins:

$0, 1, 8, 21, 40, 65, 96, 133, 176, 225, 280, 341, \ldots$

Also see

• Equivalence of Definitions of Octagonal Number