Definition:Octagonal Number/Definition 2
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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:
- $0, 1, 8, 21, 40, 65, 96, 133, 176, 225, 280, 341, \ldots$