Definition:Octagonal Number/Definition 1

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Definition

Octagonal numbers are defined as:

$O_n = \begin{cases} 0 & : n = 0 \\ O_{n - 1} + 6 n - 5 & : n > 0 \end{cases}$

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


Examples of Octagonal Numbers

The first few octagonal numbers are as follows:


OctagonNumbers.png


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