Definition:Heptagonal Number/Definition 2

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Definition

Heptagonal numbers are defined as:

$\ds H_n = \sum_{i \mathop = 1}^n \paren {5 i - 4} = 1 + 6 + \cdots + \paren {5 \paren {n - 1} - 4} + \paren {5 n - 4}$

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


Examples of Heptagonal Numbers

The first few heptagonal numbers are as follows:


File:HeptagonNumbers.png


Sequence of Heptagonal Numbers

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

$0, 1, 7, 18, 34, 55, 81, 112, 148, 189, 235, 286, 342, 403, 469, 540, \ldots$


Also see