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:
Sequence of Heptagonal Numbers
The sequence of heptagonal numbers, for $n \in \Z_{\ge 0}$, begins:
- $0, 1, 7, 18, 34, 55, 81, 112, 148, 189, 235, 286, 342, 403, 469, 540, \ldots$