Definition:Hexagonal Number/Definition 2

Definition

Hexagonal numbers are defined as:

$\ds H_n = \sum_{i \mathop = 1}^n \paren {4 \paren {i - 1} + 1} = 1 + 5 + \cdots + \paren {4 \paren {n - 2} + 1} + \paren {4 \paren {n - 1} + 1}$

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

Examples of Hexagonal Numbers

The first few hexagonal numbers are as follows:

Sequence of Hexagonal Numbers

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

$0, 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, \ldots$

Also see

• Equivalence of Definitions of Hexagonal Number