Definition:Hexagonal Number/Definition 3

Definition

Hexagonal numbers are defined as the sequence:

$\forall n \in \N: H_n = \map P {6, n} = \begin{cases}

0 & : n = 0 \\ \map P {6, n - 1} + 4 \paren {n - 1} + 1 & : n > 0 \end{cases}$ where $\map P {k, n}$ denotes the $k$-gonal numbers.

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