Definition:Hexagonal Number/Definition 1

Definition

Hexagonal numbers are defined as:

$H_n = \begin{cases}

0 & : n = 0 \\ H_{n - 1} + 4 \paren {n - 1} + 1 & : n > 0 \end{cases}$

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