# Definition:Centered Hexagonal Number

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## Definition

A **centered hexagonal number** is a figurate number which is represented by:

- a point in the center
- all other points surrounding the center at the points of a triangular lattice.

## Examples of Centered Hexagonal Numbers

The first few centered hexagonal numbers are as follows:

### Sequence of Centered Hexagonal Numbers

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

- $1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, 469, 547, 631, 721, 817, 919, \ldots$

## Also known as

A **centered hexagonal number** can also be referred to as a **hex number**.

However, as this can be confused with a **hexagonal number** this neat and compact term is discouraged on $\mathsf{Pr} \infty \mathsf{fWiki}$.

## Also see

- Results about
**centered hexagonal numbers**can be found here.

## Linguistic Note

A **centered hexagonal number** is rendered in British English as **centred hexagonal number**, on account of the British spelling of **centre**.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $19$ - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $37$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $19$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $37$