Definition:Centered Hexagonal Number

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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.