Definition:Centered Hexagonal Number

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.

The first few centered hexagonal numbers are as follows:

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

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

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 $\mathsf{Pr} \infty \mathsf{fWiki}$.

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