In mathematics and combinatorics, a centered hexagonal number, or centered hexagon number, is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice. The following figures illustrate this arrangement for the first four centered hexagonal numbers:

Centered hexagonal numbers should not be confused with cornered hexagonal numbers, which are figurate numbers in which the associated hexagons share a vertex.

The sequence of hexagonal numbers starts out as follows (sequence A003215 in the OEIS):

The nth centered hexagonal number is given by the formula

Expressing the formula as

shows that the centered hexagonal number for n is 1 more than 6 times the (n − 1)th triangular number.

In the opposite direction, the index n corresponding to the centered hexagonal number ${\displaystyle H=H(n)}$ can be calculated using the formula

This can be used as a test for whether a number H is centered hexagonal: it will be if and only if the above expression is an integer.