A centered hexagonal number (or hex number) counts dots in a hexagon with a dot at the centre and successive hexagonal rings around it: \(1, 7, 19, 37, 61, 91, 127, 169, \ldots\), given by \(3k(k-1)+1\). They're the pattern you get stacking cannonballs or packing circles in the densest 2-D arrangement, and the cross-section of a graphite/graphene lattice.
A lovely identity: the centered hexagonal numbers are exactly \(1\) plus six times the [[triangular]] numbers, and the partial sums of the centered hexagonal numbers are the cubes — \(1, 8, 27, 64, \ldots\) — so \(n^3\) is a sum of the first \(n\) hex numbers. They are distinct from the ordinary [[hexagonal]] numbers.