hexagonal number

hexagonal number (plural hexagonal numbers)

1. (mathematics) The number of dots in a figure made up of partially overlapping dotted regular hexagons (6k dots arranged into a regular hexagon) of perimeter 6k for k = 1 ... n which grow out of a common vertex (and two shared or partially shared sides); a.k.a. “cornered hexagonal number”; ${\displaystyle H_{n+1}=6\Delta _{n}-n^{2}+1}$ where ${\displaystyle \Delta _{n}}$ denotes the n^th triangular number.

   Hypernym: triangular number

   Hyponym: even perfect number

2. (mathematics) The number of dots in a figure made up of regular dotted hexagons (of perimeter 6k for k = 1 ... n) arranged concentrically around an extra dot at their common center; a.k.a. “centered hexagonal number”; ${\displaystyle H_{n+1}=1+6\Delta _{n}}$.

• figurate number