Hexagonal number

English

Noun

1. Template:Lb 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”; $H_{n+1}=6{\mathrm{\Delta }}_n-n^2+1$ where ${\mathrm{\Delta }}_n$ denotes the n^th triangular number.

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2. Template:Lb 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”; $H_{n+1}=1+6{\mathrm{\Delta }}_n$.

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Translations

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