hexagonal number

Fetched 2026-10-26 (cache).

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Noun

1. {{lb|en|mathematics}} The number of dots in a figure made up of partially overlapping dotted regular [[hexagon]]s (6''k'' dots arranged into a regular hexagon) of [[perimeter]] 6''k'' for ''k'' = 1 ... ''n'' which grow out of a common vertex (and two shared or partially shared sides); a.k.a. “cornered hexagonal number”; <math> H_{n+1} = 6 \Delta_n - n^2 + 1 </math> where <math>\Delta_n</math> denotes the ''n''^th [[triangular number]].
2. {{lb|en|mathematics}} The number of dots in a figure made up of regular dotted hexagons (of perimeter 6''k'' for ''k'' = 1 ... ''n'') arranged [[concentrically]] around an extra dot at their common center; a.k.a. “centered hexagonal number”; <math>H_{n+1} = 1 + 6 \Delta_n </math>.

Source: Wiktionary · CC BY-SA 4.0 (Wiktionary dump) · cached copy, not a rewrite.