hexagonal number

Noun

 * 1)  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”; $$ H_{n+1} = 6 \Delta_n - n^2 + 1 $$ where $$\Delta_n$$ denotes the nth triangular number.
 * 2)  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”; $$H_{n+1} = 1 + 6 \Delta_n $$.
 * 1)  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”; $$H_{n+1} = 1 + 6 \Delta_n $$.
 * 1)  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”; $$H_{n+1} = 1 + 6 \Delta_n $$.

Translations

 * German: Sechseckszahl