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A 'hexagonal number' is a figurate number, the number of points in the union of ''n'' hexagons with partly two common sides, as shown in [1]. The hexagonal number for ''n'' is given by the formula 2''n''²−''n''. The first few hexagonal numbers are:
1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378, 435, 496, 561, 630, 703, 780, 861, 946
Every hexagonal number is a triangular number, but not every triangular number is a hexagonal number. Like a triangular number, the digital root in base 10 of a hexagonal number can only be 1, 3, 6, or 9.
Any integer greater than 1791 can be expressed as a sum of at most four hexagonal numbers, a fact proven by Adrien-Marie Legendre in 1830.
Hexagonal numbers can be rearranged into rectangular numbers ''n'' long and 2''n''−1 tall (or vice versa).
Hexagonal numbers should not be confused with centered hexagonal numbers, which model the standard packaging of Vienna sausages. To avoid ambiguity, hexagonal numbers are sometimes called "cornered hexagonal numbers".

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★ Mathworld entry on Hexagonal Number