hexagonal number

A is a figurate number that represents a hexagon. The hexagonal number for $n$ is given by the formula $n(2n-1)$. 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, etc., listed in A000384 of Sloane’s OEIS. Like a triangular number, the base 10 digital root of a hexagonal number can only be 1, 3, 6 or 9. Every hexagonal number is a triangular number, but not every triangular number is a hexagonal number.

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 should not be confused with centered hexagonal numbers, which model the standard packaging of Vienna sausages.

Title hexagonal number HexagonalNumber 2013-03-22 17:50:51 2013-03-22 17:50:51 PrimeFan (13766) PrimeFan (13766) 4 PrimeFan (13766) Definition msc 11D09