Definition:Hexagonal Number/Definition 2

Definition
Hexagonal numbers are defined as:
 * $\displaystyle H_n = \sum_{i \mathop = 1}^n \left({4 \left({i - 1}\right) + 1}\right) = 1 + 5 + \cdots + \left({4 \left({n-2}\right) + 1}\right) + \left({4 \left({n - 1}\right) + 1}\right)$

for $n = 1, 2, 3, \ldots$

Also see

 * Equivalence of Definitions of Hexagonal Number