Definition:Hexagonal Number/Definition 1

Definition
Hexagonal numbers are defined as:
 * $H_n = \begin{cases}

0 & : n = 0 \\ H_{n - 1} + 4 \paren {n - 1} + 1 & : n > 0 \end{cases}$ for $n = 1, 2, 3, \ldots$

Also see

 * Equivalence of Definitions of Hexagonal Number