\begin{definition}[Definition:Hexagonal Number/Definition 2]
Hexagonal numbers are defined as:
:$\ds H_n = \sum_{i \mathop = 1}^n \paren {4 \paren {i - 1} + 1} = 1 + 5 + \cdots + \paren {4 \paren {n - 2} + 1} + \paren {4 \paren {n - 1} + 1}$
for $n = 1, 2, 3, \ldots$
\end{definition}