\begin{definition}[Definition:Hexagonal Number/Definition 1]
Hexagonal numbers are defined as:
:$H_n = \begin{cases}
0 & : n = 0 \\
H_{n-1} + 4 \left({n-1}\right) + 1 & : n > 0 \end{cases}$
for $n = 1, 2, 3, \ldots$
\end{definition}