\begin{definition}[Definition:Pentagonal Number/Definition 1]
Pentagonal numbers are defined as
:$P_n = \begin{cases}
0 & : n = 0 \\
P_{n-1} + 3 n - 2 & : n > 0 \end{cases}$
for $n = 1, 2, 3, \ldots$
\end{definition}