Definition:Pentagonal Number/Definition 1

Definition
Pentagonal numbers are defined as
 * $P_n = \begin{cases}

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

Also see

 * Equivalence of Definitions of Pentagonal Number