Definition:Pentagonal Number/Definition 1

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

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

Also see

 * Equivalence of Definitions of Pentagonal Number