Definition:Pentagonal Number/Definition 2

Definition
Pentagonal numbers are defined as
 * $\displaystyle P_n = \sum_{i \mathop = 1}^n \left({3 \left({i - 1}\right) + 1}\right) = 1 + 4 + \cdots + \left({3 \left({n-2}\right) + 1}\right) + \left({3 \left({n-1}\right) + 1}\right)$.

for $n = 1, 2, 3, \ldots$

Also see

 * Equivalence of Definitions of Pentagonal Number