Definition:Generalized Pentagonal Number/Definition 2

Definition
The generalized pentagonal numbers are the integers obtained from formula:
 * $GP \left({n}\right) = \begin{cases} \dfrac {m \left({3 m + 1}\right)} 2 & : n = 2 m \\

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

Also see

 * Equivalence of Definitions of Generalized Pentagonal Number