Definition:Pentagonal Number/Definition 3

Definition
Pentagonal numbers are defined as the sequence:
 * $\forall n \in \N: P_n = \map P {5, n} = \begin {cases}

0 & : n = 0 \\ \map P {5, n - 1} + 3 \paren {n - 1} + 1 & : n > 0 \end {cases}$ where $\map P {k, n}$ denotes the $k$-gonal numbers.

Also see

 * Equivalence of Definitions of Pentagonal Number