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

Examples of Pentagonal Numbers

The first few pentagonal numbers are as follows:

Sequence of Pentagonal Numbers

The sequence of pentagonal numbers, for $n \in \Z_{\ge 0}$, begins:

$0, 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, \ldots$

Also see

• Equivalence of Definitions of Pentagonal Number