Definition:Pentagonal Number/Definition 2

Definition

Pentagonal numbers are defined as

$\ds P_n = \sum_{i \mathop = 1}^n \paren {3 i - 2} = 1 + 4 + \cdots + \paren {3 \paren {n - 1} - 2} + \paren {3 n - 2}$

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