Definition:Heptagonal Number/Definition 1

Definition

Heptagonal numbers are defined as:

$H_n = \begin{cases} 0 & : n = 0 \\ H_{n - 1} + 5 n - 4 & : n > 0 \end{cases}$

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

Examples of Heptagonal Numbers

The first few heptagonal numbers are as follows:

File:HeptagonNumbers.png

Sequence of Heptagonal Numbers

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

$0, 1, 7, 18, 34, 55, 81, 112, 148, 189, 235, 286, 342, 403, 469, 540, \ldots$

Also see

• Equivalence of Definitions of Heptagonal Number