Definition:Heptagonal Number/Definition 3

Definition

Heptagonal numbers are defined as the sequence:

$\forall n \in \N: H_n = \map P {7, n} = \begin{cases}

0 & : n = 0 \\ \map P {7, n - 1} + 5 \paren {n - 1} + 1 & : n > 0 \end{cases}$ where $\map P {k, n}$ denotes the $k$-gonal numbers.

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