# Definition:Hexagonal Pyramidal Number

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## Definition

**Hexagonal pyramidal numbers** are those denumerating a collection of objects which can be arranged in the form of a hexagonal pyramid.

The $n$th **hexagonal pyramidal number** $P_n$ is defined as:

- $\displaystyle P_n = \sum_{k \mathop = 1}^n H_k$

where $H_k$ is the $k$th hexagonal number.

### Sequence

The sequence of hexagonal pyramidal numbers begins as follows:

- $0, 1, 7, 22, 50, 95, 161, 252, 372, 525, 715, 946, 1222, 1547, 1925, 2360, 2856, \ldots$

## Also known as

**Hexagonal pyramidal numbers** are also known as **greengrocers' numbers**.

## Also see

- Definition:Pyramidal Number
- Definition:Tetrahedral Number
- Definition:Square Pyramidal Number
- Definition:Pentagonal Pyramidal Number

- Results about
**hexagonal pyramidal numbers**can be found here.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $55$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $55$