Definition:Hexagonal Pyramidal Number

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:

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

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

• Closed Form for Hexagonal Pyramidal Numbers

• 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): $55$