Definition:Hexagonal Pyramidal Number

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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.


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

  • Results about hexagonal pyramidal numbers can be found here.