# Definition:Square Pyramidal Number

## Definition

Square pyramidal numbers are those denumerating a collection of objects which can be arranged in the form of a square pyramid.

The $n$th square pyramidal number $P_n$ is defined as:

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

where $S_k$ is the $k$th square number.

### Sequence

The sequence of square pyramidal numbers begins as follows:

$1, 5, 14, 30, 55, 91, 140, 204, 285, 385, 506, 650, \ldots$

## Also known as

A square pyramidal number is also known by the more unwieldy term square-based pyramidal number.

## Also see

• Results about square pyramidal numbers can be found here.