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:

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

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

• Closed Form for Square Pyramidal Numbers

• Definition:Pyramidal Number
• Definition:Tetrahedral Number

• Results about square pyramidal numbers can be found here.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $14$
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $55$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $14$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $55$