Definition:Square Pyramidal Number
Jump to navigation
Jump to search
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
- 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): $55$