# Definition:Tetrahedral Number

## Definition

Tetrahedral numbers are those denumerating a collection of objects which can be arranged in the form of a regular tetrahedron.

The $n$th tetrahedral number $H_n$ is defined as:

$\displaystyle H_n = \sum_{k \mathop = 1}^n T_k$

where $T_k$ is the $k$th triangular number.

### Sequence

The sequence of tetrahedral numbers begins as follows:

$0, 1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, 364, \ldots$