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:
 * $\ds H_n = \sum_{k \mathop = 1}^n T_k$

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

Also see

 * Closed Form for Tetrahedral Numbers: $H_n = \dfrac {n \paren {n + 1} \paren {n + 2} } 6$