tetrahedral number

An integer of the form


where n is a nonnegative integer. Sometimes referred to as Tn, tetrahedral numbersMathworldPlanetmath are listed in A000292 of Sloane’s OEIS. 2|Tn except when n1mod4.

With tn the nth triangular numberMathworldPlanetmath, the nth tetrahedral number can be calculated with this formula:


Another way to calculate tetrahedral numbers is with the binomial coefficientDlmfDlmfMathworldPlanetmath


This means that tetrahedral numbers can be looked up in Pascal’s triangle.

Tetrahedral numbers have practical applications in sphere packing.

Title tetrahedral number
Canonical name TetrahedralNumber
Date of creation 2013-03-22 15:56:34
Last modified on 2013-03-22 15:56:34
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 7
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A99
Synonym triangular pyramidal number