tetrahedral number


An integer of the form

(n2+n)(n+2)6,

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:

Tn=i=1nti.

Another way to calculate tetrahedral numbers is with the binomial coefficientDlmfDlmfMathworldPlanetmath

Tn=(n+23).

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