CENTERED CUBE NUMBER

A 'centered cube number' is a centered figurate number that represents a cube. The centered cube number for ''n'' is given by the equation
:$n^3\; +\; (n\; +\; 1)^3.$
The first few centered cube numbers are
1, 9, 35, 91, 189, 341, 559, 855, 1241, 1729, 2331, 3059, 3925, 4941, 6119, 7471, 9009, 10745, 12691, 14859, 17261, 19909, 22815, 25991, 29449, 33201, 37259, 41635, 46341, 51389, 56791, 62559, 68705, 75241, 82179, 89531, 97309, 105525.
If $C\_n$ is the ''n''th centered cube number and $P\_n$ is the ''n''th square pyramidal number, then
:$C\_n=P\_n\; +4P\_\{n-1\}+P\_\{n-2\}.$
Centered cube numbers have applications in modelling the shells of atoms.

Contents

See also

See also

★ cube number

★ figurate number

★ centered number