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

:$n^3\; +\; (n\; +\; 1)^3.$

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. OEIS|id=A005898

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.

ee also

*cube number
*figurate number
*centered number