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

$n^3 %2B (n %2B 1)^3.$

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. (sequence A005898 in OEIS)

If $C_n$ is the nth centered cube number and $P_n$ is the nth square pyramidal number, then

$C_n=P_n %2B4P_{n-1}%2BP_{n-2}.$

Centered cube numbers have applications in modelling the shells of atoms.

Centered cube number

See also