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

n³ + (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. (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 + 4P_{n − 1} + P_{n − 2}.

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

See also

• Cube number
• Figurate number
• Centered polygonal number