Centered cube number

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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 Cn is the nth centered cube number and Pn is the nth square pyramidal number, then

Cn = Pn + 4Pn − 1 + Pn − 2.

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

[edit] See also

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