Centered Cube Number

A Figurate Number of the form,

$${\it CCub}_n=n^3+(n-1)^3=(2n-1)(n^2-n+1).$$

The first few are 1, 9, 35, 91, 189, 341, ... (Sloane's A005898). The Generating Function for the centered cube numbers is

$${x(x^3+5x^2+5x+1)\over(x-1)^4}=x+9x^2+35x^3+91x^4+\ldots.$$

See also Cubic Number

References

Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, p. 51, 1996.

Sloane, N. J. A. Sequence A005898/M4616 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.