Stella Octangula Number

A Figurate Number of the form,

$${\it StOct}_n=O_n+8T_{n-1}=n(2n^2-1).$$

The first few are 1, 14, 51, 124, 245, ... (Sloane's A007588). The Generating Function for the stella octangula numbers is

$${x(x^2+10x+1)\over(x-1)^4}=x+14x^2+51x^3+124x^4+\ldots.$$

References

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

Sloane, N. J. A. Sequence A007588/M4932 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.