Heptagonal Number

$\begin{figure}\begin{center}\BoxedEPSF{HeptagonalNumber.epsf scaled 600}\end{center}\end{figure}$

A Figurate Number of the form . The first few are 1, 7, 18, 34, 55, 81, 112, ... (Sloane's A000566). The Generating Function for the heptagonal numbers is

$\begin{displaymath} {x(4x+1)\over(1-x)^3}=x+7x^2+18x^3+34x^4+\ldots. \end{displaymath}$

References

Sloane, N. J. A. Sequence A000566/M4358 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.