Decagonal Number

$\begin{figure}\begin{center}\BoxedEPSF{DecagonalNumber.epsf scaled 700}\end{center}\end{figure}$

A Figurate Number of the form . The first few are 1, 10, 27, 52, 85, ... (Sloane's A001107). The Generating Function giving the decagonal numbers is

$\begin{displaymath} {x(7x+1)\over(1-x)^3}=x+10x^2+27x^3+52x^4+\ldots. \end{displaymath}$

References

Sloane, N. J. A. Sequence A001107/M4690 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.