info prev up next book cdrom email home

Centered Pentagonal Number

\begin{figure}\begin{center}\BoxedEPSF{CenteredPentagonalNumber.epsf scaled 650}\end{center}\end{figure}

A Centered Polygonal Number consisting of a central dot with five dots around it, and then additional dots in the gaps between adjacent dots. The general term is $(5n^2-5n+2)/2$, and the first few such numbers are 1, 6, 16, 31, 51, 76, ... (Sloane's A005891). The Generating Function of the centered pentagonal numbers is


See also Centered Square Number, Centered Triangular Number


Sloane, N. J. A. Sequence A005891/M4112 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

© 1996-9 Eric W. Weisstein