info prev up next book cdrom email home

Centered Triangular Number

\begin{figure}\begin{center}\BoxedEPSF{CenteredTriangularNumber.epsf scaled 575}\end{center}\end{figure}

A Centered Polygonal Number consisting of a central dot with three dots around it, and then additional dots in the gaps between adjacent dots. The general term is $(3n^2-3n+2)/2$, and the first few such numbers are 1, 4, 10, 19, 31, 46, 64, ... (Sloane's A005448). The Generating Function giving the centered triangular numbers is


See also Centered Pentagonal Number, Centered Square Number


Sloane, N. J. A. Sequence A005448/M3378 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