Centered Triangular Number

Author

Eric W. Weisstein
June 12, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/CenteredTriangularNumber.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/CenteredTriangularNumber.html.

©2006 Wolfram Research, Inc. except for portions noted otherwise

Graphic

Show[Graphics[CenteredPolygonalDiagram[3,3]],
AspectRatio->Automatic,PlotRange->All,ImageSize->200]

Definition

Table[(3n^2+3n+2)/2,{n,0,5}]

Generating Function

Series[(((x^2)+x+1)/(((1-x))^3)),{x,0,5}]

<<DiscreteMath`RSolve`

SeriesTerm[(((x^2)+x+1)/(((1-x))^3)),{x,0,n}]