Centered Square Number

Author

Eric W. Weisstein
August 14, 2003

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

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

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

<<Figurate`

Graphic

Show[Graphics[CenteredPolygonalDiagram[4,3]],
AspectRatio->Automatic,PlotRange->All,ImageSize->200]

Definition

Simplify[n^2+(n-1)^2/.n->n+1]

Table[(n^2)+(((1+n))^2),{n,0,5}]

Generating Function

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