Centered Pentagonal Number

Author

Eric W. Weisstein
August 14, 2003

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

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

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

Graphic

Show[Graphics[CenteredPolygonalDiagram[5,3]],
AspectRatio->Automatic,PlotRange->All,ImageSize->200]

Definition

Simplify[(5n^2-5n+2)/2/.n->n+1]

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

Generating Function

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