An Integer of the form , where is an Integer. The odd numbers are therefore ..., ,
, 1, 3, 5, 7, ... (Sloane's A005408), which are also the Gnomic Numbers. The
Generating Function for the odd numbers is

Since the odd numbers leave a remainder of 1 when divided by two, for odd . Integers which are not odd are called Even.

**References**

Sloane, N. J. A. Sequence
A005408/M2400
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
*The Encyclopedia of Integer Sequences.* San Diego: Academic Press, 1995.

© 1996-9

1999-05-26