An Integer of the form , where is an Integer. The even numbers are therefore ..., , ,
0, 2, 4, 6, 8, 10, ... (Sloane's A005843). Since the even numbers are integrally divisible by two,
for
even . An even number for which
is called a Singly Even Number, and an even number for
which
is called a Doubly Even Number. An integer which is not even is called an Odd Number.
The Generating Function of the even numbers is

**References**

Sloane, N. J. A. Sequence
A005843/M0985
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

1999-05-25