Given rods of length 1, 2, ..., , how many distinct triangles can be made? Lengths for which

obviously do not give triangles, but all other combinations of three rods do. The answer is

The values for , 2, ...are 0, 0, 0, 1, 3, 7, 13, 22, 34, 50, ... (Sloane's A002623). Somewhat surprisingly, this sequence is also given by the Generating Function

**References**

Honsberger, R. *More Mathematical Morsels.* Washington, DC: Math. Assoc. Amer., pp. 278-282, 1991.

Sloane, N. J. A. Sequence
A002623/M2640
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