The Integer Sequence 1, 0, 1, 1, 2, 1, 3, 2, 4, 3, 5, 4, 7, 5, 8, 7, 10, 8, 12, 10, 14, 12, 16, 14, 19, 16, 21, 19,
... (Sloane's A005044) given by the Coefficients of the Maclaurin Series for
. The number
of different Triangles which have Integral sides and Perimeter is given
by

(1) | |||

(2) | |||

(3) |

where and are Partition Functions, with giving the number of ways of writing as a sum of terms, is the Nint function, and is the Floor Function (Jordan

**References**

Andrews, G. ``A Note on Partitions and Triangles with Integer Sides.'' *Amer. Math. Monthly* **86**, 477, 1979.

Honsberger, R. *Mathematical Gems III.* Washington, DC: Math. Assoc. Amer., pp. 39-47, 1985.

Jordan, J. H.; Walch, R.; and Wisner, R. J. ``Triangles with Integer Sides.'' *Amer. Math. Monthly* **86**, 686-689, 1979.

Sloane, N. J. A. Sequence
A005044/M0146
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