Alcuin's Sequence
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 numberof different Triangles which have Integral sides and Perimeter 
is givenby
 |  |  | (1) |
|  | (2) | |
|  | (3) |
where
and 
are Partition Functions, with 
giving the number of ways ofwriting as a sum of 
terms, 
is the Nint function, and 
is the Floor Function (Jordanet al. 1979, Andrews 1979, Honsberger 1985). Strangely enough, 
for 
, 4, ... is precisely Alcuin's sequence.See also Partition Function P, Triangle
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. SequenceA005044/M0146in ``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.
- Minkowski Convex Body Theorem
- Minkowski Geometry
- Minkowski-Hlawka Theorem
- Minkowski Integral Inequality
- Minkowski Measure
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- Minkowski Sum Inequality
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