Triangle Counting
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. SequenceA002623/M2640in ``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.
- Attractor
- Auction
- Augend
- Augmented Amicable Pair
- Augmented Dodecahedron
- Augmented Hexagonal Prism
- Augmented Pentagonal Prism
- Augmented Polyhedron
- Augmented Sphenocorona
- Augmented Triangular Prism
- Augmented Tridiminished Icosahedron
- Augmented Truncated Cube
- Augmented Truncated Dodecahedron
- Augmented Truncated Tetrahedron
- Aureum Theorema
- Aurifeuillean Factorization
- Ausdehnungslehre
- Authalic Latitude
- Autocorrelation
- Automorphic Function
- Automorphic Number
- Automorphism
- Automorphism Group
- Autonomous
- Autoregressive Model