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.
- Riesz's Theorem
- Riffle Shuffle
- Rigby Points
- Right Angle
- Right Conoid
- Right Hyperbola
- Right Line
- Right Strophoid
- Right Strophoid Inverse Curve
- Right Triangle
- Rigid
- Rigidity Theorem
- Rigid Motion
- Ring
- Ring Cyclide
- Ring Function
- Ringoid
- Ring Torus
- Risch Algorithm
- Rising Factorial
- Rivest-Shamir-Adleman Number
- RMS
- r(n)
- Robbin Constant
- Robbins Algebra