Given rods of length 1, 2, ..., , how many distinct triangles can be made? Lengths for which
(1)
obviously do not give triangles, but all other combinations of three rods do. The answer is
(2)
The values for ,
2, ... are 0, 0, 0, 1, 3, 7, 13, 22, 34, 50, ... (OEIS A002623).
Somewhat surprisingly, this sequence is also given by the generating
function
Honsberger, R. More Mathematical Morsels. Washington, DC: Math. Assoc. Amer., pp. 278-282,
1991.Sloane, N. J. A. Sequence A002623/M2640
in "The On-Line Encyclopedia of Integer Sequences."
, how many distinct triangles 
can be made? Lengths for which
,
2, ... are 0, 0, 0, 1, 3, 7, 13, 22, 34, 50, ... (OEIS A002623).
Somewhat surprisingly, this sequence is also given by the generating
function
