%I A098737
%S A098737 1,3,8,6,15,27,10,24,42,64,15,35,60,90,125,21,48,81,120,165,216,28,63,
%T A098737 105,154,210,273,343,36,80,132,192,260,336,420,512,45,99,162,234,315,
%U A098737 405,504,612,729,55,120,195,280,375,480,595,720,855,1000,66,143,231,330
%N A098737 Triangle read by rows: number of triangles formed by lines from two vertices 
               of a triangle to the opposite side that segment the opposite sides 
               into m and n segments. Since f(m,n) = f(n,m), it suffices to give 
               the results in a triangular table.
%C A098737 Frank Buss gave this as a puzzle; K. L. Metlov solved it, submitting 
               his result in the J language created by Kenneth Iverson. The program 
               given below is only five tokens long. J defines a series of three 
               functions to be a "fork" defined by x (f g h ) y = (x f y) g (f h 
               y) - a generalization of the usual mathematical practice of writing 
               (f + g) y to mean (f y) + (g y). J also has a primitive "half" and 
               has a dummy function "cap" whose purpose is to permit more forks 
               to be written. 3 (* * +) 5 is thus (3 * 5) * (3 + 5) or 120. cap 
               half 3 (* * +) 5 is thus 60.
%F A098737 f(m, n) = 1/2 * (m * n) * (m + n)
%e A098737 f(3,5) is 60, from 1/2 * (3 * 5) * (3 + 5) or 1/2 * 15 * 8.
%t A098737 t[m_, n_] := (m*n)(m + n)/2; Flatten[ Table[ t[m, n], {m, 10}, {n, m}]] 
               (from Robert G. Wilson v Nov 04 2004)
%o A098737 (J language) cap half * * +
%Y A098737 Sequence in context: A021725 A080939 A155724 this_sequence A164654 A072396 
               A001175
%Y A098737 Adjacent sequences: A098734 A098735 A098736 this_sequence A098738 A098739 
               A098740
%K A098737 easy,nonn,tabl
%O A098737 1,2
%A A098737 Eugene McDonnell (eemcd(AT)mac.com), Oct 29 2004
%E A098737 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 04 2004