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A320543 (1/2) * number of ways to select 3 distinct points forming a triangle of unsigned area = 1 from a rectangle of grid points with side lengths j and k, written as triangle T(j,k), j<=k.

%I A320543 #10 Oct 22 2018 14:28:46
%S A320543 0,3,16,8,35,72,15,62,125,212,24,95,190,319,476,35,136,269,450,669,
%T A320543 936,48,183,360,601,892,1245,1652,63,238,467,776,1149,1602,2123,2724,
%U A320543 80,299,584,967,1430,1991,2636,3379,4188,99,368,717,1186,1751,2436,3223,4130,5117,6248
%N A320543 (1/2) * number of ways to select 3 distinct points forming a triangle of unsigned area = 1 from a rectangle of grid points with side lengths j and k, written as triangle T(j,k), j<=k.
%e A320543 The triangle begins:
%e A320543    0
%e A320543    3  16
%e A320543    8  35  72
%e A320543   15  62 125 212
%e A320543   24  95 190 319 476
%e A320543   35 136 269 450 669 936
%e A320543 .
%e A320543 a(2) = T(1,2) = 3 = 6/2 because the following 6 triangles of area 1 can be made by selecting 3 grid points from the [0,1]X[0,2] rectangle:
%e A320543   (0,0) (0,2) (1,0),
%e A320543   (0,0) (0,2) (1,1),
%e A320543   (0,0) (0,2) (1,2),
%e A320543   (0,0) (1,0) (1,2),
%e A320543   (0,1) (1,0) (1,2),
%e A320543   (0,2) (1,0) (1,2).
%Y A320543 Cf. A005563, A320539, A320541, A320544.
%K A320543 nonn,tabl
%O A320543 1,2
%A A320543 _Hugo Pfoertner_, Oct 16 2018