OFFSET
1,2
COMMENTS
T(n,k) = (1/4) * number of ways to select 3 distinct points forming a triangle of unsigned area = 1/2 from a rectangle of grid points with side lengths n and k.
Permutations of the 3 points are not counted separately.
LINKS
Seiichi Manyama, Rows n = 1..140, flattened
EXAMPLE
The triangle begins:
1
3 8
6 16 31
10 26 50 80
15 39 75 120 179
21 54 103 164 244 332
28 72 137 218 324 441 585
...
a(1) = 1 because 4 triangles of area 1/2 in a [0 1]X[0 1] square can be formed by cutting the unit square into 2 triangles along the diagonals.
MAPLE
T := proc(m, n) local a, i, j; a:=0;
for i from 1 to m do for j from 1 to n do
if gcd(i, j)=1 then a:=a+(m+1-i)*(n+1-j); fi; od: od: a; end;
for m from 1 to 12 do lprint([seq(T(m, n), n=1..m)]); od: # N. J. A. Sloane, Feb 04 2020
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Hugo Pfoertner, Oct 15 2018
EXTENSIONS
Replaced definition (now a comment) by explicit formula. - N. J. A. Sloane, Feb 04 2020
STATUS
approved