A190022 Number of obtuse triangles, distinct up to congruence, on an n X n grid (or geoboard).

0, 0, 2, 12, 39, 95, 193, 355, 597, 943, 1426, 2071, 2904, 3977, 5306, 6956, 8963, 11370, 14225, 17587, 21515, 26053, 31310, 37282, 44061, 51785, 60436, 70127, 80939, 92952, 106267, 120982, 137124, 154841, 174225, 195366, 218394, 243457, 270505, 299749, 331441

Offset: 1

Author

Martin Renner, May 04 2011

Keywords

• nonn

Examples

			For n = 3 the two obtuse triangles are:
*..   *..
*..   *..
.*.   ..*
		

Links

• Eric Weisstein's World of Mathematics, Geoboard.
• Eric Weisstein's World of Mathematics, Obtuse Triangle.

Crossrefs

Cf. A028419, A189979, A190021.

Cf. A103428.

Programs

Maple

Triangles:=proc(n) local TriangleSet, i, j, k, l, A, B, C; TriangleSet:={}: for i from 0 to n do for j from 0 to n do for k from 0 to n do for l from 0 to n do A:=i^2+j^2: B:=k^2+l^2: C:=(i-k)^2+(j-l)^2: if A^2+B^2+C^2<>2*(A*B+B*C+C*A) then TriangleSet:={op(TriangleSet), sort([sqrt(A), sqrt(B), sqrt(C)])}: fi: od: od: od: od: return(TriangleSet); end:
IsObtuseTriangle:=proc(T) if T[1]^2+T[2]^2
				

Formula

a(n) = A028419(n) - A190021(n) - A189979(n).

Extensions

a(21)-a(40) from Martin Renner, May 08 2011