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 A190022 Number of obtuse triangles, distinct up to congruence, on a (n X n)-grid (or geoboard) 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Barile, Margherita: MathWorld -- Geoboard. Weisstein, Eric W.: MathWorld -- Obtuse Triangle. FORMULA a(n) = A028419(n) - A190021(n) - A189979(n). EXAMPLE For n = 3 the two obtuse triangles are: *..   *.. *..   *.. .*.   ..* 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

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Last modified October 23 09:28 EDT 2019. Contains 328345 sequences. (Running on oeis4.)