A028419 Congruence classes of triangles which can be drawn using lattice points in n X n grid as vertices.
0, 1, 8, 29, 79, 172, 333, 587, 963, 1494, 2228, 3195, 4455, 6050, 8032, 10481, 13464, 17014, 21235, 26190, 31980, 38666, 46388, 55144, 65131, 76449, 89132, 103337, 119184, 136757, 156280, 177796, 201430, 227331, 255668, 286606, 320294, 356884, 396376, 439100, 485427, 535049, 588457, 645803
Offset: 0
Keywords
Links
- Ron Knott, Table of n, a(n) for n = 0..60
- D. Rusin, Lattice Problem (Triangles) [Dead link]
- D. Rusin, Lattice Problem (Triangles) [Cached copy]
Programs
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Maple
a:=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(nops(TriangleSet)); end: # Martin Renner, May 03 2011
Extensions
More terms from Chris Cole (chris(AT)questrel.com), Jun 28 2003
a(36)-a(39) from Martin Renner, May 08 2011