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

0,3

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]

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

Crossrefs

Cf. A028492, A189979, A190021, A190022, A189978, A190313, A189978, A190313.

Sequence in context: A299260 A290312 A374974 * A046664 A333510 A055536

Adjacent sequences: A028416 A028417 A028418 * A028420 A028421 A028422

Keyword

nonn

Author

David J. Rusin

Extensions

More terms from Chris Cole (chris(AT)questrel.com), Jun 28 2003

a(36)-a(39) from Martin Renner, May 08 2011

Status

approved