A054875 Number of pairwise incongruent triangles with integer sides and positive integer area and longest side of length n.

0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 2, 0, 3, 1, 3, 1, 0, 3, 2, 0, 0, 3, 4, 4, 0, 1, 2, 7, 0, 1, 0, 3, 3, 2, 5, 0, 6, 7, 4, 4, 0, 2, 4, 0, 0, 5, 0, 6, 7, 10, 4, 1, 3, 4, 0, 4, 0, 10, 3, 0, 3, 1, 11, 3, 0, 8, 1, 5, 0, 4, 6, 7, 13, 0, 3, 9, 0, 10, 0, 6, 0

Offset: 1

Author

Henry Bottomley, May 26 2000

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A054876, A055592, A070787, A123323, A239246, A322105.

Programs

Mathematica

okQ[x_, y_, z_] := If[x + y <= z, False, Module[{s = (x + y + z)/2}, IntegerQ[ Sqrt[s(s-x)(s-y)(s-z)]]] ]; a[n_] := Module[{num = 0}, Do[Do[If[okQ[x,y,n], num++], {x,1,y}], {y,1,n}]; num]; Array[a, 100] (* Amiram Eldar, Nov 22 2018 *)

Extensions

Name and offset changed to align with 2012 changes to A054876 by Peter Munn, Nov 23 2018