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

1,13

Links

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

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 *)

Crossrefs

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

Sequence in context: A098006 A336916 A082650 * A324115 A029239 A162201

Adjacent sequences: A054872 A054873 A054874 * A054876 A054877 A054878

Keyword

nonn

Author

Henry Bottomley, May 26 2000

Extensions

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

Status

approved