A054876 Number of pairwise incongruent triangles with integer sides and positive integer area and second longest side of length n.

0, 0, 0, 1, 2, 0, 0, 1, 0, 3, 0, 2, 4, 1, 4, 1, 4, 0, 0, 6, 1, 0, 0, 3, 10, 5, 0, 4, 6, 6, 0, 1, 1, 7, 7, 2, 5, 1, 8, 10, 6, 2, 0, 2, 5, 0, 0, 3, 0, 13, 13, 14, 6, 0, 7, 5, 0, 8, 0, 14, 9, 1, 3, 1, 23, 3, 0, 13, 2, 9, 0, 6, 7, 9, 19, 4, 1, 12, 0, 14, 0, 8, 0

Offset: 1

Author

Henry Bottomley, May 26 2000

Keywords

• nonn

Examples

			a(10) is 3 because there are three different integer-sided, integer-area triangles with middle side length 10, namely [9,10,17], [10,10,12], and [10,10,16].
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A054875.

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,n,z], num++], {x,1,n}], {z,n,2n}]; num]; Array[a, 100, 0] (* Amiram Eldar, Jun 19 2019 *)

Extensions

Definition corrected and offset changed by James R. Buddenhagen, Jan 16 2012

More terms from Amiram Eldar, Jun 19 2019