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

1,5

Links

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

Example

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].

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 *)

Crossrefs

Cf. A054875.

Sequence in context: A171912 A306605 A363929 * A109502 A323887 A349913

Adjacent sequences: A054873 A054874 A054875 * A054877 A054878 A054879

Keyword

nonn

Author

Henry Bottomley, May 26 2000

Extensions

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

More terms from Amiram Eldar, Jun 19 2019

Status

approved