login
Number of pairwise incongruent triangles with integer sides and positive integer area and second longest side of length n.
2

%I #19 Jun 19 2019 17:47:46

%S 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,

%T 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,

%U 3,0,13,2,9,0,6,7,9,19,4,1,12,0,14,0,8,0

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

%H Amiram Eldar, <a href="/A054876/b054876.txt">Table of n, a(n) for n = 1..1000</a>

%e 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].

%t 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 *)

%Y Cf. A054875.

%K nonn

%O 1,5

%A _Henry Bottomley_, May 26 2000

%E Definition corrected and offset changed by _James R. Buddenhagen_, Jan 16 2012

%E More terms from _Amiram Eldar_, Jun 19 2019