%I #23 Nov 18 2018 10:37:32
%S 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,
%T 0,2,0,0,0,1,0,2,0,1,0,0,0,1,0,2,0,0,0,3,0,1,0,0,0,1,0,0,0,3,0,1,0,1,
%U 0,2,0,1,0,0,0,1,0,1,0,2,0,0,0,5,0,0,0,0,0,3
%N Number of integer triangles with an integer area having relatively prime sides a, b and c such that a + b + c = n.
%C From _Peter Kagey_, Jan 30 2018: (Start)
%C a(k) > 0 if and only if k is in A096468.
%C Records appear at indices 12, 36, 54, 84, 98, 162, 242, 338, 484, 578, ....
%C a(2k - 1) = 0 for all integers k > 0.
%C (End)
%H Peter Kagey, <a href="/A070138/b070138.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HeronianTriangle.html">Heronian Triangle</a>.
%H R. Zumkeller, <a href="/A070080/a070080.txt">Integer-sided triangles</a>
%Y Cf. A051493, A051516, A070088, A070109, A070143, A096468, A239246.
%K nonn
%O 1,36
%A _Reinhard Zumkeller_, May 05 2002
%E Corrected by _T. D. Noe_, Jun 17 2004