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Number of integer triangles with an integer area having relatively prime sides a, b and c such that a + b + c = n.
17

%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