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%I #31 Oct 10 2020 09:21:55
%S 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,
%T 0,2,0,0,0,1,0,2,0,1,0,0,0,2,0,0,0,0,0,3,0,1,0,0,0,3,0,0,0,2,0,1,0,1,
%U 0,2,0,3,0,0,0,1,0,1,0,3,0,0,0,8,0,0,0,1,0,4,0,0,0,0,0,4,0,3,0,1
%N Number of integer-sided triangles with sides a,b,c, a<b<c, a+b+c=n that have integer area.
%C No such triangles with odd perimeter (see A051516).
%C Records occur at: 1, 12, 36, 54, 84, 108, 192, 216, 294, 324, 378, 420, 432, 540, 588, 756, 972, 1176, 1452, 1764, 1944, 2028, 2352, 2904, 2916, 3024, 3072, 3402, 3468, 3780, 3888, 4116, 5292, 6348, 6804, 8748, 10164, ... - _Antti Karttunen_, Sep 25 2018
%H Antti Karttunen, <a href="/A024153/b024153.txt">Table of n, a(n) for n = 1..12021</a> (terms 1..1000 from Seiichi Manyama)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HeronianTriangle.html">Heronian Triangle</a>.
%o (PARI) A024153(n) = if(n%2,0,my(k=0, t, p=n/2); for(a=1,n,for(b=1+max(a,(p-a)),n-(a+1),my(c=n-(a+b)); if((c<=b),break); if(((t = (p*(p-a)*(p-b)*(p-c))) > 0)&&issquare(t),k++))); (k)); \\ _Antti Karttunen_, Sep 25 2018
%Y Cf. A051516, A070139, A070203, A188158, A301384.
%K nonn
%O 1,36
%A _Clark Kimberling_
%E a(100) corrected by _Seiichi Manyama_, Sep 13 2018
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