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Number of acute integer triangles with perimeter n and relatively prime side lengths.
8

%I #6 Mar 30 2012 18:50:20

%S 0,0,1,0,1,0,1,1,1,1,2,1,3,1,2,2,5,2,5,3,3,4,6,3,6,4,7,6,10,4,10,7,8,

%T 7,10,7,14,8,12,8,17,10,17,12,13,14,20,12,21,14,18,16,25,15,23,18,22,

%U 20,30,16,32,21,29,23,32,21,38,27,33,26,43,25

%N Number of acute integer triangles with perimeter n and relatively prime side lengths.

%C a(n) = A051493(n) - A070102(n) - A070109(n).

%H R. Zumkeller, <a href="/A070080/a070080.txt">Integer-sided triangles</a>

%e For n=10 there are A005044(10) = 2 integer triangles: [2,4,4] and [3,3,4]; both are acute, but GCD(2,4,4)>1, therefore a(9) = 1.

%Y Cf. A070080, A070081, A070082, A070093, A070096, A070099, A070084, A070119.

%K nonn

%O 1,11

%A _Reinhard Zumkeller_, May 05 2002