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Number of integer-sided triangles with sides a,b,c, a<b<c, a+b+c=n that are right triangles.
17

%I #15 Jun 07 2017 07:06:00

%S 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,

%T 0,1,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,2,0,0,0,0,0,0,0,0,

%U 0,1,0,1,0,0,0,0,0,0,0,1,0,0,0,2,0,0,0,0,0,2,0,0,0,0,0,1,0,0,0,0

%N Number of integer-sided triangles with sides a,b,c, a<b<c, a+b+c=n that are right triangles.

%C Also number of right integer triangles with perimeter n having integral inradius. - _Reinhard Zumkeller_, May 05 2002

%C Every integer-sided right triangle has integer inradius. If the triple is [p^2-q^2,2pq,p^2+q^2] then inradius = pq-q^2. - _Michael Somos_, Sep 13 2005

%H Seiichi Manyama, <a href="/A024155/b024155.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Incircle.html">Incircle</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RightTriangle.html">Right Triangle</a>.

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

%F a(n) = A070201(n) - A070205(n) - A070206(n).

%Y Cf. A005044, A070093, A070101.

%K nonn

%O 1,60

%A _Clark Kimberling_