Search: id:A070201
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%I A070201
%S A070201 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,
%T A070201 2,0,0,0,1,0,2,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,3,0,0,0,2,0,1,0,1,0,2,
%U A070201 0,2,0,0,0,1,0,1,0,2,0,0,0,8,0,0,0,1,0,3
%N A070201 Number of integer triangles with perimeter n having integral inradius.
%C A070201 a(n) = #{k | A070083(k) = n and A070200(k) = exact inradius};
%C A070201 a(n) = A070203(n) + A070204(n);
%C A070201 a(n) = A070205(n) + A070206(n) + A024155(n);
%C A070201 a(odd) = 0.
%H A070201 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Incircle.html">Incircle</a>.
%H A070201 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HeronsFormula.html">Heron's Formula</a>.
%H A070201 R. Zumkeller, <a href="a070080.txt">Integer-sided triangles</a>
%e A070201 a(36)=2, as there are two integer triangles with integer inradius having 
               perimeter=32:
%e A070201 First: [A070080(368), A070081(368), A070082(368)] = [9,10,17], for s=A070083(368)/
               2=(9+10+17)/2=18: inradius = SquareRoot((s-9)*(s-10)*(s-17)/s) = 
               SquareRoot(9*8*1/18) = SquareRoot(4) = 2; therefore A070200(368)=2.
%e A070201 2nd: [A070080(370), A070081(370), A070082(370)] = [9,12,15], for s=A070083(370)/
               2=(9+12+15)/2=18: inradius = SquareRoot((s-9)*(s-12)*(s-15)/s) = 
               SquareRoot(9*6*3/18) = SquareRoot(9) = 3; therefore A070200(370)=3.
%Y A070201 Cf. A070209, A070202, A070208, A005044, A070140.
%Y A070201 Sequence in context: A003475 A135767 A070203 this_sequence A070138 A024153 
               A079127
%Y A070201 Adjacent sequences: A070198 A070199 A070200 this_sequence A070202 A070203 
               A070204
%K A070201 nonn
%O A070201 1,36
%A A070201 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 05 2002

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