Search: id:A070086
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%I A070086
%S A070086 0,1,2,1,2,3,2,3,4,4,4,2,4,4,6,5,6,7,3,5,5,7,8,6,7,8,9,3,6,6,9,7,10,11,
%T A070086 7,9,10,11,12,4,6,8,10,8,12,12,14,8,10,12,13,12,15,16,4,7,9,12,10,14,
%U A070086 10,15,16,17,9,12,13,15,14,17,18,19,5,8,10
%N A070086 Areas of integer triangles [A070080(n), A070081(n), A070082(n)], rounded 
               values.
%C A070086 Triangles [A070080(A070142(n)), A070081(A070142(n)), A070082(A070142(n))] 
               have integer areas = a(A070142(k))= A070149(k).
%H A070086 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HeronsFormula.html">Heron's Formula</a>.
%H A070086 R. Zumkeller, <a href="a070080.txt">Integer-sided triangles</a>
%F A070086 a(n) = SquareRoot(s*(s-u)*(s-v)*(s-w)), where u=A070080(n), v=A070081(n), 
               w=A070082(n) and s=A070083(n)/2=(u+v+w)/2.
%e A070086 [A070080(25), A070081(25), A070082(25)]=[3,5,6] and s=A070083(25)/2=(3+5+6)/
               2=7: a(25)=SquareRoot(s*(s-3)*(s-5)*(s-6)) = SquareRoot(7*(7-3)*(7-5)*(7-6)) 
               = SquareRoot(7*4*2*1) = SquareRoot(56) = 7.48331, rounded = 7.
%Y A070086 Cf. A051516, A055595, A069596, A069594, A069599, A046131.
%Y A070086 Sequence in context: A008611 A025798 A161064 this_sequence A162618 A036576 
               A127255
%Y A070086 Adjacent sequences: A070083 A070084 A070085 this_sequence A070087 A070088 
               A070089
%K A070086 nonn
%O A070086 1,3
%A A070086 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 05 2002

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