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Search: id:A070086
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| 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, 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, 10, 15, 16, 17, 9, 12, 13, 15, 14, 17, 18, 19, 5, 8, 10
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Triangles [A070080(A070142(n)), A070081(A070142(n)), A070082(A070142(n))] have integer areas = a(A070142(k))= A070149(k).
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LINKS
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Eric Weisstein's World of Mathematics, Heron's Formula.
R. Zumkeller, Integer-sided triangles
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FORMULA
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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.
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EXAMPLE
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[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.
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CROSSREFS
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Cf. A051516, A055595, A069596, A069594, A069599, A046131.
Adjacent sequences: A070083 A070084 A070085 this_sequence A070087 A070088 A070089
Sequence in context: A116939 A008611 A025798 this_sequence A036576 A127255 A076827
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 05 2002
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