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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; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Triangles [A070080(A070142(n)), A070081(A070142(n)), A070082(A070142(n))] have integer areas = a(A070142(k))= A070149(k).
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LINKS
| Eric Weisstein's World of Mathematics, Heron's Formula.
R. Zumkeller, Integer-sided triangles
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FORMULA
| 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
| [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
| Cf. A051516, A055595, A069596, A069594, A069599, A046131.
Sequence in context: A008611 A025798 A161064 * A162618 A036576 A171729
Adjacent sequences: A070083 A070084 A070085 * A070087 A070088 A070089
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 05 2002
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