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Search: id:A074076
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| A074076 |
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One-sixth the magnitude of the least-area primitive Heronian triangle whose middle side has median and altitude points distant N=2n+1 apart. |
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1
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OFFSET
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1,1
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COMMENT
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Such a triangle has sides N*u +/- M, 2*M*u (the latter being cut into M*u +/- N by the corresponding altitude}, and inradius M*(N - M)*v. The first entry, in particular, is associated with sequence A023039. If, however, N=2n, the least-area primitive Heronian is Pythagorean of magnitude N *(N^2 - 1), with sides N^2 +/- 1, 2*N and inradius N - 1.
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FORMULA
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a(n) = M*D*u*v/6, where (u, v) is the fundamental solution to x^2 - D*y^2 = 1, with M = 2*A074075; D = A074074. {Note that D = N^2 - M^2.}
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CROSSREFS
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Cf. A074074, A074075, A023039, A002349, A002350.
Sequence in context: A004297 A053401 A042741 this_sequence A084274 A091032 A091753
Adjacent sequences: A074073 A074074 A074075 this_sequence A074077 A074078 A074079
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KEYWORD
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hard,more,nonn
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Aug 28 2002
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