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A074076 One-sixth the magnitude of the least-area primitive Heronian triangle whose middle side has median and altitude points distant N=2n+1 apart. +0
1
60, 4620, 2024, 5984, 11480, 22960, 41580 (list; graph; listen)
OFFSET

1,1

COMMENT

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.

FORMULA

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.}

CROSSREFS

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

KEYWORD

hard,more,nonn

AUTHOR

Lekraj Beedassy (blekraj(AT)yahoo.com), Aug 28 2002

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.


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