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A055595 Area of congruent triangles with integer sides and positive integer area, ordered by longest side, then second longest side and finally shortest side. 11
6, 12, 12, 24, 48, 30, 60, 54, 24, 84, 48, 36, 60, 120, 108, 66, 42, 96, 84, 126, 60, 108, 192, 90, 150, 84, 168, 120, 36, 204, 240, 210, 210, 60, 120, 216, 132, 300, 96, 336, 72, 192, 144, 240, 480, 294, 84, 252, 360, 432, 114, 156, 180, 210, 420, 120, 210, 420 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Ray Chandler, Table of n, a(n) for n = 1..10000

A. Dendane, Heron's Formula For Area of a Triangle-Geometry Calculator

FORMULA

a(n) = sqrt(s(n)*(s(n)-A055592(n))*(s(n)-A055593(n))*(s(n)-A055594(n))) where s(n) = (A055592(n)+A055593(n)+A055594(n))/2 i.e. half the perimeter of the triangle

MATHEMATICA

max = 42; triangles = Reap[Do[s = (a+b+c)/2; area = Sqrt[s*(s-a)*(s-b)*(s-c)]; If[IntegerQ[area] && area > 0, Sow[{a, b, c, area}]], {a, 1, max}, {b, a, max}, {c, b, max}]][[2, 1]]; A055595 = Sort[triangles, #1[[3]]*max^2 + #1[[2]]*max + #1[[1]] < #2[[3]]* max^2 + #2[[2]]*max + #2[[1]] &][[All, 4]](* Jean-Fran├žois Alcover, Jun 12 2012 *)

CROSSREFS

Cf. A055592, A055593, A055594.

Sequence in context: A330921 A183688 A298016 * A132632 A223352 A063648

Adjacent sequences:  A055592 A055593 A055594 * A055596 A055597 A055598

KEYWORD

nonn

AUTHOR

Henry Bottomley, May 26 2000

STATUS

approved

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Last modified September 20 16:50 EDT 2021. Contains 347586 sequences. (Running on oeis4.)