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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
OFFSET
1,1
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-François Alcover, Jun 12 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, May 26 2000
STATUS
approved