A055595 Area of triangles with integer sides and positive integer area, ordered by longest side, then second longest side and finally shortest side.

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

Comments

This is the ordering of triangles used for A316841.

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-François Alcover, Jun 12 2012 *)

Crossrefs

The sides are given by A055592, A055593, A055594.

Cf. A046131, A070786, A316841, A316853.

Range of values: A188158.

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