A046131 Areas of scalene integer Heronian triangles (A046128, A046129, A046130) sorted by increasing c and b.

6, 24, 30, 54, 24, 84, 36, 60, 66, 42, 96, 84, 126, 90, 150, 84, 120, 36, 204, 210, 210, 60, 216, 132, 96, 336, 72, 144, 240, 294, 84, 252, 360, 114, 156, 180, 210, 120, 210, 420, 168, 270, 264, 168, 384, 240, 468, 126, 180, 336, 336, 504, 264, 330, 486, 216

Offset

0,1

Comments

This is the ordering of triangles used for A316841.

Links

Table of n, a(n) for n=0..55.

Eric Weisstein's World of Mathematics, Heronian Triangle.

Mathematica

sideMax = 60; r[c_] := Reap[Do[ p = (a + b + c)/2; red = Reduce[ area > 1 && a < b < c && area^2 == p*(p - a)*(p - b)*(p - c), area, Integers]; If[red =!= False, sol = {a, b, c, area} /. {ToRules[red]}; Sow[sol]], {b, 1, c - 1}, {a, c - b, b - 1}]]; triangles = Flatten[ Reap[ Do[rc = r[c]; If[rc[[2]] =!= {}, Sow[rc[[2, 1]]]], {c, 5, sideMax}]][[2, 1]] , 2]; Sort[ triangles, Which[#1[[3]] < #2[[3]], True, #1[[3]] > #2[[3]], False, #1[[2]] < #2[[2]], True,  #1[[2]] > #2[[2]], False, #1[[1]] <= #2[[1]], True, True, False] &][[All, 4]] (* Jean-François Alcover, Oct 29 2012 *)

Crossrefs

The sides are given by A046128, A046129, A046130.

Cf. A055595, A072294, A316841, A316853.

Range of values: A383413.

Sequence in context: A110926 A131906 A185210 * A009111 A009112 A057101

Adjacent sequences: A046128 A046129 A046130 * A046132 A046133 A046134

Keyword

nonn

Author

Eric W. Weisstein

Status

approved