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A046131 Areas of scalene integer Heronian triangles (A046128, A046129, A046130) sorted by increasing c and b. 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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-Fran├žois Alcover, Oct 29 2012 *)

CROSSREFS

Cf. A046128, A046129, A046130.

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

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Last modified March 2 19:18 EST 2021. Contains 341756 sequences. (Running on oeis4.)