A046129 Middle side b of scalene integer Heronian triangles sorted by increasing c and b.

4, 8, 12, 12, 13, 14, 10, 15, 13, 15, 16, 17, 20, 17, 20, 24, 24, 25, 25, 25, 21, 25, 24, 25, 26, 28, 29, 20, 30, 28, 29, 34, 29, 20, 26, 30, 35, 25, 28, 34, 35, 36, 26, 30, 32, 37, 39, 28, 40, 40, 34, 40, 37, 39, 36, 39, 40, 42, 35, 34, 40, 41, 41, 48, 30, 35, 37, 38, 40

Offset

0,1

Links

Table of n, a(n) for n=0..68.

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, 2]] (* Jean-François Alcover, Oct 29 2012 *)

Crossrefs

Cf. A046128, A046130, A046131.

Sequence in context: A072905 A086481 A329507 * A092930 A009012 A046084

Adjacent sequences: A046126 A046127 A046128 * A046130 A046131 A046132

Keyword

nonn

Author

Eric W. Weisstein

Status

approved