%I #11 Sep 14 2019 17:16:53
%S 4,8,12,12,13,14,10,15,13,15,16,17,20,17,20,24,24,25,25,25,21,25,24,
%T 25,26,28,29,20,30,28,29,34,29,20,26,30,35,25,28,34,35,36,26,30,32,37,
%U 39,28,40,40,34,40,37,39,36,39,40,42,35,34,40,41,41,48,30,35,37,38,40
%N Middle side b of scalene integer Heronian triangles sorted by increasing c and b.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HeronianTriangle.html">Heronian Triangle.</a>
%t 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 *)
%Y Cf. A046128, A046130, A046131.
%K nonn
%O 0,1
%A _Eric W. Weisstein_