

A046129


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


4



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
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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]] (* JeanFrançois Alcover, Oct 29 2012 *)


CROSSREFS

Cf. A046128, A046130, A046131.
Sequence in context: A158457 A072905 A086481 * A092930 A009012 A046084
Adjacent sequences: A046126 A046127 A046128 * A046130 A046131 A046132


KEYWORD

nonn


AUTHOR

Eric W. Weisstein


STATUS

approved



