OFFSET
1,1
LINKS
Jean-François Alcover, Table of n, a(n) for n = 1..1265
Eric Weisstein's World of Mathematics, Heronian Triangle.
Reinhard Zumkeller, Integer-sided triangles
EXAMPLE
MATHEMATICA
m = 500 (* max perimeter *);
sides[per_] := Select[Reverse /@ IntegerPartitions[per, {3}, Range[ Ceiling[per/2]]], #[[1]] < per/2 && #[[2]] < per/2 && #[[3]] < per/2 &];
triangles = DeleteCases[Table[sides[per], {per, 3, m}], {}] // Flatten[#, 1]& // SortBy[Total[#] m^3 + #[[1]] m^2 + #[[2]] m + #[[1]] &];
area[{a_, b_, c_}] := With[{p = (a+b+c)/2}, Sqrt[p(p-a)(p-b)(p-c)]];
Select[area /@ triangles, IntegerQ] (* Jean-François Alcover, Oct 12 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, May 05 2002
STATUS
approved