OFFSET
1,2
COMMENTS
Such a triangle has middle side 2*x'.
LINKS
Jean-François Alcover, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = x'*y'/2, where (x', y') is the fundamental solution to x^2 - 3*y^2 = d^2, where d=A072330(n).
MATHEMATICA
terms = 1000;
nmax = 12 terms;
okQ[n_] := AllTrue[FactorInteger[n][[All, 1]], MatchQ[Mod[#, 12], 1|11]&];
A072330 = Select[Range[nmax], okQ];
a[n_] := Module[{a, b, c, d, p, area}, d = If[n <= Length[A072330], A072330[[n]], Print["nmax = ", nmax, " insufficient"]; Exit[]]; If[n == 1, 1, For[b = 2 d, True, b++, a = b - d; c = b + d; p = (a + b + c)/2; If[IntegerQ[p] && IntegerQ[area = Sqrt[p (p - a) (p - b) (p - c)]] && GCD[a, b, c] == 1, Return[area/6]]]]];
a /@ Range[terms] (* Jean-François Alcover, Mar 07 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Lekraj Beedassy, Jul 18 2002
EXTENSIONS
Edited, corrected and extended by Ray Chandler, Jul 03 2004
STATUS
approved