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%I #11 Aug 06 2017 14:29:19
%S 336,360,384,432,456,480,528,576,624,672,720,840,960,1056,1176,1200,
%T 1224,1296,1584,1680,1944,2064,2088,2184,2328,2520,2736,2856,3240,
%U 3696,4440,4488,4896,5256,6600,7728,9240,9360,9384,17688,34320
%N Areas of integer-sided triangles whose area equals 4 times their perimeter.
%C There are no further terms.
%C For a(10)=672, there are 2 solutions: (28,60,80), (20,70,78).
%C For a(12)=840, there are 3 solutions: (35,73,102), (25,84,101), (21,89,100).
%e The areas 336,360,384,432,456, ... pertain respectively to triangles with sides (26,28,30), (25,29,36), (24,32,40), (30,30,48), (25,38,51), ..., equal 4 times their perimeter 84,90,96,108,114,...
%t f[a_, b_, c_] := Block[{P = Total[{a, b, c}]/2}, Sqrt[P (P - a) (P - b) (P - c)]]; Sort@ Map[f @@ # &, Select[Union@ Map[Sort, Tuples[Range@ 200, {3}]], f @@ # == 4 Total@ # &] ] (* _Michael De Vlieger_, Jul 03 2017 *)
%Y Cf. A098030, A289218, A289219.
%Y A row of the triangle in A290451.
%K nonn,fini,full
%O 1,1
%A _Zhining Yang_, Jun 28 2017
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