A289220 Areas of integer-sided triangles whose area equals 4 times their perimeter.

336, 360, 384, 432, 456, 480, 528, 576, 624, 672, 720, 840, 960, 1056, 1176, 1200, 1224, 1296, 1584, 1680, 1944, 2064, 2088, 2184, 2328, 2520, 2736, 2856, 3240, 3696, 4440, 4488, 4896, 5256, 6600, 7728, 9240, 9360, 9384, 17688, 34320

Offset: 1

Author

Zhining Yang, Jun 28 2017

Keywords

• nonn
• fini
• full

Comments

There are no further terms.

For a(10)=672, there are 2 solutions: (28,60,80), (20,70,78).

For a(12)=840, there are 3 solutions: (35,73,102), (25,84,101), (21,89,100).

Examples

			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,...
		

Crossrefs

Cf. A098030, A289218, A289219.

A row of the triangle in A290451.

Programs

Mathematica

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 *)