A289219 Areas of integer-sided triangles whose area equals 3 times their perimeter.

192, 204, 210, 216, 240, 252, 264, 270, 324, 330, 336, 378, 384, 408, 420, 456, 462, 480, 504, 522, 540, 546, 624, 690, 714, 780, 792, 840, 876, 966, 990, 1176, 1248, 1320, 1380, 1806, 2394, 2460, 3120, 4446, 8436

Offset: 1

Author

Zhining Yang, Jun 28 2017

Keywords

• nonn
• fini
• full

Comments

There are no further terms.

For a(3)=210, there are 2 solutions (20,21,29),(17,25,28);

For a(11)=336, there are 2 solutions (14,48,50),(24,35,53);

For a(16)=456, a(22)=546, there are 2 solutions respectively too.

Examples

			The areas 192,204,210,216,240, ... pertain respectively to triangles with sides (20,20,24), (17,25,26), (20,21,29), (18,24,30), (16,30,34), ..., equal 3 times their perimeter 64,68,70,72,80, ...
		

Crossrefs

Cf. A098030, A289218.

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@ 150, {3}]], f @@ # == 3 Total@# &] ] (* Michael De Vlieger, Jul 03 2017 *)