A289218 Areas of integer-sided triangles whose area equals twice their perimeter.

84, 96, 108, 120, 132, 144, 156, 168, 180, 240, 264, 300, 324, 396, 420, 684, 1224

Offset: 1

Author

Zhining Yang, Jun 28 2017

Keywords

• fini
• full
• nonn

Comments

There are no further terms.

One term, 168, corresponds to exactly two different triangles, namely [14, 30, 40] and [10, 35, 39], both with perimeter 84. The remaining terms correspond to unique triangles. - Jeppe Stig Nielsen, Mar 04 2020

Examples

			The areas 84,96,108,120,132, ... pertain respectively to triangles with sides (13,14,15), (12,16,20), (15,15,24), (10,24,26), (11,25,30), ..., equal twice their perimeter 42,48,54,60,66,...
		

Crossrefs

Cf. A098030, A007237.

2nd row of the irregular triangle in A290451.

Cf. A332922.

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 *)

Extensions

Duplicate term 168 (previous a(9)) removed by Jeppe Stig Nielsen, Mar 04 2020