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

1,1

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

Links

Table of n, a(n) for n=1..17.

Example

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,...

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 *)

Crossrefs

Cf. A098030, A007237.

2nd row of the irregular triangle in A290451.

Cf. A332922.

Sequence in context: A349760 A045569 A219183 * A329182 A113931 A352230

Adjacent sequences: A289215 A289216 A289217 * A289219 A289220 A289221

Keyword

fini,full,nonn

Author

Zhining Yang, Jun 28 2017

Extensions

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

Status

approved