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

1,1

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.

Links

Table of n, a(n) for n=1..41.

Example

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, ...

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 *)

Crossrefs

Cf. A098030, A289218.

A row of the triangle in A290451.

Sequence in context: A206343 A206336 A206335 * A190892 A039667 A273890

Adjacent sequences: A289216 A289217 A289218 * A289220 A289221 A289222

Keyword

nonn,fini,full

Author

Zhining Yang, Jun 28 2017

Status

approved