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

1,1

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).

Links

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

Example

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,...

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, A289218, A289219.

A row of the triangle in A290451.

Sequence in context: A348822 A137522 A090487 * A060664 A261551 A247530

Adjacent sequences: A289217 A289218 A289219 * A289221 A289222 A289223

Keyword

nonn,fini,full

Author

Zhining Yang, Jun 28 2017

Status

approved