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A289220 Areas of integer-sided triangles whose area equals 4 times their perimeter. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A204796 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

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Last modified November 18 19:59 EST 2019. Contains 329288 sequences. (Running on oeis4.)