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A289218
Areas of integer-sided triangles whose area equals twice their perimeter.
7
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
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
2nd row of the irregular triangle in A290451.
Cf. A332922.
Sequence in context: A349760 A045569 A219183 * A329182 A113931 A352230
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