cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A289218 Areas of integer-sided triangles whose area equals twice their perimeter.

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%I A289218 #25 Mar 06 2020 03:35:19
%S A289218 84,96,108,120,132,144,156,168,180,240,264,300,324,396,420,684,1224
%N A289218 Areas of integer-sided triangles whose area equals twice their perimeter.
%C A289218 There are no further terms.
%C A289218 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
%e A289218 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,...
%t A289218 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 *)
%Y A289218 Cf. A098030, A007237.
%Y A289218 2nd row of the irregular triangle in A290451.
%Y A289218 Cf. A332922.
%K A289218 fini,full,nonn
%O A289218 1,1
%A A289218 _Zhining Yang_, Jun 28 2017
%E A289218 Duplicate term 168 (previous a(9)) removed by _Jeppe Stig Nielsen_, Mar 04 2020