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Four times the area of the smallest of n-tuples of Heronian triangles with equal perimeter and equal area.
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%I #21 May 01 2020 08:11:20

%S 24,840,1680,26880,196560,786240,19656000,365601600,1392431040,

%T 19061602560,68229120960,272916483840

%N Four times the area of the smallest of n-tuples of Heronian triangles with equal perimeter and equal area.

%C Kurz's paper reports the first 10 values in a table on page 193, (erroneously labeling them as areas), but the last two values are incorrect since correspond to n-tuples which are not minimal.

%H Sascha Kurz, <a href="http://serdica-comp.math.bas.bg/index.php/serdicajcomputing/article/view/48">On the generation of Heronian triangles</a>, Serdica Journal of Computing Vol. 2 (2008), 181-196.

%e The first 3 entries and corresponding triangles:

%e a(1) = 4*A = 4*6 = 24, p = 12, T = (3, 4, 5);

%e a(2) = 4*A = 4*210 = 840, p = 70, T = (17, 25, 28), (20, 21, 29);

%e a(3) = 4*A = 4*420 = 1680, p = 98, T = (24, 37, 37), (25, 34, 39), (29, 29, 40).

%Y Cf. A198311 (perimeters), A334285 (areas).

%K nonn,hard,more

%O 1,1

%A _Peter Luschny_, Jan 21 2012

%E Name edited, a(9)-a(10) corrected and a(11)-a(12) added by _Giovanni Resta_, Apr 21 2020