A204559 Four times the area of the smallest of n-tuples of Heronian triangles with equal perimeter and equal area.

24, 840, 1680, 26880, 196560, 786240, 19656000, 365601600, 1392431040, 19061602560, 68229120960, 272916483840

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..12.

Sascha Kurz, On the generation of Heronian triangles, Serdica Journal of Computing Vol. 2 (2008), 181-196.

Example

The first 3 entries and corresponding triangles:
a(1) = 4*A = 4*6 = 24, p = 12, T = (3, 4, 5);
a(2) = 4*A = 4*210 = 840, p = 70, T = (17, 25, 28), (20, 21, 29);
a(3) = 4*A = 4*420 = 1680, p = 98, T = (24, 37, 37), (25, 34, 39), (29, 29, 40).

Crossrefs

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

Sequence in context: A275635 A158651 A265884 * A078522 A268632 A208792

Adjacent sequences: A204556 A204557 A204558 * A204560 A204561 A204562

Keyword

nonn,hard,more

Author

Peter Luschny, Jan 21 2012

Extensions

Name edited, a(9)-a(10) corrected and a(11)-a(12) added by Giovanni Resta, Apr 21 2020

Status

approved