

A334285


a(n) is the common area of the ntuple of Heronian triangles with minimal equal perimeter and equal area.


3



6, 210, 420, 6720, 49140, 196560, 4914000, 91400400, 348107760, 4765400640, 17057280240, 68229120960
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OFFSET

1,1


COMMENTS

Kurz's paper reports the first 10 values in a table on page 193, but for some reason the areas are multiplied by 4 (A204559) and the last two values are incorrect since correspond to ntuples which are not minimal.
If ntuples were sorted by area instead, a(2) would have been 168, corresponding to triangles (10, 35, 39), (14, 30, 40) with common perimeter 84.


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), 181196.
Giovanni Resta, ntuples for n=1..12


EXAMPLE

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


CROSSREFS

Cf. A198311, A204559.
Sequence in context: A201237 A120436 A136742 * A068969 A335715 A094805
Adjacent sequences: A334282 A334283 A334284 * A334286 A334287 A334288


KEYWORD

nonn


AUTHOR

Giovanni Resta, Apr 21 2020


STATUS

approved



