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A334285 a(n) is the common area of the n-tuple of Heronian triangles with minimal equal perimeter and equal area. 3
6, 210, 420, 6720, 49140, 196560, 4914000, 91400400, 348107760, 4765400640, 17057280240, 68229120960 (list; graph; refs; listen; history; text; internal format)
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 n-tuples which are not minimal.

If n-tuples 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), 181-196.

Giovanni Resta, n-tuples 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

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Last modified August 7 19:39 EDT 2020. Contains 336279 sequences. (Running on oeis4.)