A334285 a(n) is the common area of the n-tuple of Heronian triangles with minimal equal perimeter and equal area.

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

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