A099832 - OEIS

A099832

Perimeters of Pythagorean triangles that can be constructed in exactly 3 different ways.

120, 168, 180, 252, 280, 336, 396, 528, 540, 560, 600, 624, 792, 864, 880, 936, 1040, 1050, 1056, 1120, 1176, 1224, 1232, 1248, 1350, 1368, 1380, 1404, 1456, 1620, 1632, 1650, 1656, 1710, 1728, 1740, 1760, 1764, 1824, 1836, 1860, 1960, 2002, 2052, 2080

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Ray Chandler, Table of n, a(n) for n = 1..10000

Ron Knott, Pythagorean Triples and Online Calculators

Eric Weisstein's World of Mathematics, Pythagorean Triple.

Index entries related to Pythagorean Triples.

EXAMPLE

a(1)=120 = 20+48+52 = 24+45+51 = 30+40+50; a(2)=168 = 21+72+75 = 24+70+74 = 42+56+70.

MATHEMATICA

SetSystemOptions["ReduceOptions" -> {"DiscreteSolutionBound" -> 2500}]; AllPerimeterTriples[n_Integer] /; n > 0 := Module[{result = Reduce[ Reduce[{x^2 + y^2 == z^2, z > y > x > 0, Element[{x, y, z}, Integers], x + y + z == n}, {x, y, z}]]}, If[result === False, {}, Sort[{x, y, z} /. {ToRules[result]}]]]; Select[ Range[ 2500], Length[ AllPerimeterTriples[#]] == 3 &] (* Robert G. Wilson v, Oct 17 2012 *)

CROSSREFS

Cf. A098714, A099381, A099383, A156687.

Sequence in context: A039602 A316835 A179642 * A111399 A030634 A272594

Adjacent sequences: A099829 A099830 A099831 * A099833 A099834 A099835

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Oct 27 2004

STATUS

approved