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 A099832 Perimeters of Pythagorean triangles that can be constructed in exactly 3 different ways. 2
 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. 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

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Last modified September 25 06:32 EDT 2020. Contains 337335 sequences. (Running on oeis4.)