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
KEYWORD
nonn
AUTHOR
Hugo Pfoertner, Oct 27 2004
STATUS
approved