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%I #9 Aug 11 2015 01:14:45
%S 225,361,625,900,1444,2500,3600,5776,10000,14400,23104,40000,57600,
%T 92416
%N Squares that can be written as a sum of 3 distinct nonzero squares in exactly two ways.
%t t = Sort[Select[Flatten[Table[x^2 + y^2 + z^2, {x, 400}, {y, x + 1, 400}, {z, y + 1, 400}]], # < 160006 && IntegerQ[Sqrt[#]] &]];
%t f1[l_] := Module[{t = {}}, Do[If[l[[n]] != l[[n + 1]] && l[[n]] != l[[n - 1]], AppendTo[t, l[[n]]]], {n, Length[l] - 1}]; t];
%t f2[l_] := Module[{t = {}}, Do[If[l[[n]] == l[[n + 1]], AppendTo[t, l[[n]]]], {n, Length[l] - 1}]; t];
%t s1 = Join[{First[t]}, f1[t]];
%t Complement[t, s1];
%t t = f2[t];
%t s2 = Join[{First[t]}, f1[t]]
%Y Cf. A207638, A207639.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Feb 19 2012