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Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^2=3x*y.
2

%I #4 Apr 20 2012 15:10:09

%S 0,0,0,2,2,2,6,6,6,8,8,8,14,14,14,16,18,18,22,22,22,24,24,24,30,32,32,

%T 38,38,38,44,44,46,48,48,48,56,56,56,58,58,58,62,62,62,66,66,66,76,80,

%U 82,84,84,84,92,92,92,94,94,94,104,104,104,108,112,112,116

%N Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^2=3x*y.

%C For a guide to related sequences, see A211422.

%t t[n_] := t[n] = Flatten[Table[w^2 - 3 x*y, {w, 1, n}, {x, 1, n}, {y, 1, n}]]

%t c[n_] := Count[t[n], 0]

%t t = Table[c[n], {n, 0, 70}] (* A211512 *)

%t t/2 (* integers *)

%Y Cf. A211422.

%K nonn

%O 0,4

%A _Clark Kimberling_, Apr 14 2012