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A194313 Triangular array: g(n,k)=number of fractional parts (i*sqrt(6)) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n.

%I A194313 #5 Mar 30 2012 18:57:42
%S A194313 1,1,1,0,2,1,0,2,0,2,0,2,1,1,1,0,1,2,0,2,1,0,2,1,1,1,1,1,0,2,1,1,1,1,
%T A194313 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A194313 1,0,2,2,0,1,1,1,1,1,1,1,0,1,1,2,1,1,0,1,2,1,1,1,0,1,1,2,1,2,0,1
%N A194313 Triangular array:  g(n,k)=number of fractional parts (i*sqrt(6)) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n.
%C A194313 See A194285.
%e A194313 First nine rows:
%e A194313 1
%e A194313 1..1
%e A194313 0..2..1
%e A194313 0..2..0..2
%e A194313 0..2..1..1..1
%e A194313 0..1..2..0..2..1
%e A194313 0..2..1..1..1..1..1
%e A194313 0..2..1..1..1..1..1..1
%e A194313 1..1..1..1..1..1..1..1..1
%t A194313 r = Sqrt[6];
%t A194313 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194313 g[n_, k_] := Sum[f[n, k, i], {i, 1, n}]
%t A194313 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194313 Flatten[%]    (* A194313 *)
%Y A194313 Cf. A194285.
%K A194313 nonn,tabl
%O A194313 1,5
%A A194313 _Clark Kimberling_, Aug 21 2011