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A194318 Triangular array: g(n,k)=number of fractional parts (i*sqrt(8)) in interval [(k-1)/n, k/n], for 1<=i<=2n, 1<=k<=n.

%I A194318 #5 Mar 30 2012 18:57:42
%S A194318 2,2,2,2,2,2,1,2,2,3,1,2,2,3,2,2,2,2,2,2,2,2,1,1,2,3,3,2,1,1,3,3,1,2,
%T A194318 3,2,1,2,3,1,2,3,1,2,3,1,2,2,1,3,2,2,3,1,3,1,2,2,2,2,2,3,1,3,1,3,2,2,
%U A194318 1,3,1,3,1,3,1,3,2,2,1,3,1,2,1,3,1,3,2,2,3,2,2,1,3,1,3,1,3,2,2
%N A194318 Triangular array:  g(n,k)=number of fractional parts (i*sqrt(8)) in interval [(k-1)/n, k/n], for 1<=i<=2n, 1<=k<=n.
%C A194318 See A194285.
%e A194318 First eight rows:
%e A194318 2
%e A194318 2..2
%e A194318 2..2..2
%e A194318 1..2..2..3
%e A194318 1..2..2..3..2
%e A194318 2..2..2..2..2..2
%e A194318 2..1..1..2..3..3..2
%e A194318 1..1..3..3..1..2..3..2
%t A194318 r = Sqrt[8];
%t A194318 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194318 g[n_, k_] := Sum[f[n, k, i], {i, 1, 2n}]
%t A194318 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194318 Flatten[%]    (* A194318 *)
%Y A194318 Cf. A194285.
%K A194318 nonn,tabl
%O A194318 1,1
%A A194318 _Clark Kimberling_, Aug 22 2011