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A194326 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=2n, 1<=k<=n, r=2-sqrt(2).

%I A194326 #5 Mar 30 2012 18:57:43
%S A194326 2,2,2,1,3,2,2,1,3,2,2,2,2,2,2,2,2,2,2,2,2,2,3,1,2,3,1,2,2,2,3,1,3,1,
%T A194326 3,1,2,2,1,3,2,2,2,2,2,1,3,2,2,1,3,2,3,1,2,1,3,2,2,2,2,2,2,2,2,2,2,2,
%U A194326 2,2,2,2,2,2,2,2,2,2,2,2,3,2,2,1,2,3,2,2,1,2,2,2,2,2,2,2,2,2,2
%N A194326 Triangular array:  g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=2n, 1<=k<=n, r=2-sqrt(2).
%C A194326 See A194285.
%e A194326 First ten rows:
%e A194326 2
%e A194326 2..2
%e A194326 1..3..2
%e A194326 2..1..3..2
%e A194326 2..2..2..2..2
%e A194326 2..2..2..2..2..2
%e A194326 2..3..1..2..3..1..2
%e A194326 2..2..3..1..3..1..3..1
%e A194326 2..2..1..3..2..2..2..2..2
%e A194326 1..3..2..2..1..3..2..3..1..2
%t A194326 r = 2-Sqrt[2];
%t A194326 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194326 g[n_, k_] := Sum[f[n, k, i], {i, 1, 2n}]
%t A194326 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194326 Flatten[%]    (* A194326 *)
%Y A194326 Cf. A194285.
%K A194326 nonn,tabl
%O A194326 1,1
%A A194326 _Clark Kimberling_, Aug 22 2011