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A194323 Triangular array: g(n,k)=number of fractional parts (i*sqrt(1/2)) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n.

%I A194323 #5 Mar 30 2012 18:57:43
%S A194323 1,2,2,2,4,3,4,4,4,4,5,4,5,6,5,6,5,7,6,7,5,7,7,6,7,8,7,7,8,8,8,8,8,9,
%T A194323 8,7,8,10,9,9,9,9,9,9,9,10,10,10,10,10,10,10,11,10,9,11,11,11,10,12,
%U A194323 11,11,11,11,12,10,12,13,11,11,13,12,12,11,13,13,11,12,13,13,12
%N A194323 Triangular array:  g(n,k)=number of fractional parts (i*sqrt(1/2)) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n.
%C A194323 See A194285.
%e A194323 First eight rows:
%e A194323 1
%e A194323 2..2
%e A194323 2..4..3
%e A194323 4..4..4..4
%e A194323 5..4..5..6..5
%e A194323 6..5..7..6..7..5
%e A194323 7..7..6..7..8..7..7
%e A194323 8..8..8..8..8..9..8..7
%t A194323 r = Sqrt[1/2];
%t A194323 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194323 g[n_, k_] := Sum[f[n, k, i], {i, 1, n^2}]
%t A194323 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194323 Flatten[%]    (* A194323 *)
%Y A194323 Cf. A194285.
%K A194323 nonn,tabl
%O A194323 1,2
%A A194323 _Clark Kimberling_, Aug 22 2011