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A194287 Triangular array: g(n,k)=number of fractional parts (i*sqrt(2)) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n.

%I A194287 #5 Mar 30 2012 18:57:42
%S A194287 1,2,2,3,3,3,4,4,4,4,4,6,5,5,5,6,6,7,5,6,6,7,7,8,7,6,7,7,9,7,8,9,7,9,
%T A194287 8,7,8,9,10,9,9,9,9,9,9,10,10,10,10,11,10,10,10,10,9,11,11,11,11,11,
%U A194287 11,11,11,11,12,10,12,12,12,12,12,12,12,12,12,12,12,12
%N A194287 Triangular array:  g(n,k)=number of fractional parts (i*sqrt(2)) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n.
%C A194287 See A194285.
%e A194287 First eight rows:
%e A194287 1
%e A194287 2..2
%e A194287 3..3..3
%e A194287 4..4..4..4
%e A194287 4..6..5..5..5
%e A194287 6..6..7..5..6..6
%e A194287 7..7..8..7..6..7..7
%e A194287 9..7..8..9..7..9..8..7
%t A194287 r = Sqrt[2];
%t A194287 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194287 g[n_, k_] := Sum[f[n, k, i], {i, 1, n^2}]
%t A194287 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194287 Flatten[%]    (* A194287 *)
%Y A194287 Cf. A194285.
%K A194287 nonn,tabl
%O A194287 1,2
%A A194287 _Clark Kimberling_, Aug 21 2011