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A194291 Triangular array: g(n,k)=number of fractional parts (i*sqrt(3)) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n.

%I A194291 #5 Mar 30 2012 18:57:42
%S A194291 1,2,2,2,4,3,4,3,5,4,5,5,5,5,5,5,6,7,6,5,7,7,7,7,7,7,7,7,8,8,7,9,7,9,
%T A194291 8,8,8,9,9,9,9,10,8,9,10,10,10,10,10,11,9,10,11,9,10,10,11,11,10,12,
%U A194291 11,11,12,11,11,11,11,12,13,11,12,13,12,11,13,12,11,13,13,13,13
%N A194291 Triangular array:  g(n,k)=number of fractional parts (i*sqrt(3)) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n.
%C A194291 See A194285.
%e A194291 First eight rows:
%e A194291 1
%e A194291 2..2
%e A194291 2..4..3
%e A194291 4..3..5..4
%e A194291 5..5..5..5..5
%e A194291 5..6..7..6..5..7
%e A194291 7..7..7..7..7..7..7
%e A194291 8..8..7..9..7..9..8..8
%t A194291 r = Sqrt[3];
%t A194291 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194291 g[n_, k_] := Sum[f[n, k, i], {i, 1, n^2}]
%t A194291 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194291 Flatten[%]    (* A194291 *)
%Y A194291 Cf. A194291.
%K A194291 nonn,tabl
%O A194291 1,2
%A A194291 _Clark Kimberling_, Aug 21 2011