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A194315 Triangular array: g(n,k)=number of fractional parts (i*sqrt(6)) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n.

%I A194315 #6 Mar 30 2012 18:57:42
%S A194315 1,2,2,3,3,3,4,5,3,4,4,6,5,5,5,5,6,8,4,7,6,7,7,6,7,8,7,7,6,9,8,9,7,8,
%T A194315 8,9,8,9,9,10,9,9,9,9,9,10,10,10,10,11,9,10,10,10,10,11,11,11,11,12,
%U A194315 11,10,11,11,11,11,11,12,12,12,12,14,10,12,13,12,12,12,13,13,12
%N A194315 Triangular array:  g(n,k)=number of fractional parts (i*sqrt(6)) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n.
%C A194315 See A194285.
%e A194315 First eight rows:
%e A194315 1
%e A194315 2..2
%e A194315 3..3..3
%e A194315 4..5..3..4
%e A194315 4..6..5..5..5
%e A194315 5..6..8..4..7..6
%e A194315 7..7..6..7..8..7..7
%e A194315 6..9..8..9..7..8..8..9
%t A194315 r = Sqrt[6];
%t A194315 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194315 g[n_, k_] := Sum[f[n, k, i], {i, 1, n^2}]
%t A194315 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194315 Flatten[%]    (* A194315 *)
%Y A194315 Cf. A194315.
%K A194315 nonn,tabl
%O A194315 1,2
%A A194315 _Clark Kimberling_, Aug 21 2011