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A194303 Triangular array: g(n,k)=number of fractional parts (i*sqrt(5)) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n.

%I A194303 #5 Mar 30 2012 18:57:42
%S A194303 1,2,2,3,3,3,4,4,4,4,5,4,6,5,5,6,7,7,6,5,5,7,7,7,8,7,6,7,8,9,7,9,7,9,
%T A194303 7,8,8,10,9,9,9,9,9,9,9,9,11,9,10,12,9,10,10,10,10,10,12,11,11,11,11,
%U A194303 12,11,10,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,14
%N A194303 Triangular array:  g(n,k)=number of fractional parts (i*sqrt(5)) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n.
%C A194303 See A194285.
%e A194303 First eight rows:
%e A194303 1
%e A194303 2..2
%e A194303 3..3..3
%e A194303 4..4..4..4
%e A194303 5..4..6..5..5
%e A194303 6..7..7..6..5..5
%e A194303 7..7..7..8..7..6..7
%e A194303 8..9..7..9..7..9..7..8
%t A194303 r = Sqrt[5];
%t A194303 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194303 g[n_, k_] := Sum[f[n, k, i], {i, 1, n^2}]
%t A194303 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194303 Flatten[%]    (* A194303 *)
%Y A194303 Cf. A194285.
%K A194303 nonn,tabl
%O A194303 1,2
%A A194303 _Clark Kimberling_, Aug 21 2011