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A194335 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n, r=2-tau, where tau=(1+sqrt(5))/2, the golden ratio.

%I A194335 #5 Mar 30 2012 18:57:43
%S A194335 1,2,2,3,3,3,4,4,4,4,5,5,6,5,4,5,6,7,5,7,6,6,7,8,7,6,8,7,8,8,8,9,7,8,
%T A194335 8,8,8,10,8,10,9,9,9,9,9,10,10,11,9,10,10,10,10,10,10,11,11,11,11,12,
%U A194335 11,10,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13
%N A194335 Triangular array:  g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n, r=2-tau, where tau=(1+sqrt(5))/2, the golden ratio.
%C A194335 See A194285.
%e A194335 First eight rows:
%e A194335 1
%e A194335 2..2
%e A194335 3..3..3
%e A194335 4..4..4..4
%e A194335 5..5..6..5..4
%e A194335 5..6..7..5..7..6
%e A194335 6..7..8..7..6..8..7
%e A194335 8..8..8..9..7..8..8..8
%t A194335 r = 2-GoldenRatio;
%t A194335 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194335 g[n_, k_] := Sum[f[n, k, i], {i, 1, n^2}]
%t A194335 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194335 Flatten[%]    (* A194335 *)
%Y A194335 Cf. A194285.
%K A194335 nonn,tabl
%O A194335 1,2
%A A194335 _Clark Kimberling_, Aug 22 2011