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A194295 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n^2, r=(1+sqrt(5))/2, the golden ratio.

%I A194295 #5 Mar 30 2012 18:57:42
%S A194295 1,2,2,3,3,3,4,4,4,4,4,5,6,5,5,6,7,5,7,6,5,7,8,6,7,8,7,6,8,8,8,7,9,8,
%T A194295 8,8,9,9,9,9,9,10,8,10,8,10,10,10,10,10,10,9,11,10,10,11,11,11,11,10,
%U A194295 11,12,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13
%N A194295 Triangular array:  g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n^2, r=(1+sqrt(5))/2, the golden ratio.
%C A194295 See A194285.
%e A194295 First eight rows:
%e A194295 1
%e A194295 2..2
%e A194295 3..3..3
%e A194295 4..4..4..4
%e A194295 4..5..6..5..5
%e A194295 6..7..5..7..6..5
%e A194295 7..8..6..7..8..7..6
%e A194295 8..8..8..7..9..8..8..8
%t A194295 r = GoldenRatio;
%t A194295 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194295 g[n_, k_] := Sum[f[n, k, i], {i, 1, n^2}]
%t A194295 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194295 Flatten[%]    (* A194295 *)
%Y A194295 Cf. A194295.
%K A194295 nonn,tabl
%O A194295 1,2
%A A194295 _Clark Kimberling_, Aug 21 2011