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A194297 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, r=(1+sqrt(3))/2.

%I A194297 #5 Mar 30 2012 18:57:42
%S A194297 1,1,1,1,1,1,1,2,1,0,1,1,1,1,1,1,1,2,0,2,0,1,1,1,2,0,2,0,1,1,1,1,1,1,
%T A194297 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A194297 1,1,2,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,2,1,0,1,1,2,1,0,1,2,1,1
%N A194297 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, r=(1+sqrt(3))/2.
%C A194297 See A194285.
%e A194297 First ten rows:
%e A194297 1
%e A194297 1..1
%e A194297 1..1..1
%e A194297 1..2..1..0
%e A194297 1..1..1..1..1
%e A194297 1..1..2..0..2..0
%e A194297 1..1..1..2..0..2..0
%e A194297 1..1..1..1..1..1..1..1
%e A194297 1..1..1..1..1..1..1..1..1
%e A194297 1..1..1..1..1..1..1..1..1..1
%t A194297 r = (1+Sqrt[3])/2;
%t A194297 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194297 g[n_, k_] := Sum[f[n, k, i], {i, 1, n}]
%t A194297 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194297 Flatten[%]    (* A194297 *)
%Y A194297 Cf. A194297.
%K A194297 nonn,tabl
%O A194297 1,8
%A A194297 _Clark Kimberling_, Aug 21 2011