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A194329 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=2-sqrt(3).

%I A194329 #5 Mar 30 2012 18:57:43
%S A194329 1,1,1,1,1,1,1,1,1,1,1,2,1,0,1,1,1,1,2,1,0,1,1,1,1,1,1,1,1,1,2,0,2,0,
%T A194329 1,1,1,1,1,2,1,1,0,2,0,1,1,1,1,1,1,2,0,2,0,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A194329 1,1,2,0,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,0,1,1,1,0,1,1,2,1,1,1,1,1
%N A194329 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=2-sqrt(3).
%C A194329 See A194285.
%e A194329 First eleven rows:
%e A194329 1
%e A194329 1..1
%e A194329 1..1..1
%e A194329 1..1..1..1
%e A194329 1..2..1..0..1
%e A194329 1..1..1..2..1..0
%e A194329 1..1..1..1..1..1..1
%e A194329 1..1..2..0..2..0..1..1
%e A194329 1..1..1..2..1..1..0..2..0
%e A194329 1..1..1..1..1..1..2..0..2..0
%e A194329 1..1..1..1..1..1..1..1..1..1..1
%t A194329 r = 2-Sqrt[3];
%t A194329 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194329 g[n_, k_] := Sum[f[n, k, i], {i, 1, n}]
%t A194329 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194329 Flatten[%]    (* A194329 *)
%Y A194329 Cf. A194285.
%K A194329 nonn,tabl
%O A194329 1,12
%A A194329 _Clark Kimberling_, Aug 22 2011