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A194332 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n, r=2-sqrt(3).

%I A194332 #5 Mar 30 2012 18:57:43
%S A194332 2,2,2,3,3,2,4,5,3,4,6,7,7,6,6,12,10,10,12,10,10,18,19,19,18,18,18,18,
%T A194332 32,31,34,31,33,31,32,32,57,58,57,57,56,57,57,57,56,103,102,103,103,
%U A194332 102,103,102,101,104,101,186,186,187,187,186,186,186,186,186,186
%N A194332 Triangular array:  g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n, r=2-sqrt(3).
%C A194332 See A194285.
%e A194332 First eight rows:
%e A194332 2
%e A194332 2...2
%e A194332 3...3...2
%e A194332 4...5...3...4
%e A194332 6...7...7...6...6
%e A194332 12..10..10..12..10..10
%e A194332 18..19..19..18..18..18..18
%e A194332 32..31..34..31..33..31..32..32
%t A194332 r = 2-Sqrt[3];
%t A194332 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194332 g[n_, k_] := Sum[f[n, k, i], {i, 1, 2^n}]
%t A194332 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194332 Flatten[%]    (* A194332 *)
%Y A194332 Cf. A194285.
%K A194332 nonn,tabl
%O A194332 1,1
%A A194332 _Clark Kimberling_, Aug 22 2011