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A194328 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(2).

%I A194328 #5 Mar 30 2012 18:57:43
%S A194328 2,2,2,2,3,3,4,4,4,4,6,6,7,7,6,10,11,10,11,11,11,18,18,18,18,19,18,19,
%T A194328 32,32,32,31,33,31,33,32,57,57,56,57,57,57,58,56,57,101,103,102,103,
%U A194328 101,104,102,103,102,103,185,188,186,186,185,187,187,186,187,184
%N A194328 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(2).
%C A194328 See A194285.
%e A194328 First eight rows:
%e A194328 2
%e A194328 2...2
%e A194328 2...3...3
%e A194328 4...4...4...4
%e A194328 6...6...7...7...6
%e A194328 10..11..10..11..11..11
%e A194328 18..18..18..18..19..18..19
%e A194328 32..32..32..31..33..31..33..32
%t A194328 r = 2-Sqrt[2];
%t A194328 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194328 g[n_, k_] := Sum[f[n, k, i], {i, 1, 2^n}]
%t A194328 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194328 Flatten[%]    (* A194328 *)
%Y A194328 Cf. A194285.
%K A194328 nonn,tabl
%O A194328 1,1
%A A194328 _Clark Kimberling_, Aug 22 2011