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A194336 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-tau, where tau=(1+sqrt(5))/2, the golden ratio.

%I A194336 #5 Mar 30 2012 18:57:43
%S A194336 2,2,2,3,2,3,4,4,4,4,6,7,7,6,6,11,10,12,10,11,10,18,17,19,19,17,19,19,
%T A194336 32,31,32,33,31,32,33,32,56,58,56,58,57,56,57,57,57,102,103,103,102,
%U A194336 103,102,102,103,102,102,185,187,186,187,187,186,185,185,187,186
%N A194336 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-tau, where tau=(1+sqrt(5))/2, the golden ratio.
%C A194336 See A194285.
%e A194336 First eight rows:
%e A194336 2
%e A194336 2...2
%e A194336 3...2...3
%e A194336 4...4...4...4
%e A194336 6...7...7...6...6
%e A194336 11..10..12..10..11..10
%e A194336 18..17..19..19..17..19..19
%e A194336 32..31..32..33..31..32..33..32
%t A194336 r = 2-GoldenRatio;
%t A194336 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194336 g[n_, k_] := Sum[f[n, k, i], {i, 1, 2^n}]
%t A194336 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194336 Flatten[%]    (* A194336 *)
%Y A194336 Cf. A194285.
%K A194336 nonn,tabl
%O A194336 1,1
%A A194336 _Clark Kimberling_, Aug 22 2011