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A194304 Triangular array: g(n,k)=number of fractional parts (i*sqrt(5)) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n.

%I A194304 #6 Mar 30 2012 18:57:42
%S A194304 2,2,2,2,3,3,4,4,4,4,7,6,7,6,6,11,11,11,10,10,11,18,19,18,19,17,19,18,
%T A194304 32,33,32,33,31,32,31,32,56,58,57,57,57,57,56,57,57,103,102,102,102,
%U A194304 105,101,102,103,102,102,185,188,185,187,186,187,186,185,188,184
%N A194304 Triangular array:  g(n,k)=number of fractional parts (i*sqrt(5)) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n.
%C A194304 See A194285.
%e A194304 First eight rows:
%e A194304 2
%e A194304 2...2
%e A194304 2...3...3
%e A194304 4...4...4...4
%e A194304 7...6...7...6...6
%e A194304 11..11..11..10..10..11
%e A194304 18..19..18..19..17..19..18
%e A194304 32..33..32..33..31..32..31..32
%t A194304 r = Sqrt[5];
%t A194304 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194304 g[n_, k_] := Sum[f[n, k, i], {i, 1, 2^n}]
%t A194304 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194304 Flatten[%]    (* A194304 *)
%Y A194304 Cf. A194285.
%K A194304 nonn,tabl
%O A194304 1,1
%A A194304 _Clark Kimberling_, Aug 21 2011