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A194340 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=3-sqrt(5).

%I A194340 #5 Mar 30 2012 18:57:43
%S A194340 2,2,2,3,3,2,4,4,4,4,6,6,7,6,7,11,10,10,11,11,11,18,19,17,19,18,19,18,
%T A194340 32,31,32,31,33,32,33,32,57,57,56,57,57,57,57,58,56,102,102,103,102,
%U A194340 101,105,102,102,102,103,187,184,188,185,186,187,186,187,185,188
%N A194340 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=3-sqrt(5).
%C A194340 See A194285.
%e A194340 First six rows:
%e A194340 2
%e A194340 2...2
%e A194340 3...3...2
%e A194340 4...4...4...4
%e A194340 6...6...7...6...7
%e A194340 11..10..10..11..11..11
%t A194340 r = 3-Sqrt[5];
%t A194340 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194340 g[n_, k_] := Sum[f[n, k, i], {i, 1, 2^n}]
%t A194340 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194340 Flatten[%]    (* A194340 *)
%Y A194340 Cf. A194285.
%K A194340 nonn,tabl
%O A194340 1,1
%A A194340 _Clark Kimberling_, Aug 22 2011