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%I #5 Mar 30 2012 18:57:42
%S 2,2,2,3,2,3,4,4,4,4,6,6,7,7,6,10,11,10,12,10,11,19,19,17,19,19,17,18,
%T 32,33,32,31,33,32,31,32,57,57,57,56,57,58,56,58,56,102,102,103,102,
%U 102,103,102,103,103,102,187,186,187,185,185,186,187,187,186,187
%N Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=2^n, r=(1+sqrt(5))/2, the golden ratio.
%C See A194285.
%e First seven rows:
%e 2
%e 2...2
%e 3...2...3
%e 4...4...4...4
%e 6...6...7...7...6
%e 10..11..10..12..10..11
%e 19..19..17..19..19..17..18
%t r = GoldenRatio;
%t f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t g[n_, k_] := Sum[f[n, k, i], {i, 1, 2^n}]
%t TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t Flatten[%] (* A194296 *)
%Y Cf. A194285.
%K nonn,tabl
%O 1,1
%A _Clark Kimberling_, Aug 21 2011
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