%I #5 Mar 30 2012 18:57:43
%S 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 32,31,32,33,31,32,33,32,56,58,56,58,57,56,57,57,57,102,103,103,102,
%U 103,102,102,103,102,102,185,187,186,187,187,186,185,185,187,186
%N 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 See A194285.
%e First eight rows:
%e 2
%e 2...2
%e 3...2...3
%e 4...4...4...4
%e 6...7...7...6...6
%e 11..10..12..10..11..10
%e 18..17..19..19..17..19..19
%e 32..31..32..33..31..32..33..32
%t r = 2-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[%] (* A194336 *)
%Y Cf. A194285.
%K nonn,tabl
%O 1,1
%A _Clark Kimberling_, Aug 22 2011