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%I #6 Mar 30 2012 18:57:42
%S 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 32,33,32,33,31,32,31,32,56,58,57,57,57,57,56,57,57,103,102,102,102,
%U 105,101,102,103,102,102,185,188,185,187,186,187,186,185,188,184
%N 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 See A194285.
%e First eight rows:
%e 2
%e 2...2
%e 2...3...3
%e 4...4...4...4
%e 7...6...7...6...6
%e 11..11..11..10..10..11
%e 18..19..18..19..17..19..18
%e 32..33..32..33..31..32..31..32
%t r = Sqrt[5];
%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[%] (* A194304 *)
%Y Cf. A194285.
%K nonn,tabl
%O 1,1
%A _Clark Kimberling_, Aug 21 2011
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