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%I #5 Mar 30 2012 18:57:42
%S 2,2,2,2,3,3,4,5,3,4,6,7,7,6,6,9,11,12,9,12,11,18,18,18,19,19,18,18,
%T 31,33,32,33,30,33,31,33,56,57,57,58,57,56,57,57,57,103,102,103,103,
%U 103,101,102,102,103,102,186,186,186,186,187,186,186,186,186,187
%N Triangular array: g(n,k)=number of fractional parts (i*sqrt(6)) 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...5...3...4
%e 6...7...7...6...6
%e 9...11..12..9...12..11
%e 18..18..18..19..19..18..18
%e 31..33..32..33..30..33..31..33
%t See A194285.
%t r = Sqrt[6];
%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[%] (* A194316 *)
%Y Cf. A194285.
%K nonn,tabl
%O 1,1
%A _Clark Kimberling_, Aug 21 2011
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