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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.
2

%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