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Triangular array: g(n,k)=number of fractional parts (i*sqrt(2)) 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 2,2,2,3,3,2,4,4,4,4,6,7,7,6,6,11,11,11,10,11,10,19,18,19,18,18,18,18,

%T 32,33,31,33,31,32,32,32,57,56,58,57,57,57,56,57,57,103,102,103,102,

%U 104,101,103,102,103,101,187,184,187,186,187,187,185,186,186,188

%N Triangular array: g(n,k)=number of fractional parts (i*sqrt(2)) 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 3...3...2

%e 4...4...4...4

%e 6...7...7...6...6

%e 11..11..11..10..11..10

%e 19..18..19..18..18..18..18

%e 32..33..31..33..31..32..32..32

%t r = Sqrt[2];

%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[%] (* A194288 *)

%Y Cf. A194285.

%K nonn,tabl

%O 1,1

%A _Clark Kimberling_, Aug 21 2011