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A194320 Triangular array: g(n,k)=number of fractional parts (i*sqrt(8)) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n.

%I A194320 #5 Mar 30 2012 18:57:42
%S A194320 2,2,2,2,3,3,2,6,3,5,6,6,7,7,6,11,10,11,11,11,10,19,18,18,18,18,19,18,
%T A194320 31,32,32,33,31,32,32,33,56,57,58,55,57,58,56,58,57,102,102,101,104,
%U A194320 103,102,103,102,103,102,185,186,185,186,186,186,187,186,187,187
%N A194320 Triangular array:  g(n,k)=number of fractional parts (i*sqrt(8)) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n.
%C A194320 See A194285.
%e A194320 First eight rows:
%e A194320 2
%e A194320 2...2
%e A194320 2...3...3
%e A194320 2...6...3...5
%e A194320 6...6...7...7...6
%e A194320 11..10..11..11..11..10
%e A194320 19..18..18..18..18..19..18
%e A194320 31..32..32..33..31..32..32..33
%t A194320 r = Sqrt[8];
%t A194320 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194320 g[n_, k_] := Sum[f[n, k, i], {i, 1, 2^n}]
%t A194320 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194320 Flatten[%]    (* A194320 *)
%Y A194320 Cf. A194285.
%K A194320 nonn,tabl
%O A194320 1,1
%A A194320 _Clark Kimberling_, Aug 22 2011