cp's OEIS Frontend

A194324 Triangular array: g(n,k)=number of fractional parts (i*sqrt(1/2)) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n.

%I A194324 #5 Mar 30 2012 18:57:43
%S A194324 2,2,2,2,3,3,4,4,4,4,6,6,6,8,6,11,10,11,11,11,10,19,18,18,19,18,19,17,
%T A194324 33,32,31,32,32,32,32,32,56,58,57,57,57,56,57,56,58,103,102,102,103,
%U A194324 102,102,103,103,102,102,186,186,188,184,188,186,185,187,186,186
%N A194324 Triangular array:  g(n,k)=number of fractional parts (i*sqrt(1/2)) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n.
%C A194324 See A194285.
%e A194324 First eight rows:
%e A194324 2
%e A194324 2...2
%e A194324 2...3...3
%e A194324 4...4...4...4
%e A194324 6...6...6...8...6
%e A194324 11..10..11..11..11..10
%e A194324 19..18..18..19..18..19..17
%e A194324 33..32..31..32..32..32..32..32
%t A194324 r = Sqrt[1/2];
%t A194324 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194324 g[n_, k_] := Sum[f[n, k, i], {i, 1, 2^n}]
%t A194324 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194324 Flatten[%]    (* A194324 *)
%Y A194324 Cf. A194285.
%K A194324 nonn,tabl
%O A194324 1,1
%A A194324 _Clark Kimberling_, Aug 22 2011