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A194288 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.

%I A194288 #5 Mar 30 2012 18:57:42
%S A194288 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 A194288 32,33,31,33,31,32,32,32,57,56,58,57,57,57,56,57,57,103,102,103,102,
%U A194288 104,101,103,102,103,101,187,184,187,186,187,187,185,186,186,188
%N A194288 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 A194288 See A194285.
%e A194288 First eight rows:
%e A194288 2
%e A194288 2...2
%e A194288 3...3...2
%e A194288 4...4...4...4
%e A194288 6...7...7...6...6
%e A194288 11..11..11..10..11..10
%e A194288 19..18..19..18..18..18..18
%e A194288 32..33..31..33..31..32..32..32
%t A194288 r = Sqrt[2];
%t A194288 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194288 g[n_, k_] := Sum[f[n, k, i], {i, 1, 2^n}]
%t A194288 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194288 Flatten[%]    (* A194288 *)
%Y A194288 Cf. A194285.
%K A194288 nonn,tabl
%O A194288 1,1
%A A194288 _Clark Kimberling_, Aug 21 2011