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A194292 Triangular array: g(n,k)=number of fractional parts (i*sqrt(3)) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n.

%I A194292 #5 Mar 30 2012 18:57:42
%S A194292 2,2,2,2,3,3,4,3,5,4,6,6,7,7,6,10,10,12,10,10,12,18,18,18,18,19,19,18,
%T A194292 32,32,31,33,31,34,31,32,56,57,57,57,56,57,57,58,57,101,104,101,102,
%U A194292 103,102,103,103,102,103,186,186,186,186,186,186,186,187,187
%N A194292 Triangular array:  g(n,k)=number of fractional parts (i*sqrt(3)) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n.
%C A194292 See A194285.
%e A194292 First eight rows:
%e A194292 2
%e A194292 2...2
%e A194292 2...3...3
%e A194292 4...3...5...4
%e A194292 6...6...7...7...6
%e A194292 10..10..12..10..10..12
%e A194292 18..18..18..18..19..19..18
%e A194292 32..32..31..33..31..34..31..32
%t A194292 r = Sqrt[3];
%t A194292 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194292 g[n_, k_] := Sum[f[n, k, i], {i, 1, 2^n}]
%t A194292 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194292 Flatten[%]    (* A194292 *)
%Y A194292 Cf. A194285.
%K A194292 nonn,tabl
%O A194292 1,1
%A A194292 _Clark Kimberling_, Aug 21 2011