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A194312 Triangular array: g(n,k)=number of fractional parts (i*e) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n.

%I A194312 #5 Mar 30 2012 18:57:42
%S A194312 2,2,2,3,2,3,4,5,4,3,6,7,6,6,7,10,11,11,11,11,10,18,18,18,18,18,19,19,
%T A194312 32,32,31,32,32,33,32,32,57,58,56,57,57,56,59,56,56,104,102,101,103,
%U A194312 103,102,102,103,102,102,187,186,186,186,187,185,187,186,186,187
%N A194312 Triangular array:  g(n,k)=number of fractional parts (i*e) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n.
%C A194312 See A194285.
%e A194312 First eight rows:
%e A194312 2
%e A194312 2...2
%e A194312 3...2...3
%e A194312 4...5...4...3
%e A194312 6...7...6...6...7
%e A194312 10..11..11..11..11..10
%e A194312 18..18..18..18..18..19..19
%e A194312 32..32..31..32..32..33..32..32
%t A194312 r = E;
%t A194312 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194312 g[n_, k_] := Sum[f[n, k, i], {i, 1, 2^n}]
%t A194312 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194312 Flatten[%]    (* A194312 *)
%Y A194312 Cf. A194285.
%K A194312 nonn,tabl
%O A194312 1,1
%A A194312 _Clark Kimberling_, Aug 21 2011