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A194311 Triangular array: g(n,k)=number of fractional parts (i*e) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n.

%I A194311 #6 Mar 30 2012 18:57:42
%S A194311 1,2,2,3,3,3,4,5,4,3,5,5,5,5,5,6,5,7,5,7,6,7,7,7,7,7,7,7,8,8,8,8,8,8,
%T A194311 8,8,8,10,9,9,9,9,10,9,8,10,10,9,11,10,9,10,10,11,10,11,11,11,10,12,
%U A194311 10,12,10,12,11,11,11,12,12,11,12,13,12,12,13,12,12,12,12,13,13
%N A194311 Triangular array:  g(n,k)=number of fractional parts (i*e) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n.
%C A194311 See A194285.
%e A194311 First eight rows:
%e A194311 1
%e A194311 2..2
%e A194311 3..3..3
%e A194311 4..5..4..3
%e A194311 5..5..5..5..5
%e A194311 6..5..7..5..7..6
%e A194311 7..7..7..7..7..7..7
%e A194311 8..8..8..8..8..8..8..8
%t A194311 r = E;
%t A194311 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194311 g[n_, k_] := Sum[f[n, k, i], {i, 1, n^2}]
%t A194311 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194311 Flatten[%]    (* A194311 *)
%Y A194311 Cf. A194285.
%K A194311 nonn,tabl
%O A194311 1,2
%A A194311 _Clark Kimberling_, Aug 21 2011