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A194343 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n, r=3-e.

%I A194343 #5 Mar 30 2012 18:57:43
%S A194343 1,2,2,3,3,3,3,4,5,4,5,5,5,5,5,6,7,5,7,5,6,7,7,7,7,7,7,7,8,8,8,8,8,8,
%T A194343 8,8,8,9,10,9,9,9,9,10,8,10,11,10,10,9,10,11,9,10,10,11,11,12,10,12,
%U A194343 10,12,10,11,11,11,12,12,12,13,12,12,13,12,11,12,12,11,14,12,14
%N A194343 Triangular array:  g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n, r=3-e.
%C A194343 See A194285.
%e A194343 First eight rows:
%e A194343 1
%e A194343 2..2
%e A194343 3..3..3
%e A194343 3..4..5..4
%e A194343 5..5..5..5..5
%e A194343 6..7..5..7..5..6
%e A194343 7..7..7..7..7..7..7
%e A194343 8..8..8..8..8..8..8..8
%t A194343 r = 3-E;
%t A194343 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194343 g[n_, k_] := Sum[f[n, k, i], {i, 1, n^2}]
%t A194343 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194343 Flatten[%]    (* A194343 *)
%Y A194343 Cf. A194343.
%K A194343 nonn,tabl
%O A194343 1,2
%A A194343 _Clark Kimberling_, Aug 22 2011