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A194327 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=2-sqrt(2).

%I A194327 #5 Mar 30 2012 18:57:43
%S A194327 1,2,2,3,3,3,4,4,4,4,5,5,5,6,4,6,6,5,7,6,6,7,7,6,7,8,7,7,7,8,9,7,9,8,
%T A194327 7,9,9,9,9,9,9,9,10,9,8,9,10,10,10,10,11,10,10,10,10,10,12,11,11,11,
%U A194327 11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13
%N A194327 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=2-sqrt(2).
%C A194327 See A194285.
%e A194327 First eight rows:
%e A194327 1
%e A194327 2..2
%e A194327 3..3..3
%e A194327 4..4..4..4
%e A194327 5..5..5..6..4
%e A194327 6..6..5..7..6..6
%e A194327 7..7..6..7..8..7..7
%e A194327 7..8..9..7..9..8..7..9
%t A194327 r = 2-Sqrt[2];
%t A194327 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194327 g[n_, k_] := Sum[f[n, k, i], {i, 1, n^2}]
%t A194327 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194327 Flatten[%]    (* A194327 *)
%Y A194327 Cf. A194285.
%K A194327 nonn,tabl
%O A194327 1,2
%A A194327 _Clark Kimberling_, Aug 22 2011