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A194299 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=(1+sqrt(3))/2.

%I A194299 #5 Mar 30 2012 18:57:42
%S A194299 1,3,1,3,3,3,4,5,3,4,6,5,5,5,4,6,6,7,5,7,5,7,7,7,8,6,8,6,9,8,8,9,7,8,
%T A194299 8,7,9,8,10,8,10,9,9,9,9,10,10,10,11,10,10,10,10,10,9,10,11,11,12,11,
%U A194299 11,11,11,11,11,11,11,13,12,11,13,12,12,11,13,12,12,12,13,14,13
%N A194299 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=(1+sqrt(3))/2.
%C A194299 See A194285.
%e A194299 First eight rows:
%e A194299 1
%e A194299 3..1
%e A194299 3..3..3
%e A194299 4..5..3..4
%e A194299 6..5..5..5..4
%e A194299 6..6..7..5..7..5
%e A194299 7..7..7..8..6..8..6
%e A194299 9..8..8..9..7..8..8..7
%t A194299 r = (1+Sqrt[3])/2;
%t A194299 f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t A194299 g[n_, k_] := Sum[f[n, k, i], {i, 1, n^2}]
%t A194299 TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t A194299 Flatten[%]    (* A194299 *)
%Y A194299 Cf. A194285.
%K A194299 nonn,tabl
%O A194299 1,2
%A A194299 _Clark Kimberling_, Aug 21 2011