%I
%S 1,2,2,3,3,3,4,4,4,4,5,5,6,4,5,5,5,6,7,7,6,7,6,7,8,7,7,7,8,7,9,7,9,7,
%T 9,8,9,9,9,9,9,9,9,10,8,10,10,10,10,9,12,10,9,11,9,11,11,10,11,12,11,
%U 11,11,11,12,10,12,12,12,12,12,12,12,12,12,12,12,12,14,12,14,12
%N Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k1)/n, k/n], for 1<=i<=n^2, 1<=k<=n, r=3sqrt(5).
%C See A194285.
%e First eight rows:
%e 1
%e 2..2
%e 3..3..3
%e 4..4..4..4
%e 5..5..6..7..7..6
%e 7..6..7..8..7..7..7
%e 8..7..9..7..9..7..9..8
%t r = 3Sqrt[5];
%t f[n_, k_, i_] := If[(k  1)/n <= FractionalPart[i*r] < k/n, 1, 0]
%t g[n_, k_] := Sum[f[n, k, i], {i, 1, n^2}]
%t TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
%t Flatten[%] (* A194339 *)
%Y Cf. A194285.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Aug 22 2011
