A194289 - OEIS

%I #5 Mar 30 2012 18:57:42

%S 1,1,1,1,1,1,1,1,1,1,1,0,1,2,1,0,1,2,1,1,1,1,1,1,1,1,1,1,1,1,0,2,0,2,

%T 1,1,0,2,0,1,1,2,1,1,1,0,2,0,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,

%U 1,1,1,1,0,2,1,1,1,1,1,1,1,0,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1

%N Triangular array:  g(n,k)=number of fractional parts (i*sqrt(3)) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n.

%C See A194285.

%e First eight rows:

%e 1

%e 1..1

%e 1..1..1

%e 1..1..1..1

%e 1..0..1..2..1

%e 0..1..2..1..1..1

%e 1..1..1..1..1..1..1

%e 1..1..0..2..0..2..1..1

%t r = Sqrt[3];

%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}]

%t TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]

%t Flatten[%]    (* A194289 *)

%Y Cf. A194285.

%K nonn,tabl

%O 1,14

%A _Clark Kimberling_, Aug 21 2011