A194337 - OEIS

%I #5 Mar 30 2012 18:57:43

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

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

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

%N Triangular array:  g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n, r=3-sqrt(5).

%C See A194285.

%e First nine rows:

%e 1

%e 0..2

%e 1..1..1

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

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

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

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

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

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

%t r = 3-Sqrt[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}]

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

%t Flatten[%]    (* A194337 *)

%Y Cf. A194285.

%K nonn,tabl

%O 1,3

%A _Clark Kimberling_, Aug 22 2011