A194305 - OEIS

%I #9 Apr 10 2021 08:04:17

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

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

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

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

%C See A194285.

%e First eleven rows:

%e   1;

%e   2, 0;

%e   2, 1, 0;

%e   1, 2, 1, 0;

%e   1, 1, 2, 1, 0;

%e   1, 1, 1, 1, 1, 1;

%e   1, 1, 1, 1, 1, 1, 1;

%e   0, 2, 1, 1, 1, 1, 1, 1;

%e   0, 2, 2, 1, 0, 1, 1, 1, 1;

%e   0, 2, 2, 0, 2, 1, 0, 1, 1, 1;

%e   0, 2, 0, 2, 2, 0, 2, 1, 0, 1, 1;

%t r = Pi;

%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[%]    (* A194305 *)

%Y Cf. A194285.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Aug 21 2011