A194306 Triangular array: g(n,k) = number of fractional parts (i*Pi) in interval [(k-1)/n, k/n], for 1 <= i <= 2n, 1 <= k <= n.

2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 3, 2, 2, 2, 2, 2, 0, 3, 3, 3, 1, 2, 2, 2, 2, 0, 3, 3, 0, 3, 3, 2, 1, 3, 2, 0, 4, 1, 2, 3, 0, 3, 3, 0, 3, 3, 0, 4, 0, 4, 3, 1, 3, 0, 3, 1, 2, 3, 0, 4, 0, 4, 0, 4, 0, 4, 2, 2, 2, 1, 3, 0, 4, 0, 4, 0, 4, 0, 4, 0

Offset

1,1

Comments

See A194285.

Links

Table of n, a(n) for n=1..100.

Example

First nine rows:
  3;
  3, 1;
  2, 2, 2;
  2, 2, 2, 2;
  2, 2, 3, 1, 2;
  2, 2, 2, 2, 2, 2;
  2, 2, 2, 2, 2, 2, 2;
  1, 2, 3, 2, 2, 2, 2, 2;
  0, 3, 3, 3, 1, 2, 2, 2, 2;

Mathematica

r = Pi;
f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
g[n_, k_] := Sum[f[n, k, i], {i, 1, n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194305 *)

Crossrefs

Cf. A194285.

Sequence in context: A214640 A224965 A194298 * A283325 A353707 A318438

Adjacent sequences: A194303 A194304 A194305 * A194307 A194308 A194309

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 21 2011

Status

approved