A194305 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.

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, 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, 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

Offset: 1

Author

Clark Kimberling, Aug 21 2011

Keywords

• nonn
• tabl

Comments

See A194285.

Examples

			First eleven rows:
  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, 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;
		

Crossrefs

Cf. A194285.

Programs

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 *)