A194307 Triangular array: g(n,k) = number of fractional parts (i*Pi) in interval [(k-1)/n, k/n], for 1 <= i <= n^2, 1 <= k <= n.

1, 3, 1, 4, 2, 3, 3, 5, 4, 4, 4, 5, 7, 3, 6, 6, 5, 5, 5, 8, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 8, 9, 9, 9, 8, 9, 8, 11, 10, 8, 7, 9, 11, 10, 10, 10, 11, 9, 9, 12, 9, 9, 11, 10, 12, 10, 12, 11, 10, 11, 12, 10, 11, 12, 9, 14, 11, 13, 14, 10, 13, 10, 13, 12, 11, 14, 8, 17, 11, 14

Offset: 1

Author

Clark Kimberling, Aug 21 2011

Keywords

• nonn
• tabl

Comments

See A194285.

Examples

			First eight rows:
  1;
  3, 1;
  4, 2, 3;
  3, 5, 4, 4;
  4, 5, 7, 3, 6;
  6, 5, 5, 5, 8, 7;
  7, 7, 7, 7, 7, 7, 7;
  8, 7, 7, 7, 8, 9, 9, 9;
		

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^2}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194307 *)