A194308 Triangular array: g(n,k) = number of fractional parts (i*Pi) in interval [(k-1)/n, k/n], for 1 <= i <= 2^n, 1 <= k <= n.

2, 3, 1, 3, 2, 3, 3, 5, 4, 4, 5, 7, 8, 4, 8, 10, 9, 10, 12, 12, 11, 19, 18, 18, 18, 18, 18, 19, 31, 31, 32, 32, 32, 32, 32, 34, 53, 58, 55, 61, 55, 57, 53, 60, 60, 99, 100, 100, 108, 100, 100, 108, 100, 100, 109, 180, 182, 180, 200, 182, 180, 182, 200, 180, 182

Offset: 1

Author

Clark Kimberling, Aug 21 2011

Keywords

• nonn
• tabl

Comments

See A194285.

Examples

			First six rows:
   2;
   3,  1;
   3,  2,  3;
   3,  5,  4,  4;
   5,  7,  8,  4,  8;
  10,  9, 10, 12, 12, 11;
		

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, 2^n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194308 *)