A194316 Triangular array: g(n,k)=number of fractional parts (i*sqrt(6)) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n.

2, 2, 2, 2, 3, 3, 4, 5, 3, 4, 6, 7, 7, 6, 6, 9, 11, 12, 9, 12, 11, 18, 18, 18, 19, 19, 18, 18, 31, 33, 32, 33, 30, 33, 31, 33, 56, 57, 57, 58, 57, 56, 57, 57, 57, 103, 102, 103, 103, 103, 101, 102, 102, 103, 102, 186, 186, 186, 186, 187, 186, 186, 186, 186, 187, 186

Offset: 1

Author

Clark Kimberling, Aug 21 2011

Keywords

• nonn
• tabl

Comments

See A194285.

Examples

			First eight rows:
  2
  2   2
  2   3   3
  4   5   3   4
  6   7   7   6   6
  9   11  12  9   12  11
  18  18  18  19  19  18  18
  31  33  32  33  30  33  31  33
		

Crossrefs

Cf. A194285.

Programs

Mathematica

r = Sqrt[6];
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[%]    (* A194316 *)