A194300 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n, r=(1+sqrt(3))/2.

2, 3, 1, 2, 3, 3, 4, 5, 3, 4, 6, 7, 6, 7, 6, 11, 11, 12, 9, 11, 10, 19, 17, 19, 19, 17, 20, 17, 32, 32, 33, 32, 32, 32, 32, 31, 58, 56, 57, 57, 57, 57, 57, 57, 56, 103, 102, 102, 103, 103, 102, 101, 103, 103, 102, 186, 187, 185, 186, 187, 187, 185, 186, 187, 187

Offset: 1

Author

Clark Kimberling, Aug 21 2011

Keywords

• nonn
• tabl

Comments

See A194285.

Examples

			First six rows:
2
3..1
2..3..3
4..5..3..4
6..7..6..7..6
11..11..12..9...11..10
		

Crossrefs

Cf. A194285.

Programs

Mathematica

r = (1+Sqrt[3])/2;
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[%]    (* A194300 *)