A194296 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=2^n, r=(1+sqrt(5))/2, the golden ratio.

2, 2, 2, 3, 2, 3, 4, 4, 4, 4, 6, 6, 7, 7, 6, 10, 11, 10, 12, 10, 11, 19, 19, 17, 19, 19, 17, 18, 32, 33, 32, 31, 33, 32, 31, 32, 57, 57, 57, 56, 57, 58, 56, 58, 56, 102, 102, 103, 102, 102, 103, 102, 103, 103, 102, 187, 186, 187, 185, 185, 186, 187, 187, 186, 187

Offset: 1

Author

Clark Kimberling, Aug 21 2011

Keywords

• nonn
• tabl

Comments

See A194285.

Examples

			First seven rows:
2
2...2
3...2...3
4...4...4...4
6...6...7...7...6
10..11..10..12..10..11
19..19..17..19..19..17..18
		

Crossrefs

Cf. A194285.

Programs

Mathematica

r = GoldenRatio;
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[%]    (* A194296 *)