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

1,1

Comments

See A194285.

Links

Table of n, a(n) for n=1..65.

Example

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

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 *)

Crossrefs

Cf. A194285.

Sequence in context: A178994 A306608 A143976 * A194336 A127159 A025128

Adjacent sequences: A194293 A194294 A194295 * A194297 A194298 A194299

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 21 2011

Status

approved