A194336 - OEIS

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A194336

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=2-tau, where tau=(1+sqrt(5))/2, the golden ratio.

2

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

LINKS

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

EXAMPLE

First eight rows:

2

2...2

3...2...3

4...4...4...4

6...7...7...6...6

11..10..12..10..11..10

18..17..19..19..17..19..19

32..31..32..33..31..32..33..32

MATHEMATICA

r = 2-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[%] (* A194336 *)

CROSSREFS

Sequence in context: A306608 A143976 A194296 * A127159 A025128 A058769

Adjacent sequences: A194333 A194334 A194335 * A194337 A194338 A194339

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 22 2011

STATUS

approved