A194295 - OEIS

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A194295

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

2

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 6, 5, 5, 6, 7, 5, 7, 6, 5, 7, 8, 6, 7, 8, 7, 6, 8, 8, 8, 7, 9, 8, 8, 8, 9, 9, 9, 9, 9, 10, 8, 10, 8, 10, 10, 10, 10, 10, 10, 9, 11, 10, 10, 11, 11, 11, 11, 10, 11, 12, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13

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

OFFSET

1,2

COMMENTS

LINKS

Table of n, a(n) for n=1..81.

EXAMPLE

First eight rows:

1

2..2

3..3..3

4..4..4..4

4..5..6..5..5

6..7..5..7..6..5

7..8..6..7..8..7..6

8..8..8..7..9..8..8..8

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, n^2}]

TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]

Flatten[%] (* A194295 *)

CROSSREFS

Sequence in context: A365275 A071996 A072747 * A194287 A194303 A124755

Adjacent sequences: A194292 A194293 A194294 * A194296 A194297 A194298

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 21 2011

STATUS

approved