A194300 - OEIS

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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

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

(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 six rows:

2

3..1

2..3..3

4..5..3..4

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

11..11..12..9...11..10

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 *)

CROSSREFS

Sequence in context: A344310 A362068 A255890 * A065365 A096137 A282905

Adjacent sequences: A194297 A194298 A194299 * A194301 A194302 A194303

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 21 2011

STATUS

approved