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A194333 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, r=2-tau, where tau=(1+sqrt(5))/2, the golden ratio. 2
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 0, 2, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,24

COMMENTS

See A194285.

LINKS

Table of n, a(n) for n=1..100.

EXAMPLE

First eleven rows:

1

1..1

1..1..1

1..1..1..1

1..1..1..1..1

1..1..1..1..1..1

0..1..2..1..1..1..1

1..1..1..1..1..1..1..1

1..1..1..2..1..0..2..0..1

1..1..1..1..1..1..1..1..1..1

1..1..1..1..2..1..0..1..1..1..1

MATHEMATICA

r = 2-GolenRatio;

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}]

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

Flatten[%]    (* A194333 *)

CROSSREFS

Cf. A194333.

Sequence in context: A290105 A191898 A043290 * A203640 A043289 A063775

Adjacent sequences:  A194330 A194331 A194332 * A194334 A194335 A194336

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 22 2011

STATUS

approved

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Last modified May 25 11:04 EDT 2019. Contains 323539 sequences. (Running on oeis4.)