A194337 - OEIS

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A194337

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=3-sqrt(5).

2

1, 0, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 0, 1, 0, 2, 1, 1, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 0, 2, 1, 1, 2, 0, 1, 1, 0, 2, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 2, 0, 1, 2, 0, 2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 0, 1

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

OFFSET

1,3

COMMENTS

LINKS

Table of n, a(n) for n=1..99.

EXAMPLE

First nine rows:

1

0..2

1..1..1

1..1..1..1

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

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

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

2..0..2..0..2..0..2..0

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

MATHEMATICA

r = 3-Sqrt[5];

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[%] (* A194337 *)

CROSSREFS

Sequence in context: A300547 A025452 A299202 * A365335 A376663 A299912

Adjacent sequences: A194334 A194335 A194336 * A194338 A194339 A194340

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 22 2011

STATUS

approved