A194293 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=(1+sqrt(5))/2, the golden ratio.

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

Offset

1,26

Comments

See A194285. Which rows are constant?

Links

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

Example

First ten rows:
1
1..1
1..1..1
1..1..1..1
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..0..2..0..1..2..1..1..1
1..1..1..1..1..1..1..1..1..1

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}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194293 *)

Crossrefs

Cf. A194293.

Sequence in context: A073484 A203947 A081396 * A349595 A298941 A317146

Adjacent sequences: A194290 A194291 A194292 * A194294 A194295 A194296

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 21 2011

Status

approved