A194294 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=2n, r=(1+sqrt(5))/2, the golden ratio.

2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 3, 1, 3, 1, 2, 2, 2, 2, 2, 2, 2, 3, 2, 1, 2, 2, 2, 2, 1, 2, 3, 2, 2, 2, 2, 1, 2, 3, 2, 2, 1, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2

Offset

1,1

Comments

See A194285.

Links

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

Example

First nine rows:
2
2..2
2..2..2
2..2..2..2
2..2..2..2..2
1..3..2..2..2..2
2..2..2..2..3..2..1
2..2..2..2..2..2..2..2
2..2..3..1..2..3..1..3..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, 2n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194294 *)

Crossrefs

Cf. A194285, A194293.

Sequence in context: A044926 A074264 A194302 * A263110 A044927 A343643

Adjacent sequences: A194291 A194292 A194293 * A194295 A194296 A194297

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 21 2011

Status

approved