A194297 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(3))/2.

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

Offset

1,8

Comments

See A194285.

Links

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

Example

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

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, n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194297 *)

Crossrefs

Cf. A194297.

Sequence in context: A349595 A298941 A317146 * A378387 A100544 A031214

Adjacent sequences: A194294 A194295 A194296 * A194298 A194299 A194300

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 21 2011

Status

approved