A194329 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-sqrt(3).

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

Offset

1,12

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

Mathematica

r = 2-Sqrt[3];
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[%]    (* A194329 *)

Crossrefs

Cf. A194285.

Sequence in context: A130654 A053259 A273107 * A321749 A143842 A369460

Adjacent sequences: A194326 A194327 A194328 * A194330 A194331 A194332

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 22 2011

Status

approved