A194316 Triangular array: g(n,k)=number of fractional parts (i*sqrt(6)) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n.

2, 2, 2, 2, 3, 3, 4, 5, 3, 4, 6, 7, 7, 6, 6, 9, 11, 12, 9, 12, 11, 18, 18, 18, 19, 19, 18, 18, 31, 33, 32, 33, 30, 33, 31, 33, 56, 57, 57, 58, 57, 56, 57, 57, 57, 103, 102, 103, 103, 103, 101, 102, 102, 103, 102, 186, 186, 186, 186, 187, 186, 186, 186, 186, 187

Offset

1,1

Comments

See A194285.

Links

Table of n, a(n) for n=1..65.

Example

First eight rows:
2
2...2
2...3...3
4...5...3...4
6...7...7...6...6
9...11..12..9...12..11
18..18..18..19..19..18..18
31..33..32..33..30..33..31..33

Mathematica

See A194285.
r = Sqrt[6];
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, 2^n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194316 *)

Crossrefs

Cf. A194285.

Sequence in context: A239508 A112210 A018050 * A261796 A200245 A116492

Adjacent sequences: A194313 A194314 A194315 * A194317 A194318 A194319

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 21 2011

Status

approved