A194292 Triangular array: g(n,k)=number of fractional parts (i*sqrt(3)) in interval [(k-1)/n, k/n], for 1<=i<=2^n, 1<=k<=n.

2, 2, 2, 2, 3, 3, 4, 3, 5, 4, 6, 6, 7, 7, 6, 10, 10, 12, 10, 10, 12, 18, 18, 18, 18, 19, 19, 18, 32, 32, 31, 33, 31, 34, 31, 32, 56, 57, 57, 57, 56, 57, 57, 58, 57, 101, 104, 101, 102, 103, 102, 103, 103, 102, 103, 186, 186, 186, 186, 186, 186, 186, 187, 187

Offset

1,1

Comments

See A194285.

Links

Table of n, a(n) for n=1..64.

Example

First eight rows:
2
2...2
2...3...3
4...3...5...4
6...6...7...7...6
10..10..12..10..10..12
18..18..18..18..19..19..18
32..32..31..33..31..34..31..32

Mathematica

r = 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, 2^n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194292 *)

Crossrefs

Cf. A194285.

Sequence in context: A106161 A105588 A064658 * A308403 A073578 A087866

Adjacent sequences: A194289 A194290 A194291 * A194293 A194294 A194295

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 21 2011

Status

approved