A194339 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n, r=3-sqrt(5).

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 4, 5, 5, 5, 6, 7, 7, 6, 7, 6, 7, 8, 7, 7, 7, 8, 7, 9, 7, 9, 7, 9, 8, 9, 9, 9, 9, 9, 9, 9, 10, 8, 10, 10, 10, 10, 9, 12, 10, 9, 11, 9, 11, 11, 10, 11, 12, 11, 11, 11, 11, 12, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 14, 12, 14, 12

Offset

1,2

Comments

See A194285.

Links

Table of n, a(n) for n=1..82.

Example

First eight rows:
1
2..2
3..3..3
4..4..4..4
5..5..6..7..7..6
7..6..7..8..7..7..7
8..7..9..7..9..7..9..8

Mathematica

r = 3-Sqrt[5];
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^2}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194339 *)

Crossrefs

Cf. A194285.

Sequence in context: A058032 A056155 A157684 * A194335 A026099 A049727

Adjacent sequences: A194336 A194337 A194338 * A194340 A194341 A194342

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 22 2011

Status

approved