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A194303 Triangular array:  g(n,k)=number of fractional parts (i*sqrt(5)) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n. 2
1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 4, 6, 5, 5, 6, 7, 7, 6, 5, 5, 7, 7, 7, 8, 7, 6, 7, 8, 9, 7, 9, 7, 9, 7, 8, 8, 10, 9, 9, 9, 9, 9, 9, 9, 9, 11, 9, 10, 12, 9, 10, 10, 10, 10, 10, 12, 11, 11, 11, 11, 12, 11, 10, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 14 (list; table; graph; refs; listen; history; text; internal format)
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..4..6..5..5

6..7..7..6..5..5

7..7..7..8..7..6..7

8..9..7..9..7..9..7..8

MATHEMATICA

r = 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[%]    (* A194303 *)

CROSSREFS

Cf. A194285.

Sequence in context: A072747 A194295 A194287 * A124755 A033810 A253272

Adjacent sequences:  A194300 A194301 A194302 * A194304 A194305 A194306

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 21 2011

STATUS

approved

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Last modified April 13 00:24 EDT 2021. Contains 342934 sequences. (Running on oeis4.)