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A194315 Triangular array:  g(n,k)=number of fractional parts (i*sqrt(6)) in interval [(k-1)/n, k/n], for 1<=i<=n^2, 1<=k<=n. 2
1, 2, 2, 3, 3, 3, 4, 5, 3, 4, 4, 6, 5, 5, 5, 5, 6, 8, 4, 7, 6, 7, 7, 6, 7, 8, 7, 7, 6, 9, 8, 9, 7, 8, 8, 9, 8, 9, 9, 10, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 11, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 14, 10, 12, 13, 12, 12, 12, 13, 13, 12 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A194285.

LINKS

Table of n, a(n) for n=1..81.

EXAMPLE

First eight rows:

1

2..2

3..3..3

4..5..3..4

4..6..5..5..5

5..6..8..4..7..6

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

6..9..8..9..7..8..8..9

MATHEMATICA

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, n^2}]

TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]

Flatten[%]    (* A194315 *)

CROSSREFS

Cf. A194315.

Sequence in context: A145703 A029095 A212295 * A288577 A159270 A165103

Adjacent sequences:  A194312 A194313 A194314 * A194316 A194317 A194318

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 21 2011

STATUS

approved

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Last modified November 22 10:59 EST 2019. Contains 329389 sequences. (Running on oeis4.)