A194314 - OEIS

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A194314

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

2

2, 2, 2, 1, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 1, 2, 1, 4, 1, 2, 2, 1, 2, 3, 2, 2, 2, 2, 1, 3, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 3, 2, 1, 2, 2, 3, 2, 1, 2, 2, 1, 3, 3, 1, 2, 2, 2, 3, 2, 1, 2, 1, 3, 2, 3, 1, 2, 2, 2, 3, 2, 2, 1, 2, 2, 2, 3, 1, 3, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

LINKS

Table of n, a(n) for n=1..99.

EXAMPLE

First nine rows:

2

2..2

1..2..3

2..2..2..2

2..2..3..2..1

2..1..4..1..2..2

1..2..3..2..2..2..2

1..3..2..3..1..2..2..2

2..2..2..2..2..2..2..2..2

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, 2n}]

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

Flatten[%] (* A194314 *)

CROSSREFS

Sequence in context: A333212 A182597 A290491 * A006371 A000177 A319815

Adjacent sequences: A194311 A194312 A194313 * A194315 A194316 A194317

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 21 2011

STATUS

approved