A194313 - OEIS

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A194313

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

2

1, 1, 1, 0, 2, 1, 0, 2, 0, 2, 0, 2, 1, 1, 1, 0, 1, 2, 0, 2, 1, 0, 2, 1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 1, 2, 1, 2, 0, 1

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

OFFSET

1,5

COMMENTS

LINKS

Table of n, a(n) for n=1..100.

EXAMPLE

First nine rows:

1

1..1

0..2..1

0..2..0..2

0..2..1..1..1

0..1..2..0..2..1

0..2..1..1..1..1..1

0..2..1..1..1..1..1..1

1..1..1..1..1..1..1..1..1

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}]

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

Flatten[%] (* A194313 *)

CROSSREFS

Sequence in context: A328777 A244553 A231167 * A127476 A140397 A120614

Adjacent sequences: A194310 A194311 A194312 * A194314 A194315 A194316

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 21 2011

STATUS

approved