A194321 - OEIS

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A194321

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

2

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

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

OFFSET

1,13

COMMENTS

LINKS

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

EXAMPLE

First eleven rows:

1

1..1

1..1..1

1..1..1..1

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

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

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

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

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

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

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

MATHEMATICA

r = Sqrt[1/2];

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[%] (* A194321 *)

CROSSREFS

Sequence in context: A174341 A168516 A294335 * A194852 A158854 A376632

Adjacent sequences: A194318 A194319 A194320 * A194322 A194323 A194324

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 22 2011

STATUS

approved