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.

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

Offset

1,13

Comments

See A194285.

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

Cf. A194285.

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