A194322 Triangular array: g(n,k)=number of fractional parts (i*sqrt(1/2)) in interval [(k-1)/n, k/n], for 1<=i<=2n, 1<=k<=n.

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

Offset

1,1

Comments

See A194285.

Links

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

Example

First ten rows:
2
2..2
2..2..2
2..1..3..2
2..2..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..3..1..2..3..1..2..3..2..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, 2n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194322 *)

Crossrefs

Cf. A194285.

Sequence in context: A190311 A117005 A263204 * A052010 A138471 A102669

Adjacent sequences: A194319 A194320 A194321 * A194323 A194324 A194325

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 22 2011

Status

approved