A194326 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=2n, 1<=k<=n, r=2-sqrt(2).

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

Mathematica

r = 2-Sqrt[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[%]    (* A194326 *)

Crossrefs

Cf. A194285.

Sequence in context: A078687 A133138 A348193 * A295277 A194290 A329028

Adjacent sequences: A194323 A194324 A194325 * A194327 A194328 A194329

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 22 2011

Status

approved