A194309 Triangular array: g(n,k)=number of fractional parts (i*e) 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 0, 1, 2, 0, 1, 2, 1, 0, 2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 0, 2, 0, 2, 2, 0, 2, 0, 1, 0, 2, 0, 2, 1, 1, 1, 1, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0

Offset

1,13

Comments

See A194285.

Links

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

Example

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

Mathematica

r = E;
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[%]    (* A194309 *)

Crossrefs

Cf. A194285.

Sequence in context: A284562 A349542 A087102 * A369936 A374326 A318829

Adjacent sequences: A194306 A194307 A194308 * A194310 A194311 A194312

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 21 2011

Status

approved