A194333 Triangular array: g(n,k)=number of fractional parts (i*r) in interval [(k-1)/n, k/n], for 1<=i<=n, 1<=k<=n, r=2-tau, where tau=(1+sqrt(5))/2, the golden ratio.

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

Offset

1,24

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

Mathematica

r = 2-GolenRatio;
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[%]    (* A194333 *)

Crossrefs

Cf. A194333.

Sequence in context: A191898 A043290 A356153 * A203640 A043289 A063775

Adjacent sequences: A194330 A194331 A194332 * A194334 A194335 A194336

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 22 2011

Status

approved