A208189 Number of distinct n-colored necklaces with 8 beads per color.

1, 1, 810, 394397776, 3111284141045598, 191417861328837588057432, 60192781171721237282811209918160, 73288704867601350013562616043249358012160, 283839436431731355577562936415156522873876247241520, 3019803425783983174717206845130801781814711776972408728524160

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..30

Formula

a(n) = Sum_{d|8} phi(8/d)*(n*d)!/(d!^n*n*8) if n>0 and a(0) = 1.

Example

a(0) =   1: the empty necklace.
a(1) =   1: {00000000}.
a(2) = 810: {0000000011111111, ..., 0101010101010101}.

Maple

with(numtheory);
a:= n-> `if`(n=0, 1, add(phi(8/d) *(n*d)!/(d!^n *8*n), d={1, 2, 4, 8})):
seq(a(n), n=0..10);

Crossrefs

Row n=8 of A208183.

Cf. A000010, A000142.

Sequence in context: A282376 A203844 A068278 * A183216 A093633 A045228

Adjacent sequences: A208186 A208187 A208188 * A208190 A208191 A208192

Keyword

nonn

Author

Alois P. Heinz, Feb 24 2012

Status

approved