A208187 Number of distinct n-colored necklaces with 6 beads per color.

1, 1, 80, 953056, 96197661156, 45695805591924048, 74171603795480180204640, 333504309246734399617946903040, 3581026866351385580856518554063502880, 82211352663724607444625251063583157979101440, 3704235885150602243096407788053997013140363354216960

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..40

Formula

a(n) = Sum_{d|6} phi(6/d)*(n*d)!/(d!^n*n*6) if n>0 and a(0) = 1.

Example

a(0) =  1: the empty necklace.
a(1) =  1: {000000}.
a(2) = 80: {000000111111, ..., 010101010101}.

Maple

with(numtheory);
a:= n-> `if`(n=0, 1, add(phi(6/d) *(n*d)!/(d!^n *6*n), d={1, 2, 3, 6})):
seq(a(n), n=0..12);

Crossrefs

Row n=6 of A208183.

Cf. A000010, A000142.

Sequence in context: A231036 A051184 A159444 * A116230 A056669 A005085

Adjacent sequences: A208184 A208185 A208186 * A208188 A208189 A208190

Keyword

nonn

Author

Alois P. Heinz, Feb 24 2012

Status

approved