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A208187 Number of distinct n-colored necklaces with 6 beads per color. 2
1, 1, 80, 953056, 96197661156, 45695805591924048, 74171603795480180204640, 333504309246734399617946903040, 3581026866351385580856518554063502880, 82211352663724607444625251063583157979101440, 3704235885150602243096407788053997013140363354216960 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 25 01:17 EDT 2019. Contains 321450 sequences. (Running on oeis4.)