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Number of distinct n-colored necklaces with 6 beads per color.
2

%I #10 Dec 01 2014 20:21:54

%S 1,1,80,953056,96197661156,45695805591924048,74171603795480180204640,

%T 333504309246734399617946903040,3581026866351385580856518554063502880,

%U 82211352663724607444625251063583157979101440,3704235885150602243096407788053997013140363354216960

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

%H Alois P. Heinz, <a href="/A208187/b208187.txt">Table of n, a(n) for n = 0..40</a>

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

%e a(0) = 1: the empty necklace.

%e a(1) = 1: {000000}.

%e a(2) = 80: {000000111111, ..., 010101010101}.

%p with(numtheory);

%p a:= n-> `if`(n=0, 1, add(phi(6/d) *(n*d)!/(d!^n *6*n), d={1, 2, 3, 6})):

%p seq(a(n), n=0..12);

%Y Row n=6 of A208183.

%Y Cf. A000010, A000142.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Feb 24 2012