cp's OEIS Frontend

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

%I A208187 #10 Dec 01 2014 20:21:54
%S A208187 1,1,80,953056,96197661156,45695805591924048,74171603795480180204640,
%T A208187 333504309246734399617946903040,3581026866351385580856518554063502880,
%U A208187 82211352663724607444625251063583157979101440,3704235885150602243096407788053997013140363354216960
%N A208187 Number of distinct n-colored necklaces with 6 beads per color.
%H A208187 Alois P. Heinz, <a href="/A208187/b208187.txt">Table of n, a(n) for n = 0..40</a>
%F A208187 a(n) = Sum_{d|6} phi(6/d)*(n*d)!/(d!^n*n*6) if n>0 and a(0) = 1.
%e A208187 a(0) =  1: the empty necklace.
%e A208187 a(1) =  1: {000000}.
%e A208187 a(2) = 80: {000000111111, ..., 010101010101}.
%p A208187 with(numtheory);
%p A208187 a:= n-> `if`(n=0, 1, add(phi(6/d) *(n*d)!/(d!^n *6*n), d={1, 2, 3, 6})):
%p A208187 seq(a(n), n=0..12);
%Y A208187 Row n=6 of A208183.
%Y A208187 Cf. A000010, A000142.
%K A208187 nonn
%O A208187 0,3
%A A208187 _Alois P. Heinz_, Feb 24 2012