cp's OEIS Frontend

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

%I A208189 #11 Dec 01 2014 20:22:46
%S A208189 1,1,810,394397776,3111284141045598,191417861328837588057432,
%T A208189 60192781171721237282811209918160,
%U A208189 73288704867601350013562616043249358012160,283839436431731355577562936415156522873876247241520,3019803425783983174717206845130801781814711776972408728524160
%N A208189 Number of distinct n-colored necklaces with 8 beads per color.
%H A208189 Alois P. Heinz, <a href="/A208189/b208189.txt">Table of n, a(n) for n = 0..30</a>
%F A208189 a(n) = Sum_{d|8} phi(8/d)*(n*d)!/(d!^n*n*8) if n>0 and a(0) = 1.
%e A208189 a(0) =   1: the empty necklace.
%e A208189 a(1) =   1: {00000000}.
%e A208189 a(2) = 810: {0000000011111111, ..., 0101010101010101}.
%p A208189 with(numtheory);
%p A208189 a:= n-> `if`(n=0, 1, add(phi(8/d) *(n*d)!/(d!^n *8*n), d={1, 2, 4, 8})):
%p A208189 seq(a(n), n=0..10);
%Y A208189 Row n=8 of A208183.
%Y A208189 Cf. A000010, A000142.
%K A208189 nonn
%O A208189 0,3
%A A208189 _Alois P. Heinz_, Feb 24 2012