OFFSET
0,5
COMMENTS
Beads may be of any number of colors. Colors may be permuted without changing the necklace structure.
Equivalently, the number of set partitions of an n-set up to rotations where no block contains cyclically adjacent elements of the n-set.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
EXAMPLE
a(6) = 12 because there are the following 12 necklace structures: ABABAB, ABABAC, ABABCD, ABACAD, ABACBC, ABACBD, ABACDC, ABACDE, ABCABC, ABCABD, ABCADE, ABCDEF.
PROG
(PARI) seq(n)={Vec(1 + intformal(sum(m=1, n, eulerphi(m) * subst(serlaplace(-1 + exp(-x + sumdiv(m, d, (exp(d*x + O(x*x^(n\m)))-1)/d))), x, x^m))/x))} \\ Andrew Howroyd, Oct 09 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Oct 05 2019
EXTENSIONS
Terms a(16) and beyond from Andrew Howroyd, Oct 09 2019
STATUS
approved