

A328150


Number of nbead necklace structures with no adjacent elements having the same color.


2



1, 0, 1, 1, 3, 3, 12, 24, 103, 387, 1819, 8933, 48632, 279484, 1716523, 11126025, 76014437, 544945399, 4089010392, 32025053060, 261213946739, 2214280580389, 19471365925297, 177319383231697, 1669735890602062, 16235408370162588, 162796351456044465, 1681427459283678177
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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 nset up to rotations where no block contains cyclically adjacent elements of the nset.


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

Row sums of A327396.
Cf. A084423.
Sequence in context: A136533 A268639 A192307 * A161804 A097342 A025236
Adjacent sequences: A328147 A328148 A328149 * A328151 A328152 A328153


KEYWORD

nonn


AUTHOR

Andrew Howroyd, Oct 05 2019


EXTENSIONS

Terms a(16) and beyond from Andrew Howroyd, Oct 09 2019


STATUS

approved



