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A328150
Number of n-bead 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
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
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 A370145
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Oct 05 2019
EXTENSIONS
Terms a(16) and beyond from Andrew Howroyd, Oct 09 2019
STATUS
approved