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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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified September 21 09:06 EDT 2021. Contains 347597 sequences. (Running on oeis4.)