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A328150
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Number of n-bead necklace structures with no adjacent elements having the same color.
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2
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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
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0,5
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COMMENTS
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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.
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LINKS
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EXAMPLE
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a(6) = 12 because there are the following 12 necklace structures: ABABAB, ABABAC, ABABCD, ABACAD, ABACBC, ABACBD, ABACDC, ABACDE, ABCABC, ABCABD, ABCADE, ABCDEF.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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