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A045628
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Number of 2n-bead black-white reversible necklaces with n black beads and fundamental period 2n.
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2
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1, 1, 1, 2, 6, 15, 46, 132, 432, 1384, 4735, 16158, 56766, 200473, 718012, 2587000, 9398080, 34324173, 126067124, 465093570, 1723171550, 6407924165, 23910560070, 89494164972, 335913861648, 1264107416450, 4768452532025
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = 1/(4*n) * Sum_{d|n} mu(n/d) * (2*n*binomial(2*floor(d/2), floor(d/2)) + binomial(2*d, d)) for n > 0. - Andrew Howroyd, Sep 28 2017
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MATHEMATICA
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a[n_] := If[n == 0, 1, Sum[MoebiusMu[n/d] (2n Binomial[ 2 Quotient[d, 2], Quotient[d, 2]] + Binomial[2d, d]), {d, Divisors[n]}]/(4n)];
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PROG
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(PARI) a(n) = if(n<1, n==0, sumdiv(n, d, moebius(n/d)*(2*n*binomial(2*(d\2), d\2) + binomial(2*d, d)))/(4*n)); \\ Andrew Howroyd, Sep 28 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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