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A045629
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Number of 2n-bead black-white complementable necklaces with n black beads.
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5
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1, 1, 2, 3, 7, 15, 44, 128, 415, 1367, 4654, 16080, 56450, 200170, 716728, 2585850, 9393119, 34319667, 126047906, 465076160, 1723097066, 6407856892, 23910271224, 89493903438, 335912741682, 1264106399934, 4768448177636, 18027218147818
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = (1/2n) * Sum_{d|n} (phi(n/d)*C(2d-1, d-1) + phi(2n/d)*2^(d-1)). - Christian G. Bower
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MATHEMATICA
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a[n_] := If[n == 0, 1, (1/(2*n))*DivisorSum[n, EulerPhi[n/#1]*Binomial[2*#1 - 1, #1 - 1] + EulerPhi[2*(n/#1)]*2^(#1 - 1)&]];
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PROG
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(PARI) a(n) = if(n==0, 1, (1/(2*n)) * sumdiv(n, d, eulerphi(n/d)*binomial(2*d-1, d-1) + eulerphi(2*n/d)*2^(d-1))); \\ Andrew Howroyd, Sep 27 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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