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A045663
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Number of 2n-bead balanced binary strings of fundamental period 2n, rotationally equivalent to complement.
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7
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1, 2, 4, 6, 16, 30, 60, 126, 256, 504, 1020, 2046, 4080, 8190, 16380, 32730, 65536, 131070, 262080, 524286, 1048560, 2097018, 4194300, 8388606, 16776960, 33554400, 67108860, 134217216, 268435440, 536870910, 1073740740, 2147483646
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum{d|n, d odd} mu(d) * 2^(n/d) for n > 0. - Andrew Howroyd, Sep 14 2019
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MATHEMATICA
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a[n_] := If[n==0, 1, 2n Total[MoebiusMu[#]*2^(n/#)& /@ Select[Divisors[n], OddQ]]/(2n)];
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PROG
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(PARI) a(n)={if(n<1, n==0, sumdiv(n, d, if(d%2, moebius(d)*2^(n/d))))} \\ Andrew Howroyd, Sep 14 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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STATUS
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approved
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