A045664 Number of 2n-bead balanced binary strings of fundamental period 2n, rotationally equivalent to reversed complement.

1, 2, 4, 18, 48, 150, 324, 882, 1920, 4536, 9900, 22506, 48240, 106470, 227556, 490950, 1044480, 2228190, 4708368, 9961434, 20950800, 44037378, 92229588, 192937938, 402549120, 838860000, 1744617420, 3623864832, 7515733680

Offset

0,2

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Formula

For n >= 1, a(n) = n*A027375(n) = 2*n*A000740(n) = n^2*A001037(n).

a(n) = 2*n*Sum_{d|n} mu(n/d)*2^(d-1) for n > 0. - Andrew Howroyd, Sep 14 2019

Mathematica

a[n_] := If[n == 0, 1, 2n Sum[MoebiusMu[n/d] 2^(d-1), {d, Divisors[n]}]];
a /@ Range[0, 30] (* Jean-François Alcover, Sep 23 2019, from PARI *)

Prog

(PARI) a(n)={if(n<1, n==0, 2*n*sumdiv(n, d, moebius(n/d)*2^(d-1)))} \\ Andrew Howroyd, Sep 14 2019

Crossrefs

Cf. A000740, A001037, A007727, A027375, A045662, A045663.

Sequence in context: A301620 A240316 A151449 * A106520 A301802 A318249

Adjacent sequences: A045661 A045662 A045663 * A045665 A045666 A045667

Keyword

nonn

Author

David W. Wilson

Status

approved