A045664 - OEIS

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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

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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