login
A045664
Number of 2n-bead balanced binary strings of fundamental period 2n, rotationally equivalent to reversed complement.
7
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
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
KEYWORD
nonn
STATUS
approved