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A045662
Number of 2n-bead balanced binary strings of fundamental period 2n, rotationally equivalent to reverse.
7
1, 2, 4, 6, 32, 50, 204, 266, 1024, 1224, 4900, 5522, 21600, 23998, 95508, 102750, 409600, 437546, 1747152, 1847522, 7380000, 7758870, 31027876, 32449826, 129752064, 135207500, 540783100, 561628620, 2246337184, 2326762742
OFFSET
0,2
LINKS
FORMULA
a(n) = 2*n*A045680(n) for n > 0.
a(n) = 2*n*Sum_{d|n} mu(n/d) * binomial(2*floor(d/2), floor(d/2)) for n > 0. - Andrew Howroyd, Sep 14 2019
MATHEMATICA
a[n_] := If[n == 0, 1, 2n Sum[MoebiusMu[n/d] Binomial[d - Mod[d, 2], Quotient[d, 2]], {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) * binomial(d-d%2, d\2))); \\ Andrew Howroyd, Sep 14 2019
CROSSREFS
KEYWORD
nonn
STATUS
approved