A045662 Number of 2n-bead balanced binary strings of fundamental period 2n, rotationally equivalent to reverse.

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

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

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

Cf. A007727, A045663, A045664, A045680.

Sequence in context: A121069 A100838 A056696 * A195324 A175877 A269265

Adjacent sequences: A045659 A045660 A045661 * A045663 A045664 A045665

Keyword

nonn

Author

David W. Wilson

Status

approved