A045680 Number of 2n-bead balanced binary necklaces of fundamental period 2n equivalent to reverse.

1, 1, 1, 1, 4, 5, 17, 19, 64, 68, 245, 251, 900, 923, 3411, 3425, 12800, 12869, 48532, 48619, 184500, 184735, 705179, 705431, 2703168, 2704150, 10399675, 10400530, 40113164, 40116599, 155113825, 155117519, 601067520, 601080137, 2333593349

Offset

0,5

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

Index entries for sequences related to Lyndon words

Formula

Moebius transform of A128014. - Andrew Howroyd, Sep 28 2017

Mathematica

a[0] = 1;
a[n_] := DivisorSum[n, MoebiusMu[n/#] Binomial[# - Mod[#, 2], Quotient[#, 2]]&];
Table[a[n], {n, 0, 34}] (* Jean-François Alcover, Jul 02 2018, after Andrew Howroyd *)

Prog

(PARI) a(n) = if(n<1, n>=0, sumdiv(n, d, moebius(n/d) * binomial(d-d%2, d\2))); \\ Andrew Howroyd, Sep 28 2017

Crossrefs

Cf. A128014.

Sequence in context: A032049 A258063 A344061 * A174352 A152021 A026678

Adjacent sequences: A045677 A045678 A045679 * A045681 A045682 A045683

Keyword

nonn

Author

David W. Wilson

Status

approved