A045677 Number of 2n-bead balanced binary necklaces which are equivalent to their complement, but not equivalent to their reverse and their reversed complement.

0, 0, 0, 0, 0, 0, 2, 2, 8, 14, 36, 62, 142, 252, 524, 968, 1928, 3600, 7044, 13286, 25740, 48916, 94364, 180314, 347630, 666996, 1286712, 2477342, 4785824, 9240012, 17880320, 34604066, 67078024, 130085052, 252583200, 490722344, 954313264

Offset

0,7

Comments

The number of 2n-bead balanced binary necklaces which are equivalent to their complement is A000013(n) and those which are equivalent to their reverse, complement and reversed complement is A045674(n). - Andrew Howroyd, Sep 28 2017

Links

Table of n, a(n) for n=0..36.

Index entries for sequences related to necklaces

Formula

a(n) = A000013(n) - A045674(n). - Andrew Howroyd, Sep 28 2017

Mathematica

A045674[n_] := A045674[n] = If[n == 0, 1, If[EvenQ[n], 2^(n/2 - 1) + A045674[n/2], 2^((n - 1)/2)]];
a[n_] := If[n == 0, 1, Sum[EulerPhi[2 d] 2^(n/d), {d, Divisors[n]}]/(2 n)] - A045674[n];
a /@ Range[0, 36] (* Jean-François Alcover, Sep 13 2019 *)

Crossrefs

Cf. A000013, A045674, A045675, A045676, A045678.

Sequence in context: A334600 A357787 A045686 * A280399 A005633 A228661

Adjacent sequences: A045674 A045675 A045676 * A045678 A045679 A045680

Keyword

nonn

Author

David W. Wilson

Status

approved