A045676 Number of 2n-bead balanced binary necklaces which are equivalent to their reverse, but not equivalent to their complement and reversed complement.

0, 0, 0, 0, 2, 2, 14, 12, 58, 54, 232, 220, 886, 860, 3360, 3304, 12730, 12614, 48348, 48108, 184224, 183732, 704376, 703384, 2702070, 2700060, 10396440, 10392408, 40108336, 40100216, 155101008, 155084752, 601047482, 601014854, 2333540428

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Comments

The number of 2n-bead balanced binary necklaces equivalent to their reverse is A128014(n) and those equivalent to their reverse, complement and reversed complement is A045674(n). - Andrew Howroyd, Sep 28 2017

Links

• Index entries for sequences related to necklaces

Crossrefs

Cf. A045674, A045675, A045677, A045678, A128014.

Programs

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_] := SeriesCoefficient[(1+x)/Sqrt[1 - 4 x^2], {x, 0, n}] - A045674[n];
a /@ Range[0, 34] (* Jean-François Alcover, Sep 13 2019 *)

Formula

a(n) = A128014(n) - A045674(n). - Andrew Howroyd, Sep 28 2017