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

0,5

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

Table of n, a(n) for n=0..34.

Index entries for sequences related to necklaces

Formula

a(n) = A128014(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_] := SeriesCoefficient[(1+x)/Sqrt[1 - 4 x^2], {x, 0, n}] - A045674[n];
a /@ Range[0, 34] (* Jean-François Alcover, Sep 13 2019 *)

Crossrefs

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

Sequence in context: A365161 A129083 A045685 * A098288 A032297 A032209

Adjacent sequences: A045673 A045674 A045675 * A045677 A045678 A045679

Keyword

nonn

Author

David W. Wilson

Status

approved