A045678 Number of 2n-bead balanced binary necklaces which are equivalent to their reversed complement, but not equivalent to their reverse and complement.

0, 0, 0, 2, 4, 12, 26, 56, 116, 240, 492, 992, 2010, 4032, 8120, 16256, 32628, 65280, 130800, 261632, 523756, 1047552, 2096096, 4192256, 8386522, 16773120, 33550272, 67100672, 134209464, 268419072, 536854400, 1073709056, 2147450740

Offset

0,4

Comments

The number of 2n-bead balanced binary necklaces which are equivalent to their reversed complement is A011782(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..32.

Index entries for sequences related to necklaces

Formula

a(2n+1) = A020522(n) = 4^n - 2^n. - Max Alekseyev, Jan 13 2006

a(n) = A011782(n) - A045674(n). - Andrew Howroyd, Sep 28 2017

Mathematica

(* b = A011782, c = A045674 *)
b[0] = 1; b[n_] := 2^(n - 1);
c[0] = 1; c[n_] := c[n] = If[EvenQ[n], 2^(n/2-1) + c[n/2], 2^((n-1)/2)];
a[n_] := b[n] - c[n];
Table[a[n], {n, 0, 32}] (* Jean-François Alcover, Oct 08 2017, after Andrew Howroyd *)

Crossrefs

Cf. A011782, A045674.

Sequence in context: A136253 A266079 A284125 * A236002 A291406 A219752

Adjacent sequences: A045675 A045676 A045677 * A045679 A045680 A045681

Keyword

nonn

Author

David W. Wilson

Status

approved