A045678 - OEIS

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

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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 *)