A045674 Number of 2n-bead balanced binary necklaces which are equivalent to their reverse, complement and reversed complement.

1, 1, 2, 2, 4, 4, 6, 8, 12, 16, 20, 32, 38, 64, 72, 128, 140, 256, 272, 512, 532, 1024, 1056, 2048, 2086, 4096, 4160, 8192, 8264, 16384, 16512, 32768, 32908, 65536, 65792, 131072, 131344, 262144, 262656, 524288, 524820, 1048576, 1049600

Offset: 0

Author

David W. Wilson

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200
• Index entries for sequences related to necklaces

Crossrefs

Cf. A045654.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = If[EvenQ[n], 2^(n/2-1) + a[n/2], 2^((n-1)/2)]; Table[a[n], {n, 0, 42}] (* Jean-François Alcover, Sep 30 2017 *)

PARI

a(n) = if(n<1, n==0, my(t=0,r=n); while(r%2==0, r=r/2; t+=2^(r-1)); t + 2^(r\2)); \\ Andrew Howroyd, Sep 29 2017

Formula

a(2n) = a(n) + 2^(n-1), a(2n+1) = 2^n. - Ralf Stephan, Nov 01 2003