A045674 - OEIS

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

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OFFSET

0,3

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..200

Index entries for sequences related to necklaces

FORMULA

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

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 *)

PROG

(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

CROSSREFS

Cf. A045654.

Sequence in context: A094858 A327851 A029940 * A276065 A325253 A143483

Adjacent sequences: A045671 A045672 A045673 * A045675 A045676 A045677

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved