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A045674 Number of 2n-bead balanced binary necklaces which are equivalent to their reverse, complement and reversed complement. 8
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A264393 A094858 A029940 * A276065 A143483 A264788

Adjacent sequences:  A045671 A045672 A045673 * A045675 A045676 A045677

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified October 22 13:07 EDT 2017. Contains 293773 sequences.