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A045674 Number of 2n-bead balanced binary necklaces which are equivalent to their reverse, complement and reversed complement. 10
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 06:02 EDT 2018. Contains 316432 sequences. (Running on oeis4.)