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A185333 Number of binary necklaces of n beads for which a cut exists producing a palindrome. 3
2, 2, 4, 3, 8, 6, 16, 9, 32, 20, 64, 34, 128, 72, 256, 129, 512, 272, 1024, 516, 2048, 1056, 4096, 2050, 8192, 4160, 16384, 8200, 32768, 16512, 65536, 32769, 131072, 65792, 262144, 131088, 524288, 262656, 1048576, 524292, 2097152 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For odd n, this corresponds to A029744, necklaces of n beads that are the same when turned over.  For even n, consider the necklace "01", which satisfies A029744 but cannot be cut to produce a palindrome.

LINKS

Hugo Pfoertner and Robert G. Wilson v, Table of n, a(n) for n = 1..1000

MATHEMATICA

f[n_] := If[OddQ@ n, 2^(n/2 + 1/2), Block[{k = IntegerExponent[n, 2] - 1}, 2^(n/2 - 1) + 2^((n/2 - 2^k)/(2^(k + 1)))]]; Array[f, 41] (* Robert G. Wilson v, Aug 08 2011 *)

CROSSREFS

Cf. A185376, A025480.

Sequence in context: A056429 A133806 A283717 * A005176 A050335 A223537

Adjacent sequences:  A185330 A185331 A185332 * A185334 A185335 A185336

KEYWORD

nonn

AUTHOR

Tony Bartoletti, Feb 20 2011

EXTENSIONS

b-file and cross-references from Hugo Pfoertner, Jul 30 2011

STATUS

approved

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Last modified June 22 08:01 EDT 2017. Contains 288605 sequences.