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A308528 Number of length-n binary words having no nontrivial prefix that is a palindrome of odd length. 1
2, 4, 4, 8, 12, 24, 40, 80, 148, 296, 568, 1136, 2232, 4464, 8848, 17696, 35244, 70488, 140680, 281360, 562152, 1124304, 2247472, 4494944, 8987656, 17975312, 35946160, 71892320, 143775792, 287551584, 575085472, 1150170944, 2300306644, 4600613288, 9201156088 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A nontrivial palindrome is one that is of length at least 2.

For n even we have a(n) = 2a(n-1), and for n odd, a(n) = A003000(n).

LINKS

Table of n, a(n) for n=1..35.

Daniel Gabric, Jeffrey Shallit, Borders, Palindrome Prefixes, and Square Prefixes, arXiv:1906.03689 [cs.DM], 2019.

EXAMPLE

For n = 5, the only words counted are 00101, 00110, 00111, 01100, 01101, 01111 and their binary complements.

CROSSREFS

Cf. A003000, A308529.

Sequence in context: A245619 A131771 A047073 * A069753 A181245 A216950

Adjacent sequences:  A308525 A308526 A308527 * A308529 A308530 A308531

KEYWORD

nonn

AUTHOR

Jeffrey Shallit, Jun 06 2019

STATUS

approved

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Last modified July 11 18:19 EDT 2020. Contains 335652 sequences. (Running on oeis4.)