

A308528


Number of lengthn 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(n1), 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



