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 A308528 Number of length-n binary words having no nontrivial prefix that is a palindrome of odd length. 1

%I

%S 2,4,4,8,12,24,40,80,148,296,568,1136,2232,4464,8848,17696,35244,

%T 70488,140680,281360,562152,1124304,2247472,4494944,8987656,17975312,

%U 35946160,71892320,143775792,287551584,575085472,1150170944,2300306644,4600613288,9201156088

%N Number of length-n binary words having no nontrivial prefix that is a palindrome of odd length.

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

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

%H Daniel Gabric, Jeffrey Shallit, <a href="https://arxiv.org/abs/1906.03689">Borders, Palindrome Prefixes, and Square Prefixes</a>, arXiv:1906.03689 [cs.DM], 2019.

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

%Y Cf. A003000, A308529.

%K nonn

%O 1,1

%A _Jeffrey Shallit_, Jun 06 2019

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Last modified August 13 19:30 EDT 2020. Contains 336451 sequences. (Running on oeis4.)