%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 lengthn 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(n1), 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
