This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A308528 #11 Jun 11 2019 03:12:25 %S A308528 2,4,4,8,12,24,40,80,148,296,568,1136,2232,4464,8848,17696,35244, %T A308528 70488,140680,281360,562152,1124304,2247472,4494944,8987656,17975312, %U A308528 35946160,71892320,143775792,287551584,575085472,1150170944,2300306644,4600613288,9201156088 %N A308528 Number of length-n binary words having no nontrivial prefix that is a palindrome of odd length. %C A308528 A nontrivial palindrome is one that is of length at least 2. %C A308528 For n even we have a(n) = 2a(n-1), and for n odd, a(n) = A003000(n). %H A308528 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 A308528 For n = 5, the only words counted are 00101, 00110, 00111, 01100, 01101, 01111 and their binary complements. %Y A308528 Cf. A003000, A308529. %K A308528 nonn %O A308528 1,1 %A A308528 _Jeffrey Shallit_, Jun 06 2019