cp's OEIS Frontend

A216958 Number of binary vectors v of length n with curling number 1 such that the concatenation v v with first term omitted also has curling number 1.

%I A216958 #45 Oct 31 2024 06:45:13
%S A216958 2,2,4,6,10,20,36,72,142,280,560,1114,2222,4436,8864,17718,35420,
%T A216958 70824,141624,283210,566394,1132728,2265390,4530726,9061318,18122518,
%U A216958 36244908,72489566,144978870,289957490,579914470,1159828430,2319656332,4639311620,9278622168
%N A216958 Number of binary vectors v of length n with curling number 1 such that the concatenation v v with first term omitted also has curling number 1.
%C A216958 See A216730 for definitions.
%C A216958 I would very much like to have a formula or recurrence for this sequence.
%C A216958 Alternatively, the number of squares of length 2n over a binary alphabet having no proper prefix that is a square.  Here by a square I mean a word of the form xx, where x is any word. - _Jeffrey Shallit_, Nov 29 2013
%H A216958 N. J. A. Sloane, <a href="/A216958/b216958.txt">Table of n, a(n) for n = 1..100</a> [Based on _Allan Wilks_'s b-file for A122536]
%H A216958 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.
%H A216958 Daniel Gabric, Jeffrey Shallit, <a href="https://doi.org/10.1016/j.ipl.2020.106027">Borders, palindrome prefixes, and square prefixes</a>, Info. Proc. Letters 165 (2021), 106027.
%H A216958 <a href="/index/Cu#curling_numbers">Index entries for sequences related to curling numbers</a>
%F A216958 a(n) = 2*A122536(2n-1)-A122536(2n). - _R. J. Mathar_, Oct 31 2024
%e A216958 Taking the alphabet to be {2,3}, v = 32232 has curling number 1, but 2232.32232 has curling number 2, so is not counted here.
%Y A216958 Cf. A216730, A122536, A216959, A216960, A216961.
%Y A216958 First column of A218875.
%K A216958 nonn
%O A216958 1,1
%A A216958 _N. J. A. Sloane_, Sep 27 2012
%E A216958 a(31)-a(35) from _N. J. A. Sloane_, Oct 25 2012