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.

2, 2, 4, 6, 10, 20, 36, 72, 142, 280, 560, 1114, 2222, 4436, 8864, 17718, 35420, 70824, 141624, 283210, 566394, 1132728, 2265390, 4530726, 9061318, 18122518, 36244908, 72489566, 144978870, 289957490, 579914470, 1159828430, 2319656332, 4639311620, 9278622168

Offset

1,1

Comments

See A216730 for definitions.

I would very much like to have a formula or recurrence for this sequence.

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

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..100 [Based on Allan Wilks's b-file for A122536]

Daniel Gabric, Jeffrey Shallit, Borders, Palindrome Prefixes, and Square Prefixes, arXiv:1906.03689 [cs.DM], 2019.

Daniel Gabric, Jeffrey Shallit, Borders, palindrome prefixes, and square prefixes, Info. Proc. Letters 165 (2021), 106027.

Index entries for sequences related to curling numbers

Example

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.

Crossrefs

Cf. A216730, A122536, A216959, A216960, A216961.

First column of A218875.

Sequence in context: A007560 A032237 A276061 * A318849 A339587 A293014

Adjacent sequences: A216955 A216956 A216957 * A216959 A216960 A216961

Keyword

nonn

Author

N. J. A. Sloane, Sep 27 2012

Extensions

a(31)-a(35) from N. J. A. Sloane, Oct 25 2012

Status

approved