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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. 8
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 (list; graph; refs; listen; history; text; internal format)
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.

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 A293014 A124346

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

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Last modified October 19 13:01 EDT 2019. Contains 328222 sequences. (Running on oeis4.)