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A191755 Number of square binary words: binary words of length 2n obtained by self-shuffling. 3
1, 2, 6, 22, 82, 320, 1268, 5102, 20632, 83972, 342468, 1399296, 5720966, 23396618, 95654386, 390868900, 1596000418 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Self-shuffle means shuffle of word with itself, and shuffle means "not-necessarily-perfect shuffle".  In other words, the shuffle of two strings x and y is the set of strings obtained by scanning left-to-right through the strings, choosing arbitrarily at each step a symbol from x or y.

See A192296 for the number of ternary words of length 2n obtained by self-shuffling.

LINKS

Table of n, a(n) for n=0..16.

J. Erickson, How hard is unshuffling a string?, August 16 2010.  See in particular comment by "Radu GRIGore", Aug 20 2010 at 7:53.

Samuele Giraudo, S. Vialette, Unshuffling Permutations, arXiv preprint arXiv:1601.05962 [cs.DS], 2016.

D. Henshall, N. Rampersad, and J. Shallit, Shuffling and unshuffling, Bull. EATCS, No. 107, June 2012, pp. 131-142.

EXAMPLE

a(2) = 6 because {0000, 0011, 0101, 1010, 1100, 1111} are all generated by self-shuffling.

CROSSREFS

Cf. A192296, A279200 (square permutations).

Sequence in context: A072547 A150229 A150230 * A150231 A150232 A150233

Adjacent sequences:  A191752 A191753 A191754 * A191756 A191757 A191758

KEYWORD

nonn,hard,more,nice

AUTHOR

Jeffrey Shallit, Jun 15 2011

EXTENSIONS

a(0)-a(9) confirmed and a(10)-a(13) added by John W. Layman, Jun 28 2011

a(0)-a(13) confirmed by Joerg Arndt, Jul 13 2011

Added a(14) and a(15), Joerg Arndt, Jul 18 2011

Added a(16), Joerg Arndt, Feb 04 2017

STATUS

approved

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Last modified September 22 08:23 EDT 2018. Contains 315270 sequences. (Running on oeis4.)