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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, 6511211718, 26538617050, 108060466284 (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 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, arXiv:1106.5767 [cs.FL], 2011. 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 Added a(17)-a(19) and confirmed a(14)-a(16), Bert Dobbelaere, Oct 02 2018 STATUS approved

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Last modified November 14 19:03 EST 2018. Contains 317214 sequences. (Running on oeis4.)