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A191755 Number of square binary words: binary words of length 2n obtained by self-shuffling. 3


%S 1,2,6,22,82,320,1268,5102,20632,83972,342468,1399296,5720966,

%T 23396618,95654386,390868900,1596000418,6511211718,26538617050,

%U 108060466284

%N Number of square binary words: binary words of length 2n obtained by self-shuffling.

%C 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.

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

%H J. Erickson, <a href="http://cstheory.stackexchange.com/questions/34/how-hard-is-unshuffling-a-string">How hard is unshuffling a string?</a>, August 16 2010. See in particular comment by "Radu GRIGore", Aug 20 2010 at 7:53.

%H Samuele Giraudo, S. Vialette, <a href="https://arxiv.org/abs/1601.05962">Unshuffling Permutations</a>, arXiv preprint arXiv:1601.05962 [cs.DS], 2016.

%H D. Henshall, N. Rampersad, and J. Shallit, <a href="https://arxiv.org/abs/1106.5767">Shuffling and unshuffling</a>, arXiv:1106.5767 [cs.FL], 2011.

%H D. Henshall, N. Rampersad, and J. Shallit, <a href="http://bulletin.eatcs.org/index.php/beatcs/article/view/71">Shuffling and unshuffling</a>, Bull. EATCS, No. 107, June 2012, pp. 131-142.

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

%Y Cf. A192296, A279200 (square permutations).

%K nonn,hard,more,nice

%O 0,2

%A _Jeffrey Shallit_, Jun 15 2011

%E a(0)-a(9) confirmed and a(10)-a(13) added by _John W. Layman_, Jun 28 2011

%E a(0)-a(13) confirmed by _Joerg Arndt_, Jul 13 2011

%E Added a(14) and a(15), _Joerg Arndt_, Jul 18 2011

%E Added a(16), _Joerg Arndt_, Feb 04 2017

%E Added a(17)-a(19) and confirmed a(14)-a(16), _Bert Dobbelaere_, Oct 02 2018

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Last modified December 16 06:18 EST 2019. Contains 330016 sequences. (Running on oeis4.)