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A331850
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Largest cardinality of a set obtained by self-shuffling a binary word of length n.
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1
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1, 2, 4, 9, 18, 54, 120, 324, 900, 2406, 6400, 19600, 50176, 148042, 442325, 1373070, 3954113
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OFFSET
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1,2
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COMMENTS
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The self-shuffle of a length-n word w is the set of all length-2n words that can be obtained by interleaving w with itself, as in the shuffle of a deck of cards (but not a perfect shuffle).
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LINKS
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FORMULA
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For n = 1..17 the values a(n) are achieved by the lexicographically least strings given below:
1 : 0
2 : 01
3 : 010
4 : 0110
5 : 00110
6 : 011001
7 : 0110001
8 : 01100110
9 : 011000110
10 : 0110001110
11 : 01110001110
12 : 011100001110
13 : 0111000001110
14 : 01100011110001
15 : 011000011110001
16 : 0111000011110001
17 : 01110000011110001
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EXAMPLE
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For n = 3 one can obtain {010010, 001010, 010100, 001100} by self-shuffling 010, so a(3) = 4.
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PROG
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(Python) # uses a() in A191755; a(n)[2] generates the lex. least argmax
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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