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A331850
Largest cardinality of a set obtained by self-shuffling a binary word of length n.
1
1, 2, 4, 9, 18, 54, 120, 324, 900, 2406, 6400, 19600, 50176, 148042, 442325, 1373070, 3954113
OFFSET
1,2
COMMENTS
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).
FORMULA
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
EXAMPLE
For n = 3 one can obtain {010010, 001010, 010100, 001100} by self-shuffling 010, so a(3) = 4.
PROG
(Python) # uses a() in A191755; a(n)[2] generates the lex. least argmax
print([a(n)[1] for n in range(1, 9)]) # Michael S. Branicky, Sep 28 2021
CROSSREFS
Cf. A191755.
Sequence in context: A362037 A368422 A283877 * A373808 A081490 A292478
KEYWORD
nonn,more
AUTHOR
Jeffrey Shallit, Jan 29 2020
EXTENSIONS
a(11)-a(13) from Giovanni Resta, Jan 29 2020
a(14)-a(15) from Giovanni Resta, Jan 30 2020
a(16)-a(17) from Bert Dobbelaere, Feb 08 2020
STATUS
approved