|
%I #23 Sep 28 2021 09:06:45
%S 1,2,4,9,18,54,120,324,900,2406,6400,19600,50176,148042,442325,
%T 1373070,3954113
%N Largest cardinality of a set obtained by self-shuffling a binary word of length n.
%C 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).
%F For n = 1..17 the values a(n) are achieved by the lexicographically least strings given below:
%F 1 : 0
%F 2 : 01
%F 3 : 010
%F 4 : 0110
%F 5 : 00110
%F 6 : 011001
%F 7 : 0110001
%F 8 : 01100110
%F 9 : 011000110
%F 10 : 0110001110
%F 11 : 01110001110
%F 12 : 011100001110
%F 13 : 0111000001110
%F 14 : 01100011110001
%F 15 : 011000011110001
%F 16 : 0111000011110001
%F 17 : 01110000011110001
%e For n = 3 one can obtain {010010, 001010, 010100, 001100} by self-shuffling 010, so a(3) = 4.
%o (Python) # uses a() in A191755; a(n)[2] generates the lex. least argmax
%o print([a(n)[1] for n in range(1, 9)]) # _Michael S. Branicky_, Sep 28 2021
%Y Cf. A191755.
%K nonn,more
%O 1,2
%A _Jeffrey Shallit_, Jan 29 2020
%E a(11)-a(13) from _Giovanni Resta_, Jan 29 2020
%E a(14)-a(15) from _Giovanni Resta_, Jan 30 2020
%E a(16)-a(17) from _Bert Dobbelaere_, Feb 08 2020
|
