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A297618 a(n) is the length of longest subsequence common to both the n-th Thue-Morse word and its bitwise complement. 1
1, 2, 5, 12, 26, 54, 110, 226, 462, 942, 1908, 3850, 7752, 15614, 31416, 63150, 126964, 254870, 511086, 1024796, 2053960, 4116976 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The n-th Thue-Morse word is the n-th iterate of the morphism mu(0) = 01, mu(1) = 10.  Thus mu^1(0) = 01, mu^2(0) = 0110, mu^3(0) = 01101001, etc.

Here by "subsequence" we mean "not necessarily contiguous subsequence".

Recently, Joakim Blikstad has proved that a(n) = 2^n(1-o(1)). - Jeffrey Shallit, Oct 26 2018

LINKS

Table of n, a(n) for n=1..22.

J. Berstel, Combinatorics on Words Examples and Problems, talk in Turku, Finland, May 24 2006.

Joakim Blikstad, On the longest common subsequence of Thue-Morse words, arXiv:1904.00248 [cs.DM], 2019.

Wikipedia, Longest common subsequence problem

EXAMPLE

For n = 3, a longest common subsequence between mu^3(0) = 01101001 and its bitwise complement 10010110 is 01010.

CROSSREFS

Cf. A010060.

Sequence in context: A221949 A262803 A026622 * A198896 A026688 A116726

Adjacent sequences:  A297615 A297616 A297617 * A297619 A297620 A297621

KEYWORD

nonn,more

AUTHOR

Jeffrey Shallit, Jan 01 2018

STATUS

approved

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Last modified December 6 04:20 EST 2021. Contains 349562 sequences. (Running on oeis4.)