A297618 a(n) is the length of longest subsequence common to both the n-th Thue-Morse word and its bitwise complement.

1, 2, 5, 12, 26, 54, 110, 226, 462, 942, 1908, 3850, 7752, 15614, 31416, 63150, 126964, 254870, 511086, 1024796, 2053960, 4116976

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 * A360785 A198896 A026688

Adjacent sequences: A297615 A297616 A297617 * A297619 A297620 A297621

Keyword

nonn,more

Author

Jeffrey Shallit, Jan 01 2018

Status

approved