A352227 Number of length-n blocks in the Thue-Morse sequence with intertwining pattern AB AB AB... .

0, 2, 2, 4, 4, 6, 8, 8, 8, 10, 12, 14, 16, 16, 16, 16, 16, 18, 20, 22, 24, 26, 28, 30, 32, 32, 32, 32, 32, 32, 32, 32, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 66, 68

Offset

1,2

Comments

The intertwining pattern is the list of consecutive occurrences of a block x and its binary complement x' in the Thue-Morse sequence A010060, where A codes an occurrence of x and B codes an occurrence of x'.

Links

Table of n, a(n) for n=1..67.

J. Shallit, Intertwining of Complementary Thue-Morse Factors, arxiv preprint arXiv:2203.02917 [cs.FL], March 6 2022.

Formula

For n>=2, a(n) = 2*A006165(n-1).

Example

For n = 4, the four length-four blocks with intertwining pattern ABABAB... are 0110, 1101, 1010, 0100.

Crossrefs

Cf. A006165, A010060. Related to A352228.

Sequence in context: A123067 A218897 A218064 * A334001 A341731 A183002

Adjacent sequences: A352224 A352225 A352226 * A352228 A352229 A352230

Keyword

nonn

Author

Jeffrey Shallit, Mar 08 2022

Status

approved