OFFSET
0,2
COMMENTS
"Counted up to cyclic shift" means two blocks that are cyclic shifts of each other are treated as the same.
It is known that a(n) >= (4/3)n - 4 for n >= 0 and a(n) <= 2n-4 for n >= 3.
LINKS
C. Krawchuk and N. Rampersad, Cyclic complexity of some infinite words and generalizations, INTEGERS 18A (2018), #A12.
Jeffrey Shallit, Proof of a conjecture of Krawchuk and Rampersad, arXiv:2301.11473 [math.CO], 2023.
Jeffrey Shallit, Proof of a conjecture of Krawchuk and Rampersad on the cyclic complexity of the Thue-Morse sequence, Integers (2023) Vol. 23, #A44.
FORMULA
There is a linear representation of rank 10 to compute a(n), so it can be computed efficiently.
EXAMPLE
For n = 5 the a(5) = 4 blocks counted are {00110, 01101, 10011, 10100}.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Jan 26 2023
STATUS
approved