A360106 Number of length-n blocks of the Fibonacci infinite word (A003849), counted up to cyclic shift.

1, 2, 2, 2, 3, 2, 4, 4, 2, 7, 4, 5, 8, 2, 9, 9, 4, 13, 5, 9, 14, 2, 16, 9, 9, 19, 4, 17, 17, 5, 23, 9, 15, 24, 2, 25, 18, 9, 29, 9, 21, 29, 4, 33, 17, 17, 35, 5, 31, 29, 9, 39, 15, 25, 40, 2, 42, 25, 18, 45, 9, 37, 39, 9, 49, 21, 29, 51, 4, 49, 37, 17, 55, 17

Offset

0,2

Comments

"Counted up to cyclic shift" means two blocks that are cyclic shifts of each other are treated as the same.

Links

Table of n, a(n) for n=0..73.

C. Krawchuk and N. Rampersad, Cyclic complexity of some infinite words and generalizations, INTEGERS 18A (2018), #A12.

Formula

There is a linear representation of rank 20 to compute a(n), so it can be computed efficiently.

Example

For n = 8 the a(8) = 2 blocks counted are {01001010, 10100101}.

Crossrefs

Cf. A003849.

Sequence in context: A029199 A121611 A378243 * A300066 A286545 A046798

Adjacent sequences: A360103 A360104 A360105 * A360107 A360108 A360109

Keyword

nonn

Author

Jeffrey Shallit, Jan 26 2023

Status

approved