A360106 - OEIS

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

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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}.