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A360106
Number of length-n blocks of the Fibonacci infinite word (A003849), counted up to cyclic shift.
0
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
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: A035433 A029199 A121611 * A300066 A286545 A046798
KEYWORD
nonn
AUTHOR
Jeffrey Shallit, Jan 26 2023
STATUS
approved