Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #6 Jan 26 2023 10:15:51
%S 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,
%T 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,
%U 42,25,18,45,9,37,39,9,49,21,29,51,4,49,37,17,55,17
%N Number of length-n blocks of the Fibonacci infinite word (A003849), counted up to cyclic shift.
%C "Counted up to cyclic shift" means two blocks that are cyclic shifts of each other are treated as the same.
%H C. Krawchuk and N. Rampersad, <a href="http://math.colgate.edu/~integers/sjs12/sjs12.pdf">Cyclic complexity of some infinite words and generalizations</a>, INTEGERS 18A (2018), #A12.
%F There is a linear representation of rank 20 to compute a(n), so it can be computed efficiently.
%e For n = 8 the a(8) = 2 blocks counted are {01001010, 10100101}.
%Y Cf. A003849.
%K nonn
%O 0,2
%A _Jeffrey Shallit_, Jan 26 2023