login

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”).

Number of equivalence classes of words in F_2, modulo all automorphisms of F_2, whose minimal words have length n.
1

%I #10 Oct 03 2016 12:36:31

%S 1,1,1,1,3,4,10,16,43,101,340,911,2544,7224,22616,65376,187754,545743,

%T 1653966,4832057,14027794

%N Number of equivalence classes of words in F_2, modulo all automorphisms of F_2, whose minimal words have length n.

%C F_2 is the free group on two generators.

%H Bobbe Cooper and Eric Rowland, <a href="http://arxiv.org/abs/0909.0561">Growing words in the free group on two generators</a>, Illinois Journal of Mathematics 55 (2011) 417-426.

%H Bobbe Cooper and Eric Rowland, <a href="https://arxiv.org/abs/1307.8216">Classification of automorphic conjugacy classes in the free group on two generators</a>, Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography, edited by Delaram Kahrobaei and Vladimir Shpilrain, Contemporary Mathematics 633 (2015) 13-40.

%Y A224074 is the number of root classes.

%K nonn,hard

%O 0,5

%A _Eric Rowland_, Mar 30 2013