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%I #6 Oct 13 2013 02:59:58
%S 1,1,4,9,6,22,43,49,130,266,287,786,1730,2199,5184,12193,17035,37786,
%T 88959,136814,288292,682573,1118997,2307154,5428806,9409518
%N Number of subgroups of index n of the braid group on 3 strands <a,b|aba=bab>= <c,d|c^2=d^3>, the fundamental group of the complement of a trefoil knot.
%C Found by counting homomorphisms to the symmetric group.
%e The 4 subgroups of the braid group on 3 strands of index 3 are the 3 stabilizers of one strand and the subgroup of words of total weight divisible by 3.
%K nonn,nice,more
%O 1,3
%A _Douglas Zare_, May 30 2001
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