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A061207 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. 0
1, 1, 4, 9, 6, 22, 43, 49, 130, 266, 287, 786, 1730, 2199, 5184, 12193, 17035, 37786, 88959, 136814, 288292, 682573, 1118997, 2307154, 5428806, 9409518 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Found by counting homomorphisms to the symmetric group.

LINKS

Table of n, a(n) for n=1..26.

EXAMPLE

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.

CROSSREFS

Sequence in context: A075065 A141553 A095065 * A140694 A152454 A287932

Adjacent sequences:  A061204 A061205 A061206 * A061208 A061209 A061210

KEYWORD

nonn,nice,more

AUTHOR

Douglas Zare, May 30 2001

STATUS

approved

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Last modified March 20 21:49 EDT 2019. Contains 321352 sequences. (Running on oeis4.)