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.

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

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 * A362436 A140694 A152454

Adjacent sequences: A061204 A061205 A061206 * A061208 A061209 A061210

Keyword

nonn,nice,more

Author

Douglas Zare, May 30 2001

Status

approved