A354602 a(n) is the number of trivial braids on 3 strands with 2*n crossings.

1, 4, 28, 244, 2412, 25804, 290932, 3403404, 40914508

Offset: 0

Author

Alexei Vernitski, Jul 08 2022

Keywords

• nonn
• more

Comments

In other words, a(n) is the number of products of 2*n generators in the braid group B_3 which are equal to the identity element of the group.

Only braids with an even number of crossings are considered because a braid with an odd number of crossings cannot be trivial.

If we do include the 0s corresponding to the odd values of the number of crossings, a group-theoretical name for this sequence is the cogrowth sequence of B_3.

Crossrefs

Cf. A000984 (number of trivial braids on 2 strands with 2*n crossings), A047849 (number of trivial permutations of 3 elements after 2*n adjacent transpositions).