%I #21 Aug 03 2022 10:38:41
%S 1,4,28,244,2412,25804,290932,3403404,40914508
%N a(n) is the number of trivial braids on 3 strands with 2*n crossings.
%C 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.
%C Only braids with an even number of crossings are considered because a braid with an odd number of crossings cannot be trivial.
%C 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.
%Y 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).
%K nonn,more
%O 0,2
%A _Alexei Vernitski_, Jul 08 2022