This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A354602 #21 Aug 03 2022 10:38:41 %S A354602 1,4,28,244,2412,25804,290932,3403404,40914508 %N A354602 a(n) is the number of trivial braids on 3 strands with 2*n crossings. %C A354602 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 A354602 Only braids with an even number of crossings are considered because a braid with an odd number of crossings cannot be trivial. %C A354602 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 A354602 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 A354602 nonn,more %O A354602 0,2 %A A354602 _Alexei Vernitski_, Jul 08 2022