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 A383144 #15 May 16 2025 07:19:23 %S A383144 1,1,2,6,18,68,329,1965,15455,155902,2064870,35982366,832699635, %T A383144 25731050872 %N A383144 Number of abelian/medial racks of order n, up to isomorphism. %C A383144 A rack or quandle X is medial (also called abelian) if the map X x X -> X defined by (x,y) -> y(x) is a rack homomorphism. Equivalently, the identity (xy)(uv)=(xu)(yv) holds for all elements x, y, u, and v in X. %C A383144 a(n) is also the number of medial Legendrian racks of order n up to isomorphism; see Ta, "Equivalences of...," Theorem 1.1. %C A383144 a(n) is also the number of medial generalized Legendrian quandles (also called GL-quandles or bi-Legendrian quandles) of order n up to isomorphism; see Ta, "Generalized Legendrian...," Theorem 5.5. %H A383144 Lực Ta, <a href="https://arxiv.org/abs/2505.08090">Equivalences of racks, Legendrian racks, and symmetric racks</a>, arXiv:2505.08090 [math.GT], 2025. %H A383144 Lực Ta, <a href="https://arxiv.org/abs/2504.12671">Generalized Legendrian racks: Classification, tensors, and knot coloring invariants</a>, arXiv:2504.12671 [math.GT], 2025. %H A383144 Petr Vojtěchovský and Seung Yeop Yang, <a href="https://doi.org/10.1090/mcom/3409">Enumeration of racks and quandles up to isomorphism</a>, Mathematics of Computation, 88 (2019), no. 319, 2523-2540. %Y A383144 Sequences related to medial racks and quandles: A165200, A242044, A226193, A242275, A243931, A257351, A383146, A383829, A383831. %Y A383144 Other sequences related to racks and quandles: A181769, A181770, A181771, A176077, A178432, A179010, A193024, A254434, A177886, A196111, A226173, A236146, A248908, A198147, A225744, A226172, A226174, A383145. %K A383144 nonn,hard,more %O A383144 0,3 %A A383144 _Luc Ta_, Apr 17 2025