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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.

A383830 Number of Legendrian quandles of order n, up to isomorphism.

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%I A383830 #8 May 16 2025 14:34:27
%S A383830 1,1,2,5,15,54,240,1306,9477
%N A383830 Number of Legendrian quandles of order n, up to isomorphism.
%C A383830 A Legendrian quandle is a pair (X,u) where X is a quandle and u is an involutory automorphism of X such that u(yx)=y(u(x)); see Ta, "Generalized Legendrian...," Corollary 3.13.
%C A383830 a(n) is also the number of racks X such that the kink map X -> X defined by x -> x(x) is an involution; see Ta, "Equivalences of...," Theorem 1.1.
%H A383830 Jose Ceniceros, Mohamed Elhamdadi, and Sam Nelson, <a href="https://doi.org/10.4134/CKMS.c200251">Legendrian rack invariants of Legendrian knots</a>, Communications of the Korean Mathematical Society, 36 (2021), no. 3, 623-639.
%H A383830 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 A383830 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 A383830 Lực Ta, <a href="https://github.com/luc-ta/GL-Rack-Classification">GL-Rack Classification</a>, GitHub, 2025.
%o A383830 (GAP) # See Ta, GitHub link
%Y A383830 Cf. A383828, A383829, A383831, A383145, A383146, A181769, A181770, A178432.
%Y A383830 Sequences related to racks and quandles: A383144, A181771, A176077, A179010, A193024, A254434, A177886, A196111, A226173, A236146, A248908, A165200, A242044, A226193, A242275, A243931, A257351, A198147, A225744, A226172, A226174.
%Y A383830 Sequences related to Legendrian knots: A374939, A374942, A374943, A374944, A374945, A374946, A374947.
%K A383830 nonn,hard,more
%O A383830 0,3
%A A383830 _Luc Ta_, May 11 2025