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 A387317 #12 Sep 03 2025 20:24:21 %S A387317 1,4,1,2,1,44,1,2,1,414,1,2,31,5784,1,2,1,97358,237,2,1,1917064,1,2,1, %T A387317 42406158,1 %N A387317 Number of good involutions of all nontrivial linear quandles of order n. %C A387317 A linear quandle is a pair (Z/nZ, k) where k is a unit in Z/nZ, viewed as an Alexander quandle under the operation a(b) := ka + (1-k)b. A linear quandle is trivial if and only if k = 1. %C A387317 A good involution f of a quandle Q is an involution that commutes with all inner automorphisms and satisfies the identity f(y)(x) = y^-1(x). The pair (Q,f) is called a symmetric quandle. %D A387317 Seiichi Kamada, Quandles with good involutions, their homologies and knot invariants, Intelligence of Low Dimensional Topology 2006, World Scientific Publishing Co. Pte. Ltd., 2007, 101-108. %H A387317 Lực Ta, <a href="https://arxiv.org/abs/2508.16772">Good involutions of twisted conjugation subquandles and Alexander quandles</a>, arXiv:2508.16772 [math.GT], 2025. See Table 2. %H A387317 Lực Ta, <a href="https://github.com/luc-ta/Symmetric-Linear-Quandles">Symmetric-Linear-Quandles</a>, GitHub, 2025. %H A387317 <a href="/index/Qua#quandles">Index entries for sequences related to quandles and racks</a> %F A387317 If A060594(n) = 2, then a(n) = 1 if n is odd, a(n) = 4 if n = 4, and a(n) = 2 otherwise. See Ta, Ex. 5.8 and Prop. 5.9. %F A387317 For all n >= 1, we have a(4n) >= A202828(n), with equality if and only if n = 1. See Ta, Thm. 5.11. %o A387317 (GAP) See Ta, GitHub link %Y A387317 Cf. A060594, A202828, A386233, A386234. %K A387317 nonn,more,new %O A387317 3,2 %A A387317 _Luc Ta_, Aug 26 2025 %E A387317 Some terms corrected by _Luc Ta_, Sep 03 2025