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 A366778 #43 Jan 17 2024 09:12:58 %S A366778 3,25,480,12000,350256,10780549,344680960 %N A366778 Number of nonequivalent cycles of length 2n in the (2n+1) X (2n+1) knight graph. %C A366778 A knight graph is a graph that represents all legal moves of the knight chess piece on a chessboard. Each vertex of this graph represents a square of the chessboard, and each edge connects two squares that are a knight's move apart from each other. %C A366778 Two cycles in the knight graph are called equivalent if one can be obtained from another by applying one or more of the operations of translation, rotation, and symmetry on the chessboard; otherwise, they are nonequivalent. %H A366778 Stoyan Kapralov, Valentin Bakoev, and Kaloyan Kapralov, <a href="https://doi.org/10.53656/math2023-2-1-alg">Algorithms for Construction and Enumeration of Closed Knight's Paths</a>, Mathematics and Informatics, 2, (2023), 107-114; <a href="https://arxiv.org/abs/2304.00565">arXiv:2304.00565 [math.CO]</a>, 2023. %e A366778 For n=2 the a(2)=3 solutions (in standard chess notation) are: (a1, c2, d4, b3), (a2, c1, d2, c3), and (a2, c1, d3, b3). %e A366778 Note that each of these three cycles is non-self-intersecting. For the remaining values of n there are two kind of cycles - self-intersecting and non-self-intersecting. For example, a self-intersecting cycle of length 6 is (a1, c2, b4, a2, c1, b3), while the cycle (a1, c2, e1, f3, d4, b3) is non-self-intersecting. %Y A366778 Cf. A368499, A001230, A234623, A254129, A356404. %K A366778 nonn,hard,more %O A366778 2,1 %A A366778 _Stoyan Kapralov_, Dec 15 2023