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 A367123 #15 Nov 19 2023 11:36:14 %S A367123 1,1,0,2,16800 %N A367123 Number of Hamiltonian cycles in the n-omino graph defined in A098891. %C A367123 The n-omino graph has all A000105(n) free n-ominoes as nodes, and two n-ominoes are joined by an edge if one can be obtained from the other by moving one cell. The intermediate is allowed not to be a connected (n-1)-omino; for example, there is an edge between the V and W pentominoes, but to transform one to the other the central cell must be moved, and the remaining 4 cells is not a tetromino. %C A367123 A cycle and its reverse are not both counted. %C A367123 We follow the convention in A003216 that the complete graphs on 1 and 2 nodes have 1 and 0 Hamiltonian cycles, respectively, so that a(1) = a(2) = 1 and a(3) = 0, but it could also be argued that a(1) = a(2) = 0 and/or a(3) = 1. %H A367123 Pontus von Brömssen, <a href="/A367123/a367123.svg">A Hamiltonian cycle in the hexomino graph</a>. In this cycle, all intermediates are (connected) pentominoes. %H A367123 <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>. %F A367123 a(n) > 0 for 4 <= n <= 13. %F A367123 a(n) >= A367436(n). %e A367123 For n = 4, there are a(4) = 2 Hamiltonian cycles in the tetromino graph: I-L-O-S-T-I and I-L-S-O-T-I, using conventional names of the tetrominoes. %e A367123 For n = 5, one of the a(5) = 16800 Hamiltonian cycles in the pentomino graph is I-L-P-U-V-T-N-W-Z-F-X-Y-I. %e A367123 See links for an example for n = 6. %Y A367123 Cf. A000105, A003216, A098891, A367124, A367125, A367126, A367127, A367436. %K A367123 nonn,more %O A367123 1,4 %A A367123 _Pontus von Brömssen_, Nov 05 2023