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 A193346 #41 Feb 16 2025 08:33:15 %S A193346 1,144,4960608,55493434415544000 %N A193346 Number of (directed) Hamiltonian paths on the n X n X n grid graph. %C A193346 A general purpose matrix-transfer method can be used to compute values up to a(4). Using a diagonal sweep from one corner to the opposite corner will help to reduce the number of states. - _Andrew Howroyd_, Dec 20 2015 %C A193346 Schram & Schiessel (see Links) quote a different result for a(4): 27747833510015886 undirected Hamiltonian walks, which would double to 55495667020031772 directed Hamiltonian walks. However, that number is not divisible by 8 and thus cannot be correct. - _Arun Giridhar_, Dec 15 2015 %H A193346 Raoul D. Schram and Helmut Schiessel, <a href="http://dx.doi.org/10.1088/1751-8113/46/48/485001">Exact enumeration of Hamiltonian walks on the 4x4x4 cube and applications to protein folding</a>, Journal of Physics A: Mathematical and Theoretical, vol 46 (2013), 485001. %H A193346 Raoul D. Schram and Helmut Schiessel, <a href="http://dx.doi.org/10.1088/1751-8113/49/36/369501">Corrigendum: Exact enumeration of Hamiltonian walks on the 4x4x4 cube and applications to protein folding</a>, Journal of Physics A: Mathematical and Theoretical, vol 49 (2016), 369501. %H A193346 Jamie Shepard, <a href="https://digitalcommons.andrews.edu/honors/290/">Solvability and Difficulty of the Snake Puzzle in the Cube and its Topological Variants</a>, Honors Thesis, Andrews Univ. (2024) Art. No. 290. %H A193346 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a> %H A193346 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HamiltonianPath.html">Hamiltonian Path</a> %H A193346 <a href="/index/Gra#graphs">Index entries for sequences related to graphs, Hamiltonian</a> %e A193346 For n = 1, there is a trivial Hamiltonian path of length 0. %e A193346 For n = 2, the 144 paths fall in three different equivalence classes. Two of the three classes can be derived by taking a Hamiltonian cycle on a cube and deleting a single edge. The third class is a spiral path that ends at the opposite corner from its starting point. %Y A193346 Cf. A003763, A096969. %K A193346 nonn,hard,more,bref %O A193346 1,2 %A A193346 _Eric W. Weisstein_, Jul 23 2011 %E A193346 a(4) from _Andrew Howroyd_, Nov 15 2015 %E A193346 a(1) corrected by _Arun Giridhar_, Dec 20 2015