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 A328931 Number of Hamiltonian paths in an n X n square, starting from an edge, finishing anywhere, all symmetries excluded. 1
 1, 1, 4, 51, 660, 30745, 1621471, 312637285, 72599875346, 60968508324409, 64128000370443037, 240651566540823214362, 1162174738476331286327484, 19776621796151182708398884540, 441809773825445785471324877668710 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Given an n X n grid, start from any outside edge, enter the grid, and visit every square. 1 X 1 is a trivial example. 2 X 2 can only be traversed clockwise or counterclockwise (therefore considered the same solution). For 3 X 3 with the cells labeled ABC/DEF/GHI, the four solutions are ADEBCFIHG, ADGHIFEBC, ADGHIFCE and ADGHEBCFI. All others are rotations or reflections. Discovered programmatically by exhaustive recursive search. LINKS David Lawrence, All paths up to 4 X 4 EXAMPLE All distinct paths through a 1 X 1 labyrinth visiting all cells.   +  +   |**|   +--+ . All distinct paths through a 2 X 2 labyrinth visiting all cells.   +  +--+   |  |**|   +  +  +   |     |   +--+--+ . All distinct paths through a 3 X 3 labyrinth visiting all cells.   +  +--+--+   |  |     |   +  +  +  +   |     |  |   +--+--+  +   |**      |   +--+--+--+ .   +  +--+--+   |  |   **|   +  +  +--+   |  |     |   +  +--+  +   |        |   +--+--+--+ .   +  +--+--+   |  |     |   +  +  +  +   |  |**|  |   +  +--+  +   |        |   +--+--+--+ .   +  +--+--+   |  |     |   +  +  +  +   |  |  |  |   +  +  +  +   |     |**|   +--+--+--+ CROSSREFS Cf. A120443, A121789, A145157, A265914. Sequence in context: A048995 A215639 A320645 * A235325 A230401 A293075 Adjacent sequences:  A328928 A328929 A328930 * A328932 A328933 A328934 KEYWORD nonn,more AUTHOR David Lawrence, Oct 31 2019 EXTENSIONS a(8)-a(15) from Andrew Howroyd, Oct 31 2019 STATUS approved

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Last modified February 27 18:28 EST 2020. Contains 332307 sequences. (Running on oeis4.)