The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #5 May 27 2026 00:24:50
%S 0,4,127,11336,2761827,1891984647,3720952049343
%N Number of directed self-avoiding paths in the mod n square grid graph, reduced for symmetry (with rotations, reflections, and translations not counted as distinct).
%C Here a "mod n square grid graph" is a n X n graph with wrapping allowed, e.g., a path can make a 1 unit step between the left and the right edge (same row) or the top and the bottom edge (same column) of the graph.
%C Excludes 0 length paths; including them increases each term by 1.
%e a(2) = 4, all symmetric and count as 1 each both undirected and directed:
%e X--X X--+ X--+ X--+
%e | | |
%e X X--+ ..X +..
%e Nonsymmetric paths count as 2 each when directed, e.g.:
%e X--+--+ X>>+>>+ X<<+<<+
%e | -> v and ^
%e X X X
%Y Cf. A395462 (undirected), A394066 (wrapping disallowed).
%K nonn,walk,hard,more
%O 1,2
%A _Charles L. Hohn_, May 22 2026