A396337 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).

0, 4, 127, 11336, 2761827, 1891984647, 3720952049343

Offset

1,2

Comments

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.

Excludes 0 length paths; including them increases each term by 1.

Links

Table of n, a(n) for n=1..7.

Example

a(2) = 4, all symmetric and count as 1 each both undirected and directed:
  X--X   X--+   X--+     X--+
            |      |        |
            X   X--+   ..X  +..
Nonsymmetric paths count as 2 each when directed, e.g.:
  X--+--+      X>>+>>+       X<<+<<+
        |  ->        v  and        ^
        X            X             X

Crossrefs

Cf. A395462 (undirected), A394066 (wrapping disallowed).

Sequence in context: A070781 A152421 A270959 * A291851 A128790 A267796

Adjacent sequences: A396334 A396335 A396336 * A396338 A396339 A396340

Keyword

nonn,walk,hard,more

Author

Charles L. Hohn, May 22 2026

Status

approved