A394998 Number of undirected self-avoiding paths of length n in a cubic lattice, reduced for symmetry (with rotations and reflections not counted as distinct).

1, 1, 2, 5, 15, 55, 219, 958, 4309, 20018, 93533, 441509, 2083213, 9865022, 46633704, 220795735, 1043513813, 4936239997, 23313698697, 110177945357, 520001061563

Offset

0,3

Comments

3-dimensional analog of A037245. Directed gives A394340. Unreduced gives A002902 (= A001412 / 2) for n >= 1.

Links

Table of n, a(n) for n=0..20.

Example

a(4) = 15 (with uppercase letters denoting positive direction steps in XYZ coordinates and lowercase denoting negative steps): XXXX, XXYY, XYXY, XYYX, XYYx, XYYZ, XYZX, XYZx, XXXY, XXYX, XXYx, XXYZ, XYXy, XYXZ, XYZy.

Crossrefs

Cf. A037245, A394340, A002902, A001412.

Sequence in context: A383830 A009383 A376349 * A104429 A109319 A387777

Adjacent sequences: A394995 A394996 A394997 * A394999 A395000 A395001

Keyword

nonn,more,walk

Author

Charles L. Hohn, Apr 09 2026

Status

approved