A394998 - OEIS

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).

%I #17 Apr 26 2026 00:09:15

%S 1,1,2,5,15,55,219,958,4309,20018,93533,441509,2083213,9865022,

%T 46633704,220795735,1043513813,4936239997,23313698697,110177945357,

%U 520001061563

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

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

%e 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.

%Y Cf. A037245, A394340, A002902, A001412.

%K nonn,more,walk

%O 0,3

%A _Charles L. Hohn_, Apr 09 2026