A394814 Number of directed self-avoiding cycles of length 2*n in a cubic lattice, reduced for symmetry (with rotations and reflections not counted as distinct).

1, 0, 1, 3, 13, 116, 1380, 19103, 285975, 4508313, 73709922

Offset

0,4

Links

Table of n, a(n) for n=0..10.

Example

a(4) = 13 (with uppercase letters denoting positive direction steps in XYZ coordinates and lowercase denoting negative steps): 9 symmetric cases counting 1 each: XXXYxxxy, XXYYxxyy, XXYYxyxy, XXYxZyxz, XXYZxxyz, XXYZxxzy, XXYZyxxz, XYXZxyxz, XYZyxYzy, plus 2 nonsymmetric cases counting 2 each: XXYZxyxz, XXYZxzxy.

Crossrefs

Cf. A394959 (2-dimensional), A394796 (undirected), A394340 (directed paths), A001409 (undirected, all orientations), A001413 (all walks, all orientations).

Sequence in context: A093011 A262147 A364327 * A057865 A344210 A260847

Adjacent sequences: A394811 A394812 A394813 * A394815 A394816 A394817

Keyword

nonn,more,walk

Author

Charles L. Hohn, May 01 2026

Status

approved