A396017 Number of primitive undirected self-avoiding paths of length n in the square lattice; i.e., A037245 with nonprimitive paths excluded.

1, 1, 3, 6, 21, 48, 146, 374, 1041, 2767, 7599, 20335, 55312, 148508, 401587, 1078120, 2905750, 7791872, 20949044, 56108088, 150561505, 402790471, 1079193820, 2884163147, 7717665942, 20607086269, 55082558748, 146961256062, 392462843328, 1046372618275

Offset

1,3

Comments

Here a primitive path is one which is not a repetition of a smaller path or congruent to a smaller path, e.g. the 3 cases for n = 4 which are counted in A037245 and not counted here (denoted here as positive direction steps in XY coordinates) are: path XYXY, which is a repetition of smaller primitive path XY, path XXYY, which is congruent to smaller primitive path XY, and path XXXX, which is both a repetition of and congruent to smaller primitive path X.

Links

Table of n, a(n) for n=1..30.

Formula

a(p) = A037245(p) - 1 for prime p.

Crossrefs

Cf. A037245.

Sequence in context: A076102 A094282 A124493 * A136331 A063683 A389563

Adjacent sequences: A396013 A396014 A396015 * A396018 A396019 A396020

Keyword

nonn,walk

Author

Charles L. Hohn, May 14 2026

Status

approved