A389941 a(n) = the number of non-isomorphic non-adjacent self-avoiding paths in an n X n grid which leave unused cells divided into groups of size n.

1, 1, 2, 3, 3, 6, 17, 74, 266, 3677

Offset

1,3

Comments

a(1) = 1 because of the case of a 1-cell path leaving 0 regions of size n = 1.

Solutions only differing by any combination of translation, rotation and reflection are counted only once.

Links

Table of n, a(n) for n=1..10.

Example

For n = 4 the solutions are:
  O - - O   O O - -   - O - -
  O - - O   O - - O   - O - O
  O O O O   O O O O   - O - O
  - - - -,  - - - -,  - O O O
For n = 10 a solution is:
  O - - - O O O O O O
  O - - - O - - - - O
  O O O - O - - O - O
  - - O - O O - O - O
  - - O - - O O O - O
  - - O O O - - - O O
  - - - - O - O O O -
  O O O O O - O - - -
  O - - - - - O - - -
  O O O O O O O - - -

Crossrefs

Cf. A331968, A331986, A332920.

Sequence in context: A173094 A087989 A028257 * A100228 A111003 A347904

Adjacent sequences: A389938 A389939 A389940 * A389942 A389943 A389944

Keyword

nonn,hard,walk,more

Author

Eric Fox, Oct 19 2025

Status

approved