A375859 In an n X n grid draw straight walls between cells, starting at a border, such that the resulting figure is connected and has only one-cell wide paths; a(n) is the number of solutions up to rotations.

1, 1, 17, 278, 6299, 151928, 3980838, 112842972, 3477284215, 116563600340, 4243245979546, 167133229071276, 7090692397872054, 322501848961962040, 15654927191595331100, 807745569550956567160, 44138380646154800057431, 2546015709192980766909132, 154576479598442363146107882

Offset: 1

Author

Andrew Howroyd, Aug 31 2024

Keywords

• nonn

Comments

See A375770 and A375817 for additional information.

Examples

			a(3) = 17. The A375770(3) = 10 distinct solutions with their multiplicities are:
  ._._._.   ._._._.   ._._._.   ._._._.   ._._._.
  |     |   |   | |   |   | |   | | | |   |   ._|
  | | | |   | |   |   | | | |   |     |   | |   |
  |_|_|_|   |_|_|_|   |_|_._|   |_|_|_|   |_|_|_|
    (1)       (2)       (2)       (1)       (2)
  ._._._.   ._._._.   ._._._.   ._._._.   ._._._.
  | | ._|   |   | |   |   ._|   |_. ._|   |_. | |
  |     |   | | ._|   | | ._|   |     |   |   ._|
  |_|_|_|   |_|_._|   |_|_._|   |_|_|_|   |_|_._|
    (2)       (2)       (2)       (1)       (2)
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A375770 (up to rotations and reflections), A375817 (not reduced for symmetry), A375860 (up to symmetries of rectangle).

Programs

PARI

\\ See PARI link in A375770 for program code.
vector(20, n, A375859(n)) \\ Andrew Howroyd, Sep 03 2024