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

1,3

Comments

See A375770 and A375817 for additional information.

Links

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

Example

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

Prog

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

Crossrefs

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

Sequence in context: A029811 A113076 A159503 * A245940 A188063 A012235

Adjacent sequences: A375856 A375857 A375858 * A375860 A375861 A375863

Keyword

nonn,new

Author

Andrew Howroyd, Aug 31 2024

Status

approved