A375860 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 symmetries of the rectangle.

1, 2, 19, 298, 6351, 152516, 3982186, 112862604, 3477324887, 116564337340, 4243247421102, 167133260332116, 7090692457208714, 322501850458391072, 15654927194390330084, 807745569631252715576, 44138380646303320082391, 2546015709197766295214940, 154576479598451154017930998

Offset: 1

Author

Andrew Howroyd, Aug 31 2024

Keywords

• nonn

Comments

See A375770 for additional information.

Examples

			a(3) = 19. The A375770(3) = 10 distinct solutions with their multiplicities are:
  ._._._.   ._._._.   ._._._.   ._._._.   ._._._.
  |     |   |   | |   |   | |   | | | |   |   ._|
  | | | |   | |   |   | | | |   |     |   | |   |
  |_|_|_|   |_|_|_|   |_|_._|   |_|_|_|   |_|_|_|
    (2)       (2)       (2)       (2)       (2)
  ._._._.   ._._._.   ._._._.   ._._._.   ._._._.
  | | ._|   |   | |   |   ._|   |_. ._|   |_. | |
  |     |   | | ._|   | | ._|   |     |   |   ._|
  |_|_|_|   |_|_._|   |_|_._|   |_|_|_|   |_|_._|
    (2)       (2)       (2)       (2)       (1)
		

Links

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

Crossrefs

Main diagonal of A375861.

Cf. A375770, A375817, A375859.

Programs

PARI

\\ See PARI link in A375770 for program code.
vector(20, n, A375860(n)) \\ Andrew Howroyd, Sep 03 2024