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

1,2

Comments

See A375770 for additional information.

Links

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

Example

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

Prog

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

Crossrefs

Main diagonal of A375861.

Cf. A375770, A375817, A375859.

Sequence in context: A293946 A365652 A094476 * A304637 A119773 A137647

Adjacent sequences: A375857 A375858 A375859 * A375861 A375862 A375863

Keyword

nonn

Author

Andrew Howroyd, Aug 31 2024

Status

approved