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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.
6
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
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.
Sequence in context: A293946 A365652 A094476 * A304637 A119773 A137647
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Aug 31 2024
STATUS
approved