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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.

%I A375860 #10 Sep 03 2024 23:03:40
%S A375860 1,2,19,298,6351,152516,3982186,112862604,3477324887,116564337340,
%T A375860 4243247421102,167133260332116,7090692457208714,322501850458391072,
%U A375860 15654927194390330084,807745569631252715576,44138380646303320082391,2546015709197766295214940,154576479598451154017930998
%N 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.
%C A375860 See A375770 for additional information.
%H A375860 Andrew Howroyd, <a href="/A375860/b375860.txt">Table of n, a(n) for n = 1..100</a>
%e A375860 a(3) = 19. The A375770(3) = 10 distinct solutions with their multiplicities are:
%e A375860   ._._._.   ._._._.   ._._._.   ._._._.   ._._._.
%e A375860   |     |   |   | |   |   | |   | | | |   |   ._|
%e A375860   | | | |   | |   |   | | | |   |     |   | |   |
%e A375860   |_|_|_|   |_|_|_|   |_|_._|   |_|_|_|   |_|_|_|
%e A375860     (2)       (2)       (2)       (2)       (2)
%e A375860   ._._._.   ._._._.   ._._._.   ._._._.   ._._._.
%e A375860   | | ._|   |   | |   |   ._|   |_. ._|   |_. | |
%e A375860   |     |   | | ._|   | | ._|   |     |   |   ._|
%e A375860   |_|_|_|   |_|_._|   |_|_._|   |_|_|_|   |_|_._|
%e A375860     (2)       (2)       (2)       (2)       (1)
%o A375860 (PARI) \\ See PARI link in A375770 for program code.
%o A375860 vector(20, n, A375860(n)) \\ _Andrew Howroyd_, Sep 03 2024
%Y A375860 Main diagonal of A375861.
%Y A375860 Cf. A375770, A375817, A375859.
%K A375860 nonn
%O A375860 1,2
%A A375860 _Andrew Howroyd_, Aug 31 2024