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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.

%I A375859 #13 Sep 04 2024 09:57:00
%S A375859 1,1,17,278,6299,151928,3980838,112842972,3477284215,116563600340,
%T A375859 4243245979546,167133229071276,7090692397872054,322501848961962040,
%U A375859 15654927191595331100,807745569550956567160,44138380646154800057431,2546015709192980766909132,154576479598442363146107882
%N 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.
%C A375859 See A375770 and A375817 for additional information.
%H A375859 Andrew Howroyd, <a href="/A375859/b375859.txt">Table of n, a(n) for n = 1..100</a>
%e A375859 a(3) = 17. The A375770(3) = 10 distinct solutions with their multiplicities are:
%e A375859   ._._._.   ._._._.   ._._._.   ._._._.   ._._._.
%e A375859   |     |   |   | |   |   | |   | | | |   |   ._|
%e A375859   | | | |   | |   |   | | | |   |     |   | |   |
%e A375859   |_|_|_|   |_|_|_|   |_|_._|   |_|_|_|   |_|_|_|
%e A375859     (1)       (2)       (2)       (1)       (2)
%e A375859   ._._._.   ._._._.   ._._._.   ._._._.   ._._._.
%e A375859   | | ._|   |   | |   |   ._|   |_. ._|   |_. | |
%e A375859   |     |   | | ._|   | | ._|   |     |   |   ._|
%e A375859   |_|_|_|   |_|_._|   |_|_._|   |_|_|_|   |_|_._|
%e A375859     (2)       (2)       (2)       (1)       (2)
%o A375859 (PARI) \\ See PARI link in A375770 for program code.
%o A375859 vector(20, n, A375859(n)) \\ _Andrew Howroyd_, Sep 03 2024
%Y A375859 Cf. A375770 (up to rotations and reflections), A375817 (not reduced for symmetry), A375860 (up to symmetries of rectangle).
%K A375859 nonn
%O A375859 1,3
%A A375859 _Andrew Howroyd_, Aug 31 2024