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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A375817 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 not reduced for symmetries.

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%I A375817 #16 Sep 04 2024 08:47:49
%S A375817 1,4,56,1112,25000,607712,15918280,451371888,13908978792,466254401360,
%T A375817 16972978214456,668532916285104,28362769354991656,1290007395847848160,
%U A375817 62619708755213093360,3230982278203826268640,176553522584025285715304,10184062836771923067636528
%N A375817 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 not reduced for symmetries.
%C A375817 This sequence contains some, but not all of the spanning trees in A007341, a(n)<A007341(n), for n>2.
%C A375817 See A375770 for examples.
%H A375817 Andrew Howroyd, <a href="/A375817/b375817.txt">Table of n, a(n) for n = 1..100</a>
%e A375817 a(3) = 56. The A375770(3) = 10 distinct solutions with their multiplicities are:
%e A375817   ._._._.   ._._._.   ._._._.   ._._._.   ._._._.
%e A375817   |     |   |   | |   |   | |   | | | |   |   ._|
%e A375817   | | | |   | |   |   | | | |   |     |   | |   |
%e A375817   |_|_|_|   |_|_|_|   |_|_._|   |_|_|_|   |_|_|_|
%e A375817     (4)       (8)       (4)       (2)       (8)
%e A375817   ._._._.   ._._._.   ._._._.   ._._._.   ._._._.
%e A375817   | | ._|   |   | |   |   ._|   |_. ._|   |_. | |
%e A375817   |     |   | | ._|   | | ._|   |     |   |   ._|
%e A375817   |_|_|_|   |_|_._|   |_|_._|   |_|_|_|   |_|_._|
%e A375817     (8)       (8)       (8)       (4)       (2)
%o A375817 (PARI) \\ See PARI link in A375770 for program code.
%o A375817 vector(20, n, A375817(n)) \\ _Andrew Howroyd_, Sep 03 2024
%Y A375817 Main diagonal of A375858.
%Y A375817 Cf. A007341, A375770 (up to rotations and reflections), A375859 (up to rotations), A375860 (up to symmetries of the rectangle).
%K A375817 nonn
%O A375817 1,2
%A A375817 _Lars Blomberg_, Aug 30 2024
%E A375817 Terms corrected and extended by _Andrew Howroyd_, Sep 03 2024