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