A375859 - OEIS

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 #13 Sep 04 2024 09:57:00

%S 1,1,17,278,6299,151928,3980838,112842972,3477284215,116563600340,

%T 4243245979546,167133229071276,7090692397872054,322501848961962040,

%U 15654927191595331100,807745569550956567160,44138380646154800057431,2546015709192980766909132,154576479598442363146107882

%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 up to rotations.

%C See A375770 and A375817 for additional information.

%H Andrew Howroyd, <a href="/A375859/b375859.txt">Table of n, a(n) for n = 1..100</a>

%e a(3) = 17. The A375770(3) = 10 distinct solutions with their multiplicities are:

%e ._._._. ._._._. ._._._. ._._._. ._._._.

%e | | | | | | | | | | | | | ._|

%e | | | | | | | | | | | | | | | |

%e |_|_|_| |_|_|_| |_|_._| |_|_|_| |_|_|_|

%e (1) (2) (2) (1) (2)

%e ._._._. ._._._. ._._._. ._._._. ._._._.

%e | | ._| | | | | ._| |_. ._| |_. | |

%e | | | | ._| | | ._| | | | ._|

%e |_|_|_| |_|_._| |_|_._| |_|_|_| |_|_._|

%e (2) (2) (2) (1) (2)

%o (PARI) \\ See PARI link in A375770 for program code.

%o vector(20, n, A375859(n)) \\ _Andrew Howroyd_, Sep 03 2024

%Y Cf. A375770 (up to rotations and reflections), A375817 (not reduced for symmetry), A375860 (up to symmetries of rectangle).

%K nonn

%O 1,3

%A _Andrew Howroyd_, Aug 31 2024