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A333247 Number of self-avoiding closed paths on an n X n grid which pass through NW and SW corners.

%I A333247 #132 Apr 07 2020 11:03:06
%S A333247 1,4,47,1843,232905,92729439,115234959344,442748883422394
%N A333247 Number of self-avoiding closed paths on an n X n grid which pass through NW and SW corners.
%C A333247 a(11) = 188829168009674568016545. - _Seiichi Manyama_, Apr 07 2020
%e A333247 a(2) = 1;
%e A333247    +--*
%e A333247    |  |
%e A333247    +--*
%e A333247 a(3) = 4;
%e A333247    +--*--*   +--*--*   +--*      +--*
%e A333247    |     |   |     |   |  |      |  |
%e A333247    *     *   *  *--*   *  *--*   *  *
%e A333247    |     |   |  |      |     |   |  |
%e A333247    +--*--*   +--*      +--*--*   +--*
%o A333247 (Python)
%o A333247 # Using graphillion
%o A333247 from graphillion import GraphSet
%o A333247 import graphillion.tutorial as tl
%o A333247 def A333247(n):
%o A333247     universe = tl.grid(n - 1, n - 1)
%o A333247     GraphSet.set_universe(universe)
%o A333247     cycles = GraphSet.cycles().including(1).including(n)
%o A333247     return cycles.len()
%o A333247 print([A333247(n) for n in range(2, 10)])
%Y A333247 Cf. A271507, A333246, A333323, A333466.
%K A333247 nonn,more
%O A333247 2,2
%A A333247 _Seiichi Manyama_, Mar 23 2020