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A333323 Number of self-avoiding closed paths on an n X n grid which pass through NW and SE corners.

%I A333323 #49 Nov 29 2022 01:34:36
%S A333323 1,3,42,1799,232094,92617031,115156685746,442641690778179,
%T A333323 5224287477491915786,188825256606226776728029,
%U A333323 20879416139356164466643759334,7057757437924198729598570424130207,7287699030020917172151307665469211016474,22973720258279267139936821063450448822110219653
%N A333323 Number of self-avoiding closed paths on an n X n grid which pass through NW and SE corners.
%H A333323 Anthony J. Guttmann and Iwan Jensen, <a href="/A333323/b333323.txt">Table of n, a(n) for n = 2..27</a>
%H A333323 Anthony J. Guttmann and Iwan Jensen, <a href="https://arxiv.org/abs/2208.06744">Self-avoiding walks and polygons crossing a domain on the square and hexagonal lattices</a>, arXiv:2208.06744 [math-ph], Aug 13 2022, Table D2 (with offset 1).
%H A333323 Anthony J. Guttmann and Iwan Jensen, <a href="https://arxiv.org/abs/2211.14482">The gerrymander sequence, or A348456</a>, arXiv:2211.14482 [math.CO], 2022.
%e A333323 a(2) = 1;
%e A333323    +--*
%e A333323    |  |
%e A333323    *--+
%e A333323 a(3) = 3;
%e A333323    +--*--*   +--*--*   +--*
%e A333323    |     |   |     |   |  |
%e A333323    *--*  *   *     *   *  *--*
%e A333323       |  |   |     |   |     |
%e A333323       *--+   *--*--+   *--*--+
%o A333323 (Python)
%o A333323 # Using graphillion
%o A333323 from graphillion import GraphSet
%o A333323 import graphillion.tutorial as tl
%o A333323 def A333323(n):
%o A333323     universe = tl.grid(n - 1, n - 1)
%o A333323     GraphSet.set_universe(universe)
%o A333323     cycles = GraphSet.cycles().including(1).including(n * n)
%o A333323     return cycles.len()
%o A333323 print([A333323(n) for n in range(2, 10)])
%Y A333323 Cf. A007764, A333246, A333247, A333466.
%Y A333323 Cf. A121785, A356610-A356616, A354511.
%K A333323 nonn
%O A333323 2,2
%A A333323 _Seiichi Manyama_, Mar 23 2020
%E A333323 a(11) from _Seiichi Manyama_, Apr 07 2020
%E A333323 a(10) and a(12)-a(15) from _Vaclav Kotesovec_, Aug 16 2022 (computed by _Anthony Guttmann_)