A333323 - OEIS

%I #49 Nov 29 2022 01:34:36

%S 1,3,42,1799,232094,92617031,115156685746,442641690778179,

%T 5224287477491915786,188825256606226776728029,

%U 20879416139356164466643759334,7057757437924198729598570424130207,7287699030020917172151307665469211016474,22973720258279267139936821063450448822110219653

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

%H Anthony J. Guttmann and Iwan Jensen, <a href="/A333323/b333323.txt">Table of n, a(n) for n = 2..27</a>

%H 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 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 a(2) = 1;

%e    +--*

%e    |  |

%e    *--+

%e a(3) = 3;

%e    +--*--*   +--*--*   +--*

%e    |     |   |     |   |  |

%e    *--*  *   *     *   *  *--*

%e       |  |   |     |   |     |

%e       *--+   *--*--+   *--*--+

%o (Python)

%o # Using graphillion

%o from graphillion import GraphSet

%o import graphillion.tutorial as tl

%o def A333323(n):

%o     universe = tl.grid(n - 1, n - 1)

%o     GraphSet.set_universe(universe)

%o     cycles = GraphSet.cycles().including(1).including(n * n)

%o     return cycles.len()

%o print([A333323(n) for n in range(2, 10)])

%Y Cf. A007764, A333246, A333247, A333466.

%Y Cf. A121785, A356610-A356616, A354511.

%K nonn

%O 2,2

%A _Seiichi Manyama_, Mar 23 2020

%E a(11) from _Seiichi Manyama_, Apr 07 2020

%E a(10) and a(12)-a(15) from _Vaclav Kotesovec_, Aug 16 2022 (computed by _Anthony Guttmann_)