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A333246 Number of self-avoiding closed paths on an n X n grid which pass through NW corner.

%I A333246 #114 Jan 31 2022 03:14:52
%S A333246 1,7,97,4111,532269,212372937,263708907211,1013068026356375,
%T A333246 11955420069208095719,432101605951906251627393,
%U A333246 47778407166747833830058004149,16149888968763663448192636077980753,16675786862526496319891707194153887550751,52568166380872328447478940416604864445574575709
%N A333246 Number of self-avoiding closed paths on an n X n grid which pass through NW corner.
%F A333246 a(n) = A333439(n) - 1 for n > 1.
%e A333246 a(2) = 1;
%e A333246    +--*
%e A333246    |  |
%e A333246    *--*
%e A333246 a(3) = 7;
%e A333246    +--*      +--*--*   +--*--*   +--*
%e A333246    |  |      |     |   |     |   |  |
%e A333246    *--*      *--*--*   *     *   *  *
%e A333246                        |     |   |  |
%e A333246                        *--*--*   *--*
%e A333246    +--*--*   +--*--*   +--*
%e A333246    |     |   |     |   |  |
%e A333246    *  *--*   *--*  *   *  *--*
%e A333246    |  |         |  |   |     |
%e A333246    *--*         *--*   *--*--*
%o A333246 (Python)
%o A333246 # Using graphillion
%o A333246 from graphillion import GraphSet
%o A333246 import graphillion.tutorial as tl
%o A333246 def A333246(n):
%o A333246     universe = tl.grid(n - 1, n - 1)
%o A333246     GraphSet.set_universe(universe)
%o A333246     cycles = GraphSet.cycles().including(1)
%o A333246     return cycles.len()
%o A333246 print([A333246(n) for n in range(2, 10)])
%Y A333246 Cf. A140517, A333247, A333323, A333438, A333439, A333466.
%K A333246 nonn
%O A333246 2,2
%A A333246 _Seiichi Manyama_, Mar 23 2020
%E A333246 a(11), a(13) from _Seiichi Manyama_, Apr 07 2020
%E A333246 a(10), a(12), a(14)-a(15) from _Andrew Howroyd_, Jan 30 2022