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 A333466 Number of self-avoiding closed paths on an n X n grid which pass through four corners ((0,0), (0,n-1), (n-1,n-1), (n-1,0)). 9
 1, 1, 11, 373, 44930, 17720400, 22013629316, 84579095455492 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 COMMENTS a(11) = 36061721109572407840288. - Seiichi Manyama, Apr 07 2020 LINKS Table of n, a(n) for n=2..9. EXAMPLE a(2) = 1; +--+ | | +--+ a(3) = 1; +--*--+ | | * * | | +--*--+ a(4) = 11; +--*--*--+ +--*--*--+ +--*--*--+ | | | | | | *--*--* * *--* *--* *--* * | | | | | | *--*--* * *--* *--* *--* * | | | | | | +--*--*--+ +--*--*--+ +--*--*--+ +--*--*--+ +--*--*--+ +--*--*--+ | | | | | | * *--*--* * *--* * * *--* | | | | | | | | * *--*--* * * * * * *--* | | | | | | | | +--*--*--+ +--* *--+ +--*--*--+ +--*--*--+ +--*--*--+ +--* *--+ | | | | | | | | * * * * * *--* * | | | | | | * *--* * * * * *--* * | | | | | | | | | | +--* *--+ +--*--*--+ +--* *--+ +--* *--+ +--* *--+ | | | | | | | | * *--* * * * * * | | | | | | * * * *--* * | | | | +--*--*--+ +--*--*--+ PROG (Python) # Using graphillion from graphillion import GraphSet import graphillion.tutorial as tl def A333466(n): universe = tl.grid(n - 1, n - 1) GraphSet.set_universe(universe) cycles = GraphSet.cycles() for i in [1, n, n * (n - 1) + 1, n * n]: cycles = cycles.including(i) return cycles.len() print([A333466(n) for n in range(2, 10)]) (Ruby) def search(x, y, n, used) return 0 if x < 0 || n <= x || y < 0 || n <= y || used[x + y * n] return 1 if x == 0 && y == 1 && [n - 1, n * (n - 1), n * n - 1].all?{|i| used[i] == true} cnt = 0 used[x + y * n] = true @move.each{|mo| cnt += search(x + mo[0], y + mo[1], n, used) } used[x + y * n] = false cnt end def A(n) return 1 if n < 3 @move = [[1, 0], [-1, 0], [0, 1], [0, -1]] used = Array.new(n * n, false) search(0, 0, n, used) end def A333466(n) (2..n).map{|i| A(i)} end p A333466(6) CROSSREFS Main diagonal of A333513. Cf. A003763, A140517, A333246, A333247, A333323. Sequence in context: A291973 A024149 A353934 * A018893 A051862 A006698 Adjacent sequences: A333463 A333464 A333465 * A333467 A333468 A333469 KEYWORD nonn,more AUTHOR Seiichi Manyama, Mar 22 2020 STATUS approved

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Last modified October 4 01:05 EDT 2023. Contains 365872 sequences. (Running on oeis4.)