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Number of Hamiltonian paths from NW to SW corners in an n X n grid.
16

%I #65 Jul 25 2023 10:13:05

%S 1,1,2,8,86,1770,88418,8934966,2087813834,1013346943033,

%T 1111598871478668,2568944901392936854,13251059359839620127088,

%U 145194816279817259193401518,3524171261632305641165676374930,182653259988707123426135593460533473

%N Number of Hamiltonian paths from NW to SW corners in an n X n grid.

%C Number of walks reaching each cell exactly once.

%H Ed Wynn, <a href="/A000532/b000532.txt">Table of n, a(n) for n = 1..19</a> (first 18 terms from KeyTo9(AT)Fans)

%H KeyTo9(AT)Fans, <a href="https://web.archive.org/web/20150911034408/https://tieba.baidu.com/f?kz=395424512">Counting paths in a grid</a> - Chinese web page giving the sequence up to 18 items.

%H Douglas M. McKenna, <a href="http://archive.bridgesmathart.org/2016/bridges2016-119.pdf">Tendril Motifs for Space-Filling, Half-Domino Curves</a>, in: Bridges Finland Conference Proceedings, 2016, pp. 119-126.

%H Douglas M. McKenna, <a href="https://archive.bridgesmathart.org/2023/bridges2023-91.html">Are Maximally Unbalanced Hilbert-Style Square-Filling Curve Motifs a Drawing Medium?</a>, Bridges Conf. Proc.; Math., Art, Music, Architecture, Culture (2023) 91-98.

%Y Main diagonal of A271592.

%Y Cf. A181688, A181689, A014524, A014585.

%Y Cf. A001184, A145157, A120443, A003763, A271507, A007764, A121785, A121789.

%Y See also A350148.

%K nonn,walk

%O 1,3

%A _Russ Cox_, Mar 15 1996

%E More terms from _Zhao Hui Du_, Jul 08 2008

%E Edited by _Franklin T. Adams-Watters_, Jul 03 2009

%E Name clarified by _Andrew Howroyd_, Apr 10 2016