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A120443 Number of (undirected) Hamiltonian paths in the n X n grid graph.

%I A120443 #54 Feb 16 2025 08:33:01
%S A120443 1,4,20,276,4324,229348,13535280,3023313284,745416341496,
%T A120443 730044829512632,786671485270308848,3452664855804347354220,
%U A120443 16652005717670534681315580,331809088406733654427925292528,7263611367960266490262600117251524
%N A120443 Number of (undirected) Hamiltonian paths in the n X n grid graph.
%H A120443 Jesper L. Jacobsen, <a href="/A120443/b120443.txt">Table of n, a(n) for n = 1..17</a>
%H A120443 J. L. Jacobsen, <a href="http://dx.doi.org/10.1088/1751-8113/40/49/003">Exact enumeration of Hamiltonian circuits, walks and chains in two and three dimensions</a>, J. Phys. A: Math. Theor. 40 (2007) 14667-14678.
%H A120443 J.-M. Mayer, C. Guez and J. Dayantis, <a href="http://dx.doi.org/10.1103/PhysRevB.42.660">Exact computer enumeration of the number of Hamiltonian paths in small square plane lattices</a>, Physical Review B, Vol. 42 Number 1, 1990.
%H A120443 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>
%H A120443 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HamiltonianPath.html">Hamiltonian Path</a>
%H A120443 <a href="/index/Gra#graphs">Index entries for sequences related to graphs, Hamiltonian</a>
%F A120443 a(n) = A096969(n) / 2 for n > 1.
%e A120443 From _Robert FERREOL_, Apr 03 2019: (Start)
%e A120443 a(3) = 20:
%e A120443 there are 4 paths similar to
%e A120443   + - + - +
%e A120443           |
%e A120443   + - + - +
%e A120443   |
%e A120443   + - + - +
%e A120443 8 paths similar to
%e A120443   + - + - +
%e A120443   |       |
%e A120443   +   + - +
%e A120443   |   |
%e A120443   +   + - +
%e A120443 and 8 paths similar to
%e A120443   + - + - +
%e A120443   |       |
%e A120443   +   +   +
%e A120443   |   |   |
%e A120443   +   + - +
%e A120443 (End)
%Y A120443 Main diagonal of A332307.
%Y A120443 Cf. A003685, A003695, A003778, A145402.
%Y A120443 Cf. A003763, A000532, A001184, A145157, A271507, A007764, A121785, A121789.
%K A120443 nonn,walk
%O A120443 1,2
%A A120443 _David Bevan_, Jul 19 2006
%E A120443 More terms from Jesper L. Jacobsen (jesper.jacobsen(AT)u-psud.fr), Dec 12 2007