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%I #53 Feb 10 2020 12:56:46
%S 1,4,20,276,4324,229348,13535280,3023313284,745416341496,
%T 730044829512632,786671485270308848,3452664855804347354220,
%U 16652005717670534681315580,331809088406733654427925292528,7263611367960266490262600117251524
%N Number of (undirected) Hamiltonian paths in the n X n grid graph.
%H Jesper L. Jacobsen, <a href="/A120443/b120443.txt">Table of n, a(n) for n = 1..17</a>
%H 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HamiltonianPath.html">Hamiltonian Path</a>
%H <a href="/index/Gra#graphs">Index entries for sequences related to graphs, Hamiltonian</a>
%F a(n) = A096969(n) / 2 for n > 1.
%e From _Robert FERREOL_, Apr 03 2019: (Start)
%e a(3) = 20:
%e there are 4 paths similar to
%e + - + - +
%e |
%e + - + - +
%e |
%e + - + - +
%e 8 paths similar to
%e + - + - +
%e | |
%e + + - +
%e | |
%e + + - +
%e and 8 paths similar to
%e + - + - +
%e | |
%e + + +
%e | | |
%e + + - +
%e (End)
%Y Main diagonal of A332307.
%Y Cf. A003685, A003695, A003778, A145402.
%Y Cf. A003763, A000532, A001184, A145157, A271507, A007764, A121785, A121789.
%K nonn,walk
%O 1,2
%A _David Bevan_, Jul 19 2006
%E More terms from Jesper L. Jacobsen (jesper.jacobsen(AT)u-psud.fr), Dec 12 2007
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