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%I #11 Dec 01 2022 11:08:07
%S 1,1,1,1,4,1,1,8,8,1,1,14,20,14,1,1,22,62,62,22,1,1,32,132,276,132,32,
%T 1,1,44,336,1006,1006,336,44,1,1,58,688,3610,4324,3610,688,58,1,1,74,
%U 1578,12010,26996,26996,12010,1578,74,1,1,92,3190,38984,109722,229348,109722,38984,3190,92,1
%N Array read by antidiagonals: T(m,n) is the number of (undirected) Hamiltonian paths in the m X n grid graph.
%H Andrew Howroyd, <a href="/A332307/b332307.txt">Table of n, a(n) for n = 1..435</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>
%F T(n,m) = T(m,n).
%e Array begins:
%e ================================================
%e m\n | 1 2 3 4 5 6 7
%e ----+-------------------------------------------
%e 1 | 1 1 1 1 1 1 1 ...
%e 2 | 1 4 8 14 22 32 44 ...
%e 3 | 1 8 20 62 132 336 688 ...
%e 4 | 1 14 62 276 1006 3610 12010 ...
%e 5 | 1 22 132 1006 4324 26996 109722 ...
%e 6 | 1 32 336 3610 26996 229348 1620034 ...
%e 7 | 1 44 688 12010 109722 1620034 13535280 ...
%e ...
%Y Rows n=1..9 are A000012, A003682, A003685, A003695, A003778, A145402, A358794, A358795, A358796.
%Y Main diagonal is A120443.
%Y Cf. A064298, A231829, A271465, A271592, A288518, A321172.
%K nonn,tabl
%O 1,5
%A _Andrew Howroyd_, Feb 09 2020
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