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A332307
Array read by antidiagonals: T(m,n) is the number of (undirected) Hamiltonian paths in the m X n grid graph.
12
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, 1, 1, 44, 336, 1006, 1006, 336, 44, 1, 1, 58, 688, 3610, 4324, 3610, 688, 58, 1, 1, 74, 1578, 12010, 26996, 26996, 12010, 1578, 74, 1, 1, 92, 3190, 38984, 109722, 229348, 109722, 38984, 3190, 92, 1
OFFSET
1,5
LINKS
J. L. Jacobsen, Exact enumeration of Hamiltonian circuits, walks and chains in two and three dimensions, J. Phys. A: Math. Theor. 40 (2007) 14667-14678.
J.-M. Mayer, C. Guez and J. Dayantis, Exact computer enumeration of the number of Hamiltonian paths in small square plane lattices, Physical Review B, Vol. 42 Number 1, 1990.
Eric Weisstein's World of Mathematics, Grid Graph
Eric Weisstein's World of Mathematics, Hamiltonian Path
FORMULA
T(n,m) = T(m,n).
EXAMPLE
Array begins:
================================================
m\n | 1 2 3 4 5 6 7
----+-------------------------------------------
1 | 1 1 1 1 1 1 1 ...
2 | 1 4 8 14 22 32 44 ...
3 | 1 8 20 62 132 336 688 ...
4 | 1 14 62 276 1006 3610 12010 ...
5 | 1 22 132 1006 4324 26996 109722 ...
6 | 1 32 336 3610 26996 229348 1620034 ...
7 | 1 44 688 12010 109722 1620034 13535280 ...
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Feb 09 2020
STATUS
approved