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A140519
Number of (undirected) Hamiltonian cycles on the n X n king graph.
10
1, 3, 16, 2830, 2462064, 22853860116, 1622043117414624, 961742089476282321684, 4601667243759511495116347104, 179517749570891592016479828267003018, 56735527086758553613684823040730404215973136, 145328824470156271670635015466987199469360063082789418
OFFSET
1,2
COMMENTS
Or, number of Hamiltonian cycles in the graph P_n X P_n (strong product of two paths of length n-1).
If the direction of the tour is to be taken into account, the numbers for n > 1 must be multiplied by 2 (see A140521).
Computed using ZDDs (ZDD = "reduced, order, zero-suppressed binary decision diagram").
REFERENCES
D. E. Knuth, The Art of Computer Programming, Section 7.1.4, in preparation.
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 1..16 [From Pettersson 2014]
Ville H. Pettersson, Enumerating Hamiltonian Cycles, The Electronic Journal of Combinatorics, Volume 21, Issue 4, 2014.
Ville Pettersson, Graph Algorithms for Constructing and Enumerating Cycles and Related Structures, Dissertation, Aalto, Finland, 2015.
Eric Weisstein's World of Mathematics, Hamiltonian Cycle
Eric Weisstein's World of Mathematics, King Graph
CROSSREFS
Sequence in context: A080273 A096404 A111824 * A285740 A174506 A109216
KEYWORD
nonn,walk
AUTHOR
Don Knuth, Jul 26 2008
EXTENSIONS
New name from Eric W. Weisstein, May 06 2019
STATUS
approved