

A140519


Number of "king tours" on an n X n board.


7



1, 3, 16, 2830, 2462064, 22853860116, 1622043117414624, 961742089476282321684, 4601667243759511495116347104, 179517749570891592016479828267003018, 56735527086758553613684823040730404215973136, 145328824470156271670635015466987199469360063082789418
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OFFSET

1,2


COMMENTS

Or, number of Hamiltonian cycles in the graph P_n X P_n.
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, zerosuppressed 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
Index entries for sequences related to graphs, Hamiltonian


CROSSREFS

Cf. A001230, A140521.
Sequence in context: A080273 A096404 A111824 * A285740 A174506 A109216
Adjacent sequences: A140516 A140517 A140518 * A140520 A140521 A140522


KEYWORD

nonn,walk


AUTHOR

Don Knuth, Jul 26 2008


STATUS

approved



