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A140519 Number of (undirected) Hamiltonian cycles on the n X n king graph. 9
1, 3, 16, 2830, 2462064, 22853860116, 1622043117414624, 961742089476282321684, 4601667243759511495116347104, 179517749570891592016479828267003018, 56735527086758553613684823040730404215973136, 145328824470156271670635015466987199469360063082789418 (list; graph; refs; listen; history; text; internal format)



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").


D. E. Knuth, The Art of Computer Programming, Section 7.1.4, in preparation.


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


Cf. A001230, A140521.

Sequence in context: A080273 A096404 A111824 * A285740 A174506 A109216

Adjacent sequences:  A140516 A140517 A140518 * A140520 A140521 A140522




Don Knuth, Jul 26 2008


New name from Eric W. Weisstein, May 06 2019



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Last modified December 7 13:08 EST 2021. Contains 349581 sequences. (Running on oeis4.)