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A003042
Number of directed Hamiltonian cycles (or Gray codes) on n-cube.
(Formerly M2053)
12
1, 2, 12, 2688, 1813091520, 71676427445141767741440
OFFSET
1,2
COMMENTS
Finding a(6) is Problem 43 in the Knuth reference.
REFERENCES
Martin Gardner, Knotted Doughnuts and Other Mathematical Entertainments. Freeman, NY, 1986, p. 24.
Donald E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, (to appear), section 7.2.1.1.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Michel Deza and Roman Shklyar, Enumeration of Hamiltonian Cycles in 6-cube, arXiv:1003.4391 [cs.DM], 2010. [There may be errors - see Haanpaa and Ostergard, 2012]
Harri Haanpaa and Patric R. J. Östergård, Counting Hamiltonian cycles in bipartite graphs, Math. Comp. 83 (2014), 979-995.
John Jungck, Genetic Codes as Codes: Towards a Theoretical Basis for Bioinformatics, International Symposium on Mathematical and Computational Biology (BIOMAT 2008), see p. 19.
Jerry Silverman, Virgil E. Vickers, and John L. Sampson, Statistical estimates of the n-bit Gray codes by restricted random generation of permutations of 1 to 2^n, IEEE Trans. Inform. Theory 29 (1983), no. 6, 894-901.
Vladimir Shevelev, Combinatorial minors of matrix functions and their applications, arXiv:1105.3154 [math.CO], 2011-2014.
Eric Weisstein's World of Mathematics, Hamiltonian Cycle
Eric Weisstein's World of Mathematics, Hypercube Graph
FORMULA
a(n) = 2 * A066037(n).
CROSSREFS
Equals A006069 divided by 2^n.
Sequence in context: A050649 A356722 A357765 * A000887 A118542 A007155
KEYWORD
nonn,nice,hard,more
EXTENSIONS
a(6) from Michel Deza, Mar 28 2010
a(6) corrected by Haanpaa and Östergård, 2012. - N. J. A. Sloane, Sep 06 2012
STATUS
approved