OFFSET
1,1
COMMENTS
More precisely, this is the number of ways of making a list of the 2^n nodes of the n-cube, with a distinguished starting position and a direction, such that each node is adjacent to the previous one and the last node is adjacent to the first.
REFERENCES
M. Gardner, Knotted Doughnuts and Other Mathematical Entertainments. Freeman, NY, 1986, p. 24.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
H. Haanpaa and Patric R. J. Östergård, Counting Hamiltonian cycles in bipartite graphs, Math. Comp. 83 (2014), 979-995.
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]
D. Sensarma, S. S. Sarma, GMDES: A graph based modified Data Encryption Standard algorithm with enhanced security, IJRET: International Journal of Research in Engineering and Technology 03:03 (2014), 653-660. See Section 2.2.
Eric Weisstein's World of Mathematics, Hamiltonian Cycle
Eric Weisstein's World of Mathematics, Hypercube Graph
FORMULA
a(n) = A003042(n)*2^n. - Max Alekseyev, Jun 15 2006
EXAMPLE
a(1) = 2: we have 1,2 or 2,1.
a(2) = 8: label the nodes 1, 2, ..., 4. Then the 8 possibilities are 1,2,3,4; 1,4,3,2; 2,3,4,1; 2,1,4,3; etc.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
EXTENSIONS
a(5) corrected by Jonathan Cross (jcross(AT)wcox.com), Oct 10 2001
Definition corrected by Max Alekseyev, Jun 15 2006
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