A091302 Number of equivalence classes of directed Hamiltonian cycles (or Gray codes) in the binary n-cube with one node marked.

1, 1, 2, 112, 15109096, 99550593673808010752

Offset: 1

Author

N. J. A. Sloane, following a suggestion of Gordon Royle, Feb 20 2004

Keywords

• nonn

Comments

Equals A066037(n)/(n!/2). See A006069, A003042, A066037 for more information.

References

• D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, (to appear), section 7.2.1.1.

Links

• Michel Deza and Roman Shklyar, Enumeration of Hamiltonian Cycles in 6-cube, arXiv:1003.4391v1 [There may be errors - see Haanpaa and Ostergard, 2012]
• Harri Haanpaa and Patric R. J. Östergård, Counting Hamiltonian cycles in bipartite graphs, Math. Comp., 88 (2014) 979-995. Final version available from http://users.tkk.fi/pat/.

Crossrefs

Cf. A006069, A003042, A066037, A159344.

Extensions

a(6) from Michel Deza, Mar 28 2010

a(6) corrected by Haanpaa and Östergård, 2012, who also provided a more precise definition. - N. J. A. Sloane, Sep 06 2012