1,3

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; and then dividing the total by 2^(n+1) because the starting node and the direction do not really matter.

The number is a multiple of n!/2 since any directed cycle starting from 0^n induces a permutation on the n bits, namely the order in which they first get set to 1.

R. J. Douglas, Bounds on the number of Hamiltonian circuits in the n-cube, Discrete Mathematics, 17 (1977), 143-146.

Harary, Hayes and Wu, A survey of the theory of hypercube graphs, Computers and Mathematics with Applications, 15(4), 1988, 7-289.

The 2-cube has a single cycle consisting of all 4 edges.

Equals A006069/2^(n+1) and A003042/2.

Cf. A006070, A091299, A003043, A091302.

Sequence in context: A013738 A076781 A055306 this_sequence A107252 A131453 A160226

Adjacent sequences: A066034 A066035 A066036 this_sequence A066038 A066039 A066040

nonn,nice

John Tromp (tromp(AT)cwi.nl), Dec 12 2001