cp's OEIS Frontend

A003042 Number of directed Hamiltonian cycles (or Gray codes) on n-cube.

%I A003042 M2053 #60 Feb 16 2025 08:32:27
%S A003042 1,2,12,2688,1813091520,71676427445141767741440
%N A003042 Number of directed Hamiltonian cycles (or Gray codes) on n-cube.
%C A003042 Finding a(6) is Problem 43 in the Knuth reference.
%D A003042 Martin Gardner, Knotted Doughnuts and Other Mathematical Entertainments. Freeman, NY, 1986, p. 24.
%D A003042 Donald E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, (to appear), section 7.2.1.1.
%D A003042 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003042 Michel Deza and Roman Shklyar, <a href="http://arxiv.org/abs/1003.4391">Enumeration of Hamiltonian Cycles in 6-cube</a>, arXiv:1003.4391 [cs.DM], 2010. [There may be errors - see Haanpaa and Ostergard, 2012]
%H A003042 Harri Haanpaa and Patric R. J. Östergård, <a href="http://dx.doi.org/10.1090/S0025-5718-2013-02741-X">Counting Hamiltonian cycles in bipartite graphs</a>, Math. Comp. 83 (2014), 979-995.
%H A003042 John Jungck, <a href="https://doi.org/10.1142/9789814271820_0019">Genetic Codes as Codes: Towards a Theoretical Basis for Bioinformatics</a>, International Symposium on Mathematical and Computational Biology (BIOMAT 2008), see p. 19.
%H A003042 Jerry Silverman, Virgil E. Vickers, and John L. Sampson, <a href="http://dx.doi.org/10.1109/TIT.1983.1056755">Statistical estimates of the n-bit Gray codes by restricted random generation of permutations of 1 to 2^n</a>, IEEE Trans. Inform. Theory 29 (1983), no. 6, 894-901.
%H A003042 Vladimir Shevelev, <a href="http://arxiv.org/abs/1105.3154">Combinatorial minors of matrix functions and their applications</a>, arXiv:1105.3154 [math.CO], 2011-2014.
%H A003042 Vladimir Shevelev, <a href="https://www.math.bgu.ac.il/~shevelev/comb_meth2014.pdf">Combinatorial minors of matrix functions and their applications</a>
%H A003042 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HamiltonianCycle.html">Hamiltonian Cycle</a>
%H A003042 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HypercubeGraph.html">Hypercube Graph</a>
%F A003042 a(n) = 2 * A066037(n).
%Y A003042 Equals A006069 divided by 2^n.
%Y A003042 Cf. A006070, A091299, A003043, A091302, A066037, A159344, A180026.
%K A003042 nonn,nice,hard,more
%O A003042 1,2
%A A003042 _N. J. A. Sloane_
%E A003042 a(6) from Michel Deza, Mar 28 2010
%E A003042 a(6) corrected by Haanpaa and Östergård, 2012. - _N. J. A. Sloane_, Sep 06 2012