[seqfan] Number of Hamiltonian cycles in the n-cube

[Charles Greathouse]

Sequence A159344 counts the number of Hamiltonian cycles in the n-cube
(modding out the full automorphism group). This sequence was brought
to my attention by the recent work of Haanpaa & Ostergard who in a
computational tour de force discover a(6).

The sequence contains a lower bound due to Abbott 1966, which is available here:
http://math.ca/10.4153/CMB-1966-068-6

a(n) is, in Abbott's terminology, h*(n); see (2) and (3) which yield
a(n) >= sqrt(294)^(2^n-4)/(n! * 2^n)
[note that I have written sqrt(294) for 7 sqrt(6)].

Unfortunately the lower bound seems incompatible with the known values
of a(n), even for a(3) and a(4) which were known to Abbott. Am I
misinterpreting the paper? Is there a typographical error? I certainly
wouldn't want to leave the sequence in its present inconsistent state.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University