login
Number of Hamiltonian paths on an n X n grid reduced for symmetry, i.e., where rotations and reflections are not counted as distinct.
3

%I #15 Apr 17 2016 03:22:51

%S 1,1,3,38,549,28728,1692417,377919174,93177169027,91255604983167,

%T 98333935794279062,431583106977641773651,2081500714709464758363648,

%U 41476136050841717002906372881,907951420995033325255530074961505

%N Number of Hamiltonian paths on an n X n grid reduced for symmetry, i.e., where rotations and reflections are not counted as distinct.

%C For odd n > 1 the only symmetry possible is rotation by 180 degrees. For even n the only symmetries are reflections either horizontally or vertically. - _Andrew Howroyd_, Apr 15 2016

%H J.-M. Mayer, C. Guez and J. Dayantis, <a href="http://dx.doi.org/10.1103/PhysRevB.42.660">Exact computer enumeration of the number of Hamiltonian paths in small square plane lattices</a>, Physical Review B, Vol. 42 Number 1, 1990.

%Y Cf. A120443, A209077, A068393.

%K nonn,walk,hard

%O 1,3

%A _Luca Petrone_, Dec 18 2015

%E a(9)-a(15) from _Andrew Howroyd_, Apr 15 2016