Number of Hamiltonian paths from NW to SW corners in an n X n grid reduced for symmetry, i.e., where reflection about the x-axis is not counted as distinct.
When n is odd there are no symmetric Hamiltonian paths from NW to SW corners, and therefore a(n) = A000532(n)/2.
REFERENCES
J. L. Jacobsen, Exact enumeration of Hamiltonian circuits, walks and chains in two and three dimensions, J. Phys. A: Math. Theor. 40 (2007) 14667-14678.
J.-M. Mayer, C. Guez and J. Dayantis, Exact computer enumeration of the number of Hamiltonian paths in small square plane lattices, Physical Review B, Vol. 42 Number 1, 1990.
