A237429 Number of nonisomorphic Hamiltonian cycles on 2n X 2n square grid of points with exactly one axis of reflective symmetry.

0, 1, 19, 1394, 281990, 377205809, 1539951848735, 44222409563201991, 3842818845468254120853, 2396657968905952750257244144

Offset: 1

Author

Ed Wynn, Feb 07 2014

Keywords

• nonn
• walk
• more

Examples

			The following two cycles with n=3 are counted only once, since they are isomorphic under the full symmetry group of the square. They have a horizontal and a vertical axis respectively.  No example has a diagonal axis, since this brings other symmetries (see A063524).
  o-o-o-o-o-o   o-o o-o o-o
  |         |   | | | | | |
  o o-o-o-o-o   o o o o o o
  | |           | | | | | |
  o o-o-o-o-o   o o o o o o
  |         |   | | | | | |
  o o-o-o-o-o   o o o o o o
  | |           | | | | | |
  o o-o-o o-o   o o-o o-o o
  |         |   |         |
  o-o-o-o-o-o   o-o-o-o-o-o
		

Links

• Ed Wynn, Enumeration of nonisomorphic Hamiltonian cycles on square grid graphs, arXiv:1402.0545 [math.CO], 2014.

Crossrefs

Cf. A209077, A227257, A237430.

Formula

a(n) = A227257(n) - A237430(n).