A237432 Number of nonisomorphic Hamiltonian cycles on (4n-2) X (4n-2) square grid of points with four-fold rotational symmetry (and no other symmetry).

0, 1, 102, 255359, 15504309761, 21955745395591600, 712319733455900182066337, 524246290066954425217045809870657

Offset: 1

Author

Ed Wynn, Feb 07 2014

Keywords

• nonn
• walk
• hard
• more

Comments

For square grids of m X m points, there are solutions only for m = (4n-2).

Examples

			The two cycles counted as a single class for n=2. These are isomorphic (here meaning isomorphic under the full symmetry group of the square), since each is a reflection of the other.
  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, A227005, A237431.

Formula

a(n) = A238819(n-1) / 2 for n > 1. - Andrew Howroyd, Apr 06 2016

Extensions

a(6)-a(8) from Andrew Howroyd, Apr 06 2016