A237430 Number of nonisomorphic Hamiltonian cycles on 2n X 2n square grid of points with two-fold rotational symmetry (and no other symmetry).

0, 0, 5, 366, 129871, 174041330, 1343294003351, 41725919954578785, 7159149948562719664049, 5065741493544986113047994120

Offset: 1

Author

Ed Wynn, Feb 07 2014

Keywords

• nonn
• walk
• more

Examples

			An example of each isomorphism class for n=3.
  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   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   o o-o o-o o
  |         |   |         |   |         |   | | |     |   | | |     |
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Links

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

Crossrefs

Cf. A209077, A227257, A237429.

Formula

a(n) = A227257(n) - A237429(n).