A237431 Number of nonisomorphic Hamiltonian cycles on 2n X 2n square grid of points with exactly two axes of reflective symmetry.

0, 1, 3, 20, 244, 6891, 378813, 47917598, 12118420172, 6998287399637

Offset

1,3

Links

Table of n, a(n) for n=1..10.

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

Example

Examples of 2 of the 3 classes for n=3. Note that all examples also have two-fold (but not four-fold) rotational symmetry.
  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

Crossrefs

Cf. A209077, A227005, A237432.

Sequence in context: A218374 A219541 A200527 * A237652 A256018 A227469

Adjacent sequences: A237428 A237429 A237430 * A237432 A237433 A237434

Keyword

nonn,walk,more

Author

Ed Wynn, Feb 07 2014

Status

approved