A209077 Number of Hamiltonian circuits (or self-avoiding rook's tours) on a 2n X 2n grid reduced for symmetry, i.e., where rotations and reflections are not counted as distinct.

1, 2, 149, 580717, 58407763266, 134528361351329451, 7015812452562871283559623, 8235314565328229583744138065519908, 216740797236120772990979350241355889872437894, 127557553423846099192878370713500303677609606263171680998

Offset: 1

Author

N. J. A. Sloane, Mar 04 2012

Keywords

• nonn

Comments

Christopher Hunt Gribble confirms a(3), and reports that there are 121 figures with group of order 1, 24 with group of order 2, and 4 with group of order 4. Then 121*(8/1) + 24*(8/2) + 4*(8/4) = 1072 = A003763(3), 121 + 24 + 4 = 149 = a(3). - N. J. A. Sloane, Feb 22 2013

References

• Jon Wild, Posting to Sequence Fans Mailing List, Dec 10 2011.

Links

• Mathoverflow, Counting Hamiltonian cycles in n x n square grid, question asked by Joseph O'Rourke, Jul 25 2018.
• Jon Wild, Illustration of a(3)
• Ed Wynn, Enumeration of nonisomorphic Hamiltonian cycles on square grid graphs, arXiv:1402.0545 [math.CO], 3 Feb 2014.
• Index entries for sequences related to graphs, Hamiltonian

Crossrefs

Cf. A003763, A120443, A140519, A140521.

Extensions

a(5)-a(10) from Ed Wynn, Feb 05 2014