A209077 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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

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

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.

Sequence in context: A142415 A068987 A273047 * A141139 A141130 A157074

Adjacent sequences: A209074 A209075 A209076 * A209078 A209079 A209080