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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. 15
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
Mathoverflow, Counting Hamiltonian cycles in n x n square grid, question asked by Joseph O'Rourke, Jul 25 2018.
Ed Wynn, Enumeration of nonisomorphic Hamiltonian cycles on square grid graphs, arXiv:1402.0545 [math.CO], 3 Feb 2014.
CROSSREFS
Sequence in context: A142415 A068987 A273047 * A141139 A141130 A157074
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 04 2012
EXTENSIONS
a(5)-a(10) from Ed Wynn, Feb 05 2014
STATUS
approved

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Last modified December 4 11:15 EST 2023. Contains 367560 sequences. (Running on oeis4.)