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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 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 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.)