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A209077
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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.
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14
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1, 2, 149, 580717, 58407763266, 134528361351329451, 7015812452562871283559623, 8235314565328229583744138065519908, 216740797236120772990979350241355889872437894, 127557553423846099192878370713500303677609606263171680998
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OFFSET
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1,2
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COMMENTS
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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
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REFERENCES
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Jon Wild, Posting to Sequence Fans Mailing List, Dec 10 2011.
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LINKS
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Table of n, a(n) for n=1..10.
Jon Wild, Illustration of a(3)
Ed Wynn, Enumeration of nonisomorphic Hamiltonian cycles on square grid graphs
Index entries for sequences related to graphs, Hamiltonian (2014), arXiv:1402.0545
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CROSSREFS
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Cf. A003763, A120443, A140519, A140521.
Sequence in context: A142415 A068987 A273047 * A141139 A141130 A157074
Adjacent sequences: A209074 A209075 A209076 * A209078 A209079 A209080
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KEYWORD
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nonn,changed
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AUTHOR
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N. J. A. Sloane, Mar 04 2012
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EXTENSIONS
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a(5)-a(10) from Ed Wynn, Feb 05 2014
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STATUS
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approved
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