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A037245
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Number of unrooted self-avoiding walks of n steps on square lattice.
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17
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1, 2, 4, 9, 22, 56, 147, 388, 1047, 2806, 7600, 20437, 55313, 148752, 401629, 1078746, 2905751, 7793632, 20949045, 56112530, 150561752, 402802376, 1079193821, 2884195424, 7717665979, 20607171273, 55082560423, 146961482787, 392462843329, 1046373230168, 2792115083878
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OFFSET
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1,2
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COMMENTS
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Or, number of 2-sided polyedges with n cells. - Ed Pegg Jr, May 13 2009
A walk and its reflection (i.e., exchange start and end of walk, what Hayes calls a "retroreflection") are considered one and the same here. - Joerg Arndt, Jan 26 2018
With A001411 as main input and counting the symmetrical shapes separately, higher terms can be computed efficiently (see formula). - Bert Dobbelaere, Jan 07 2019
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LINKS
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Eric Weisstein's World of Mathematics, Polyedge
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FORMULA
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CROSSREFS
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Asymptotically approaches (1/16) * A001411.
Cf. A266549 (closed self-avoiding walks).
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KEYWORD
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nonn,walk,hard,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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