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 A037245 Number of unrooted self-avoiding walks of n steps on square lattice. 16
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 LINKS Bert Dobbelaere, Table of n, a(n) for n = 1..60 Joerg Arndt, The a(6) = 56 walks of length 6, 2018 (pdf, 2 pages). Brian Hayes, How to avoid yourself, American Scientist 86 (1998) 314-319. Ed Pegg, Jr., Illustrations of polyforms Eric Weisstein's World of Mathematics, Polyedge FORMULA a(n) = (A001411(n) + A323188(n) + A323189(n) + 4) / 16. - Bert Dobbelaere, Jan 07 2019 CROSSREFS Asymptotically approaches (1/16) * A001411. Cf. A266549 (closed self-avoiding walks). Cf. A323188, A323189 (program). Sequence in context: A091561 A025265 A152225 * A244886 A143017 A307575 Adjacent sequences:  A037242 A037243 A037244 * A037246 A037247 A037248 KEYWORD nonn,walk,hard,nice AUTHOR EXTENSIONS a(25)-a(27) from Luca Petrone, Dec 20 2015 More terms using formula by Bert Dobbelaere, Jan 07 2019 STATUS approved

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Last modified May 31 15:41 EDT 2020. Contains 334748 sequences. (Running on oeis4.)