

A010566


Number of 2nstep 2dimensional closed selfavoiding paths on square lattice.
(Formerly N1903)


17



0, 8, 24, 112, 560, 2976, 16464, 94016, 549648, 3273040, 19781168, 121020960, 748039552, 4664263744, 29303071680, 185307690240, 1178635456752, 7535046744864, 48392012257184, 312061600211680, 2019822009608592, 13117263660884768, 85447982919036736
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OFFSET

1,2


COMMENTS

a(n) = 4n*A002931(n). There are (2n) choices for the starting point and 2 choices for the orientation, in order to produce selfavoiding closed paths from a polygon of perimeter 2n.  Philippe Flajolet, Nov 22 2003


REFERENCES

B. D. Hughes, Random Walks and Random Environments, Oxford 1995, vol. 1, p. 461.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).


LINKS



MATHEMATICA

A002931 = Cases[Import["https://oeis.org/A002931/b002931.txt", "Table"], {_, _}][[All, 2]]; a[n_] := 4n A002931[[n]];


PROG

(Python)
def num_continuations(path, dist):
(x, y) = path[1]
next = [(x+1, y), (x1, y), (x, y+1), (x, y1)]
if dist == 1:
return (0, 0) in next
else:
return sum(num_continuations(path + [c], dist  1) for c in next if c not in path)
return 4 * num_continuations([(0, 0), (1, 0)], 2 * n  1) if n >= 2 else 0


CROSSREFS



KEYWORD

nonn,nice,walk


AUTHOR



STATUS

approved



