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A266549
Number of 2n-step 2-dimensional closed self-avoiding paths on square lattice, reduced for symmetry, i.e., where rotations and reflections are not counted as distinct.
16
0, 1, 1, 3, 6, 25, 86, 414, 1975, 10479, 56572, 316577, 1800363, 10419605, 61061169, 361978851
OFFSET
1,4
COMMENTS
Differs from A057730 beginning at n = 8, since that sequence includes polyominoes with holes.
LINKS
Brendan Owen, Isoperimetrical Polyominoes, part of Andrew I. Clarke's Poly Pages.
Hugo Pfoertner, Illustration of ratio A002931(n)/a(n) using Plot2, showing apparent limit of 8.
CROSSREFS
Apparently lim A002931(n)/a(n) = 8 for increasing n, accounting for (in most cases) 4 rotations times two flips. - Joerg Arndt, Hugo Pfoertner, Jul 09 2018
Cf. A010566, A037245 (open self-avoiding walks), A316194.
Sequence in context: A148662 A148663 A361288 * A057730 A350752 A355967
KEYWORD
nonn,hard,more,nice
AUTHOR
Luca Petrone, Dec 31 2015
EXTENSIONS
a(11)-a(16) from Joerg Arndt, Jan 25 2018
STATUS
approved