

A266549


Number of 2nstep 2dimensional closed selfavoiding paths on square lattice, reduced for symmetry, i.e., where rotations and reflections are not counted as distinct.


12



0, 1, 1, 3, 6, 25, 86, 414, 1975, 10479, 56572, 316577, 1800363, 10419605, 61061169, 361978851
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OFFSET

1,4


COMMENTS

Differs from A057730 beginning at n = 8, since that sequence includes polyominoes with holes.


LINKS

Table of n, a(n) for n=1..16.
Joerg Arndt, All a(6)=25 walks of length 12, 2018
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.
Hugo Pfoertner, Illustration of polygons of perimeter <= 16.


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 selfavoiding walks), A316194.
Sequence in context: A148661 A148662 A148663 * A057730 A074432 A212650
Adjacent sequences: A266546 A266547 A266548 * A266550 A266551 A266552


KEYWORD

nonn,hard,more,nice


AUTHOR

Luca Petrone, Dec 31 2015


EXTENSIONS

a(11)a(16) from Joerg Arndt, Jan 25 2018


STATUS

approved



