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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.

%I A266549 #39 May 25 2019 06:10:32
%S A266549 0,1,1,3,6,25,86,414,1975,10479,56572,316577,1800363,10419605,
%T A266549 61061169,361978851
%N 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.
%C A266549 Differs from A057730 beginning at n = 8, since that sequence includes polyominoes with holes.
%H A266549 Joerg Arndt, <a href="/A266549/a266549.pdf">All a(6)=25 walks of length 12</a>, 2018
%H A266549 Brendan Owen, <a href="http://www.recmath.com/PolyPages/PolyPages/index.htm?Isopolyos.html">Isoperimetrical Polyominoes</a>, part of Andrew I. Clarke's Poly Pages.
%H A266549 Hugo Pfoertner, <a href="https://oeis.org/plot2a?name1=A002931&amp;name2=A266549&amp;tform1=untransformed&amp;tform2=untransformed&amp;shift=0&amp;radiop1=ratio&amp;drawpoints=true">Illustration of ratio A002931(n)/a(n) using Plot2</a>, showing apparent limit of 8.
%H A266549 Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a216194.htm">Illustration of polygons of perimeter <= 16</a>.
%Y A266549 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
%Y A266549 Cf. A010566, A037245 (open self-avoiding walks), A316194.
%K A266549 nonn,hard,more,nice
%O A266549 1,4
%A A266549 _Luca Petrone_, Dec 31 2015
%E A266549 a(11)-a(16) from _Joerg Arndt_, Jan 25 2018