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.

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

Offset: 1

Author

Luca Petrone, Dec 31 2015

Keywords

• nonn
• hard
• more
• nice

Comments

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

Links

• 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 self-avoiding walks), A316194.

Extensions

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