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

1,4

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 self-avoiding walks), A316194.

Sequence in context: A148662 A148663 A361288 * A057730 A350752 A355967

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