A316194 Number of symmetric self-avoiding polygons on square lattice with perimeter 2*n, not counting rotations and reflections as distinct.

0, 1, 1, 3, 4, 16, 23, 87, 128, 485, 739, 2798, 4352, 16507, 26132, 99302

Offset

1,4

Comments

The sequence includes polygons of 2-fold, i.e., mirror or rotational, and higher (order >= 4) symmetry.

From Anton Pirogov, Jun 17 2026: (Start)

Also number of symmetric simple matchstick polygons on the cyclotomic ring Z[zeta_4].

Terms a(9)-a(16) (perimeters 18..32) were obtained as a sub-count of the free enumeration of simple matchstick polygons on Z[zeta_4] using the tilezz library. (End)

Links

Table of n, a(n) for n=1..16.

Hugo Pfoertner, Illustration of polygons of perimeter <= 16.

Anton Pirogov, tilezz - exact cyclotomic geometry library including a polygon enumerator.

Anton Pirogov, Rat Explorer - interactive database of cyclotomic matchstick polygons.

Anton Pirogov, RatDB datasets - reproducible datasets containing the enumerated polygons.

Crossrefs

Cf. A002931, A266549, A316196, A323188, A323189.

Sequence in context: A047164 A304988 A108653 * A123773 A290433 A251582

Adjacent sequences: A316191 A316192 A316193 * A316195 A316196 A316197

Keyword

nonn,walk,more,changed

Author

Hugo Pfoertner, Jun 27 2018

Extensions

a(9)-a(16) from Anton Pirogov, Jun 17 2026

Status

approved