A316196 Number of symmetric self-avoiding polygons on hexagonal lattice with perimeter n, not counting rotations and reflections as distinct.

0, 0, 1, 1, 1, 4, 3, 10, 9, 36, 27, 129, 90, 449, 331, 1617, 1115, 6019, 4039, 22049, 15107, 82677, 55237, 313033

Offset

1,6

Comments

From Anton Pirogov, Jun 17 2026: (Start)

Also number of symmetric simple matchstick polygons on the cyclotomic ring Z[zeta_6].

Terms a(16)-a(24) were obtained as a sub-count of the free enumeration of simple matchstick polygons on Z[zeta_6] using the tilezz library. (End)

Links

Table of n, a(n) for n=1..24.

Hugo Pfoertner, Illustration of polygons of perimeter <= 11.

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. A036418, A284869, A306176.

Sequence in context: A325997 A075563 A299325 * A081617 A103252 A065763

Adjacent sequences: A316193 A316194 A316195 * A316197 A316198 A316199

Keyword

nonn,walk,more,changed

Author

Hugo Pfoertner, Jun 27 2018

Extensions

a(16)-a(24) from Anton Pirogov, Jun 17 2026

Status

approved