A316195 Number of self-avoiding polygons with perimeter 2*n and sides = 1 that have vertex angles from the set +-Pi/5, +-3*Pi/5, not counting rotations and reflections as distinct.

0, 0, 2, 1, 18, 45, 441, 2681, 23833

Offset

1,3

Comments

Holes are excluded, i.e., the boundary path may nowhere touch or intersect itself.

From Anton Pirogov, Jun 17 2026: (Start)

Also number of free simple matchstick polygons with perimeter 2*n on the cyclotomic ring Z[zeta_10] whose vertex turning angles are all odd multiples of Pi/5.

The new terms a(8)-a(9) were obtained as a sub-count of the enumeration of free simple matchstick polygons on Z[zeta_10] using the tilezz library. (End)

Links

Table of n, a(n) for n=1..9.

Contest Organizers, Al Zimmermann's Programming Contests - Snakes on a Plane, Fall 2006.

Hugo Pfoertner, Illustration of polygons of perimeter <= 14.

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. A306175, A258206, A266549, A284869.

Sequence in context: A300956 A089014 A063426 * A266010 A349960 A181870

Adjacent sequences: A316192 A316193 A316194 * A316196 A316197 A316198

Keyword

nonn,walk,more,changed

Author

Hugo Pfoertner, Jun 26 2018

Extensions

a(8)-a(9) from Anton Pirogov, Jun 17 2026

Status

approved