A316192 Number of self-avoiding polygons with perimeter n and sides = 1 that have vertex angles from the set 0, +-Pi/6, +-*Pi/3, +-Pi/2, +-2*Pi/3, +-5*Pi/6, not counting rotations and reflections as distinct.

0, 0, 1, 3, 4, 22, 69, 418, 2210, 14024, 89075, 597581, 4076855, 28499301, 202464580, 1460982297

Offset

1,4

Comments

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

From Anton Pirogov, Jun 21 2026: (Start)

Also number of free simple matchstick polygons with perimeter n on the cyclotomic ring Z[zeta_12].

The values a(11)-a(16) were determined by enumeration with the tilezz library using exact cyclotomic integer arithmetic over Z[zeta_12]. (End)

Links

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

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

Hugo Pfoertner, Illustration of polygons of perimeter <= 8.

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. A258206, A266549, A284869, A306182, A316195, A316197, A316198, A316199, A316200, A316201.

Sequence in context: A057791 A167452 A375958 * A122660 A163744 A221643

Adjacent sequences: A316189 A316190 A316191 * A316193 A316194 A316195

Keyword

nonn,walk,more,changed

Author

Hugo Pfoertner, Jul 07 2018

Extensions

a(11)-a(16) from Anton Pirogov, Jun 21 2026

Status

approved