A316200 Number of self-avoiding polygons with perimeter n and sides = 1 that have vertex angles from the set 0, +-Pi/5, +-2*Pi/5, +-3*Pi/5, +-4*Pi/5, not counting rotations and reflections as distinct.

0, 0, 0, 2, 2, 10, 15, 124, 352, 2378, 9883, 63556, 313726, 1970548, 10693249, 66850339, 384547086, 2411380580

Offset

1,4

Comments

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

Also number of free simple matchstick polygons with perimeter n on the cyclotomic ring Z[zeta_10]. - Anton Pirogov, Jun 22 2026

Links

Table of n, a(n) for n=1..18.

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

Hugo Pfoertner, Illustration of polygons of perimeter <= 9.

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, A306180, A316192, A316195, A316197, A316198, A316199, A316201.

Sequence in context: A003609 A366131 A307538 * A360636 A380119 A362745

Adjacent sequences: A316197 A316198 A316199 * A316201 A316202 A316203

Keyword

nonn,walk,more,changed

Author

Hugo Pfoertner, Jul 07 2018

Extensions

a(11) corrected and a(12)-a(18) added by Anton Pirogov, Jun 22 2026

Status

approved