A052436 Number of canonical polygons of n sides.

0, 0, 1, 3, 3, 9, 13, 52, 140, 501, 1763, 6785, 25571, 99907, 392230, 1564989, 6297892, 25601641, 104846143, 432629580

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• more

Comments

Canonical polygons are those drawn on a square unit lattice, with all sides equal to 1 or sqrt(2), without crossing sides or double vertices. Rotations and reflections do not generate different canonical polygons. There are exactly 8 convex canonical polygons: 1 with n=3, 3 with n=4, 1 with n=5, 2 with n=6, 1 with n=8. - Ronald Kyrmse, Apr 02 2025

Links

• Lars Blomberg, Examples of Canonical Polygons for n = 3..20
• Sean A. Irvine, Java program (github)
• Ronald Kyrmse, Canonical Polygons.
• Eric Weisstein's World of Mathematics, Binomial Coefficient.
• Eric Weisstein's World of Mathematics, Canonical Polygon.

Crossrefs

Cf. A307387, A307391, A307426, A307454, A307455, A307456, A307519.

Extensions

Corrected and extended by Keith Schneider (schneidk(AT)email.unc.edu), Oct 25 2007

Offset changed to 1 and a(14)-a(18) from Lars Blomberg, Feb 18 2019

a(19)-a(20) from Lars Blomberg, Apr 23 2019

a(12) corrected by Sean A. Irvine, Nov 12 2021