cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

A052436 Number of canonical polygons of n sides.

Original entry on oeis.org

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

Views

Author

Eric W. Weisstein

Keywords

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

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

A307387 a(n) is the number of canonical polygons with 4n alternating straight and diagonal edges.

Original entry on oeis.org

1, 9, 191, 8049, 418184, 24283599
Offset: 1

Views

Author

Lars Blomberg, Apr 18 2019

Keywords

Links

Crossrefs

Cf. A052436, A307387, A307391, A307426, A307454, A307455, A307456, A307519.

A307426 a(n) is the number of canonical polygons with 4n edges having 4-fold rotational symmetry.

Original entry on oeis.org

2, 2, 7, 22, 79, 289, 1145, 4655, 19314, 81242, 345785, 1484065, 6414999, 27895652
Offset: 1

Views

Author

Lars Blomberg, Apr 08 2019

Keywords

Links

Crossrefs

Cf. A052436, A307387, A307391, A307426, A307454, A307455, A307456, A307519.

A307454 a(n) is the number of canonical polygons with 2n edges having 2-fold rotational symmetry.

Original entry on oeis.org

1, 3, 9, 33, 123, 513, 2077, 8759, 37184, 159508, 688446, 2993451, 13082724
Offset: 2

Views

Author

Lars Blomberg, Apr 09 2019

Keywords

Links

Crossrefs

Cf. A052436, A307387, A307391, A307426, A307454, A307455, A307456, A307519.

A307455 a(n) is the number of canonical polygons with n edges having exactly 1 line of reflection symmetry.

Original entry on oeis.org

1, 0, 2, 2, 1, 7, 6, 28, 27, 107, 94, 488, 386, 2066, 1630, 8392, 6780, 34962, 28056, 147356, 117621, 622558, 500525, 2657666, 2149374
Offset: 3

Views

Author

Lars Blomberg, Apr 09 2019

Keywords

Comments

For n even, the symmetry line passes through two opposite vertices, or cuts through two opposite edges. For n odd it passes through one vertex and cuts the opposite edge. That explains the even-odd irregularity in the sequence.

Links

Crossrefs

Cf. A052436, A307387, A307391, A307426, A307454, A307455, A307456, A307519.

A307456 a(n) is the number of canonical polygons with 2n edges having exactly 2 lines of reflection symmetry.

Original entry on oeis.org

2, 2, 1, 4, 11, 24, 47, 99, 211, 437, 909, 1925
Offset: 2

Views

Author

Lars Blomberg, Apr 09 2019

Keywords

Links

Crossrefs

Cf. A052436, A307387, A307391, A307426, A307454, A307455, A307456, A307519.

A307519 a(n) is the number of canonical polygons with 4n edges having exactly 4 lines of reflection symmetry.

Original entry on oeis.org

2, 1, 2, 6, 10, 17, 34, 72, 142, 288, 585, 1195, 2413, 4898
Offset: 1

Views

Author

Lars Blomberg, Apr 12 2019

Keywords

Links

Crossrefs

Cf. A052436, A307387, A307391, A307426, A307454, A307455, A307456, A307519.
Showing 1-7 of 7 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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