A258206 -id:A258206 - cp's OEIS frontend

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, +-2Pi/3, +-5*Pi/6, not counting rotations and reflections as distinct.

Original entry on oeis.org

0, 0, 1, 3, 4, 22, 69, 418, 2210, 14024

Offset: 1

Hugo Pfoertner, Jul 07 2018

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

Contest Organizers, Al Zimmermann's Programming Contests - Snakes on a Plane, Fall 2006.
Hugo Pfoertner, Illustration of polygons of perimeter <= 8.

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

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

Original entry on oeis.org

0, 0, 0, 2, 2, 10, 15, 124, 352, 2378, 19405

Offset: 1

Hugo Pfoertner, Jul 07 2018

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

Contest Organizers, Al Zimmermann's Programming Contests - Snakes on a Plane, Fall 2006.
Hugo Pfoertner, Illustration of polygons of perimeter <= 9.

Cf. A258206, A266549, A284869, A306180, A316192, A316195, A316197, A316198, A316199, A316201.

A316201 Number of self-avoiding polygons with perimeter 2n and sides = 1 that have vertex angles from the set +-Pi/11, +-3Pi/11, +-5Pi/11, +-7Pi/11, +-9*Pi/11, not counting rotations and reflections as distinct.

Original entry on oeis.org

0, 0, 8, 19, 720, 10578

Offset: 1

Hugo Pfoertner, Jul 07 2018

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

Contest Organizers, Al Zimmermann's Programming Contests - Snakes on a Plane, Fall 2006.
Hugo Pfoertner, Illustration of polygons of perimeter <= 10.

Cf. A258206, A266549, A284869, A306181, A316192, A316195, A316197, A316198, A316199, A316200.

A323134 Number of polygons made of uncrossed knight's paths of length 2*n on an infinite board.

Original entry on oeis.org

0, 3, 13, 178, 3031, 64866

Offset: 1

Hugo Pfoertner, Jan 05 2019

			See Pfoertner link.

Hugo Pfoertner, Illustrations of uncrossed Knight's path polygons, (2019).

Cf. A003192, A157416, A258206, A266549, A284869, A316198.

A316193 Number of symmetric self-avoiding polygons on honeycomb net with perimeter 2*n, not counting rotations and reflections as distinct.

Original entry on oeis.org

0, 0, 1, 0, 1, 1, 3, 1, 10, 5

Offset: 1

Hugo Pfoertner, Jul 03 2018

The sequence includes polygons of 2-fold, i.e., mirror or rotational, and higher (order >= 3) symmetry.

Hugo Pfoertner, Illustration of polygons of perimeter <= 20.

Cf. A258206, A316194, A316196.

cp's OEIS Frontend

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, +-2Pi/3, +-5*Pi/6, not counting rotations and reflections as distinct.

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

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A316201 Number of self-avoiding polygons with perimeter 2n and sides = 1 that have vertex angles from the set +-Pi/11, +-3Pi/11, +-5Pi/11, +-7Pi/11, +-9*Pi/11, not counting rotations and reflections as distinct.

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A323134 Number of polygons made of uncrossed knight's paths of length 2*n on an infinite board.

Views

Author

Keywords

Examples

Links

Crossrefs

A316193 Number of symmetric self-avoiding polygons on honeycomb net with perimeter 2*n, not counting rotations and reflections as distinct.

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Author

Keywords

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cp's OEIS Frontend

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.

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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.

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A316201 Number of self-avoiding polygons with perimeter 2*n and sides = 1 that have vertex angles from the set +-Pi/11, +-3*Pi/11, +-5*Pi/11, +-7*Pi/11, +-9*Pi/11, not counting rotations and reflections as distinct.

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Author

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A323134 Number of polygons made of uncrossed knight's paths of length 2*n on an infinite board.

Views

Author

Keywords

Examples

Links

Crossrefs

A316193 Number of symmetric self-avoiding polygons on honeycomb net with perimeter 2*n, not counting rotations and reflections as distinct.

Views

Author

Keywords

Comments

Links

Crossrefs

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, +-2Pi/3, +-5*Pi/6, not counting rotations and reflections as distinct.

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

A316201 Number of self-avoiding polygons with perimeter 2n and sides = 1 that have vertex angles from the set +-Pi/11, +-3Pi/11, +-5Pi/11, +-7Pi/11, +-9*Pi/11, not counting rotations and reflections as distinct.