A316198 -id:A316198 - cp's OEIS frontend

A316199 Number of self-avoiding polygons with perimeter 2n and sides = 1 that have vertex angles from the set +-Pi/9, +-3Pi/9, +-5Pi/9, +-7Pi/9, not counting rotations and reflections as distinct.

Original entry on oeis.org

0, 0, 8, 17, 472, 7042

Offset: 1

Hugo Pfoertner, Jul 04 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 <= 12.

Cf. A306179, A316195, A316197, A316198.

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.

A346128 Numbers m such that no self-avoiding walk that can make turns from the set 0, +-Pi/4, +-Pi/2, +-3*Pi/4, of length m + 1 fits into the smallest circle that can enclose a walk of length m.

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 9, 11, 12, 13, 15, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 37, 38

Offset: 1

Hugo Pfoertner and Markus Sigg, Aug 01 2021

Closed walks (see A316198) are allowed, but except for the closed square-shaped walk of length 4 that fits into the same smallest enclosing circle as the smallest open walk of this length, no other closed walk that fits into a smaller enclosing circle than any open walk of the same length is known.

			See link for illustrations of terms corresponding to diameters D < 3.83.

Hugo Pfoertner, Examples of paths of maximum length.

Cf. A127399, A127400, A127401, A306178, A316198.

Cf. A346123-A346132 similar to this sequence with other sets of turning angles.

cp's OEIS Frontend

A316199 Number of self-avoiding polygons with perimeter 2*n and sides = 1 that have vertex angles from the set +-Pi/9, +-3*Pi/9, +-5*Pi/9, +-7*Pi/9, not counting rotations and reflections as distinct.

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

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Author

Keywords

Examples

Links

Crossrefs

A346128 Numbers m such that no self-avoiding walk that can make turns from the set 0, +-Pi/4, +-Pi/2, +-3*Pi/4, of length m + 1 fits into the smallest circle that can enclose a walk of length m.

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A316199 Number of self-avoiding polygons with perimeter 2n and sides = 1 that have vertex angles from the set +-Pi/9, +-3Pi/9, +-5Pi/9, +-7Pi/9, not counting rotations and reflections as distinct.

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.