A316195 -id:A316195 - cp's OEIS frontend

A306175 Number of unrooted self-avoiding walks with n steps that can make turns from the set +-Pi/5, +-3*Pi/5.

1, 2, 6, 19, 66, 229, 831, 2991, 10859, 39173, 141631, 510079, 1835583, 6586932, 23614821, 84492315, 302014619, 1077860479, 3843695976, 13690026688

Offset: 1

Hugo Pfoertner, Jun 23 2018

The turning angles are those of the regular pentagon, with one vertex corresponding to the forbidden U-turn. The path may neither intersect nor touch itself anywhere.

Contest Organizers, Al Zimmermann's Programming Contests - Snakes on a Plane, Fall 2006.
Hugo Pfoertner, Illustration of walks of lengths <= 5.

Cf. A266925, A037245, A151541, A306177, A306178, A306179, A306180, A306181, A306182, A316195.

a(7)-a(9) from Hugo Pfoertner, Dec 23 2018

a(10)-a(20) from Bert Dobbelaere, May 15 2025

A316197 Number of self-avoiding polygons with perimeter 2n and sides = 1 that have vertex angles from the set +-Pi/7, +-3Pi/7, +-5*Pi/7, not counting rotations and reflections as distinct.

Original entry on oeis.org

0, 0, 3, 4, 83, 533, 8329

Offset: 1

Hugo Pfoertner, Jun 28 2018

Contest Organizers, Al Zimmermann's Programming Contests - Snakes on a Plane, Fall 2006.
Hugo Pfoertner, Illustration of polygons of perimeter <= 12.

Cf. A306177, A258206, A266549, A284869, A316195.

A316198 Number of self-avoiding polygons with perimeter 2n and sides = 1 that have vertex angles from the set 0, +-Pi/4, +-Pi/2, +-3Pi/4, not counting rotations and reflections as distinct.

Original entry on oeis.org

0, 2, 6, 59, 695, 12198

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 <= 10.

Cf. A306178, A316195, A316197.

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.

A346125 Numbers m such that no self-avoiding walk that can make turns from the set +-Pi/5, +-3*Pi/5, of length m + 1 fits into the smallest circle that can enclose a walk of length m.

Original entry on oeis.org

1, 3, 5, 6, 7, 9, 11, 12, 14, 15, 17, 19, 25, 27, 28, 31, 32, 33, 34, 35, 37, 38, 39, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 57, 59

Offset: 1

Hugo Pfoertner and Markus Sigg, Jul 31 2021

Although closed walks (see A316195) would be allowed, no 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 < 5.114.

Hugo Pfoertner, Examples of paths of maximum length.

Cf. A127399, A127400, A127401, A306175, A316195.

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

cp's OEIS Frontend

A306175 Number of unrooted self-avoiding walks with n steps that can make turns from the set +-Pi/5, +-3*Pi/5.

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A316197 Number of self-avoiding polygons with perimeter 2*n and sides = 1 that have vertex angles from the set +-Pi/7, +-3*Pi/7, +-5*Pi/7, not counting rotations and reflections as distinct.

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A316198 Number of self-avoiding polygons with perimeter 2*n and sides = 1 that have vertex angles from the set 0, +-Pi/4, +-Pi/2, +-3*Pi/4, not counting rotations and reflections as distinct.

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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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A346125 Numbers m such that no self-avoiding walk that can make turns from the set +-Pi/5, +-3*Pi/5, of length m + 1 fits into the smallest circle that can enclose a walk of length m.

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A316197 Number of self-avoiding polygons with perimeter 2n and sides = 1 that have vertex angles from the set +-Pi/7, +-3Pi/7, +-5*Pi/7, not counting rotations and reflections as distinct.

A316198 Number of self-avoiding polygons with perimeter 2n and sides = 1 that have vertex angles from the set 0, +-Pi/4, +-Pi/2, +-3Pi/4, not counting rotations and reflections as distinct.

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.