A316192 -id:A316192 - cp's OEIS frontend

A346132 Numbers m such that no self-avoiding walk that can make turns from the set 0, +-Pi/6, +-2Pi/6, +-3Pi/6, +-4Pi/6, +-5Pi/6, of length m + 1 fits into the smallest circle that can enclose a walk of length m.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 29, 30, 32, 33, 34, 35, 36, 37, 41

Offset: 1

Hugo Pfoertner and Markus Sigg, Jul 21 2021

Closed walks are allowed (see A316192). The only known closed walks that fit into a smaller enclosing circle than any open walk of the same length occur for lengths 3 and 5.

			See link for illustrations of terms corresponding to diameters D < 3.23.

Hugo Pfoertner, Examples of paths of maximum length.

Cf. A127399, A127400, A127401, A306182, A316192.

Cf. A346123-A346131 similar to this sequence with other sets of turning angles.

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.

cp's OEIS Frontend

A346132 Numbers m such that no self-avoiding walk that can make turns from the set 0, +-Pi/6, +-2Pi/6, +-3Pi/6, +-4Pi/6, +-5Pi/6, of length m + 1 fits into the smallest circle that can enclose a walk of length m.

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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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cp's OEIS Frontend

A346132 Numbers m such that no self-avoiding walk that can make turns from the set 0, +-Pi/6, +-2*Pi/6, +-3*Pi/6, +-4*Pi/6, +-5*Pi/6, of length m + 1 fits into the smallest circle that can enclose a walk of length m.

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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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A346132 Numbers m such that no self-avoiding walk that can make turns from the set 0, +-Pi/6, +-2Pi/6, +-3Pi/6, +-4Pi/6, +-5Pi/6, of length m + 1 fits into the smallest circle that can enclose a walk of length m.

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.