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.

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

1,2

Comments

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.

Links

Table of n, a(n) for n=1..34.

Hugo Pfoertner, Examples of paths of maximum length.

Example

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

Crossrefs

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

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

Sequence in context: A110303 A347520 A180493 * A320249 A309066 A084981

Adjacent sequences: A346129 A346130 A346131 * A346133 A346134 A346135

Keyword

nonn,more

Author

Hugo Pfoertner and Markus Sigg, Jul 21 2021

Status

approved