A346126 Numbers m such that no self-avoiding walk of length m + 1 on the hexagonal lattice fits into the smallest circle that can enclose a walk of length m.

1, 3, 4, 7, 8, 9, 10, 12, 14, 15, 16, 19, 20, 22, 23, 24, 25, 27, 31, 32, 34, 37, 38, 39, 40, 42, 43, 44, 45, 48, 49, 55, 56, 57, 58, 60, 61

Offset

1,2

Comments

Open and closed walks are allowed. It is conjectured that all optimal paths are closed except for the trivial path of length 1. See the related conjecture in A122226.

Links

Table of n, a(n) for n=1..37.

Hugo Pfoertner, Examples of paths of maximum length.

Example

See link for illustrations of terms corresponding to diameters D <= 8.

Crossrefs

Cf. A122226, A125852, A127399, A127400, A127401, A151541, A284869, A306176, A316196.

Cf. A346123 (similar to this sequence, but for honeycomb net), A346124 (ditto for square lattice).

Cf. A346125, A346127-A346132 (similar to this sequence, but with other sets of turning angles).

Sequence in context: A198330 A232779 A086986 * A057811 A284489 A026343

Adjacent sequences: A346123 A346124 A346125 * A346127 A346128 A346129

Keyword

nonn,walk,more

Author

Hugo Pfoertner and Markus Sigg, Jul 31 2021

Status

approved