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

Author

Hugo Pfoertner and Markus Sigg, Jul 31 2021

Keywords

• nonn
• walk
• more

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.

Examples

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

Links

• Hugo Pfoertner, Examples of paths of maximum length.

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).