A122224 Length of the longest possible self avoiding path on the 2-dimensional square lattice such that the path fits into a circle of diameter n.

1, 4, 8, 14, 21, 32, 40

Offset

2,2

Comments

The path may be open or closed. For larger n several solutions with the same number of segments exist.

It is conjectured that a(n) >= A123690(n)-1, i.e., that it is always possible to find a path visiting all grid points covered by a circle, irrespective of the position of its center. - Hugo Pfoertner, Mar 02 2018

Links

Table of n, a(n) for n=2..8.

Hugo Pfoertner, Examples of compact self avoiding paths on a square lattice.

Crossrefs

Cf. A122223, A122226, A123690.

Sequence in context: A344012 A027924 A006578 * A183955 A299896 A312700

Adjacent sequences: A122221 A122222 A122223 * A122225 A122226 A122227

Keyword

hard,more,nonn

Author

Hugo Pfoertner, Sep 25 2006

Status

approved