A384037 Number of canonical representative paths with length A383980(n) touching all cells in an n X n grid.

1, 1, 1, 1, 1, 1, 3, 6, 3, 9, 42

Offset

0,7

Comments

"Path" means any continuous curve between two points.

"Touch" includes vertices and edges of grid cells.

"Canonical representative" is a single path chosen from its orbit under the Euclidean group E(2).

a(3k+2) >= 8 once A383980(3k+2) is proven, where k >= 3.

a(12) >= 52 once A383980(12) is proven.

Links

Table of n, a(n) for n=0..10.

Zoe Allen, Touching as many grid squares as possible with path of given length, Math StackExchange, Feb 18 2025.

Tamás Fülöp, Minimal path to touch every square's area in an n by n grid, Math StackExchange, Feb 18 2025.

Tamás Fülöp, C++ program, GitHub repository, Apr 3 2025.

Tamás Fülöp, All paths for a(3) - a(10), Apr 23 2025.

Tamás Fülöp, Probably all paths for a(11) - a(12), Oct 20 2025.

Crossrefs

Cf. A383980.

Sequence in context: A260303 A055373 A263333 * A328371 A134440 A129529

Adjacent sequences: A384034 A384035 A384036 * A384038 A384039 A384040

Keyword

nonn,more,hard,walk

Author

Tamás Fülöp, May 17 2025

Status

approved