A384083 Number of paths with length A383980(n) touching all cells in an n X n grid.

1, 4, 4, 8, 16, 48, 24, 64, 336

Offset

2,2

Comments

"Path" means any continuous curve between two points.

"Touch" includes vertices and edges of grid cells.

Links

Table of n, a(n) for n=2..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 with n = 3 - 10, Apr 23 2025.

Formula

a(0) = 1.

a(1) = oo.

a(n) = 8 * A384037(n) - 4*k, where n >= 3 and k = the number of symmetric paths.

Crossrefs

Cf. A383980, A384037.

Sequence in context: A261212 A112435 A232508 * A028610 A019171 A038551

Adjacent sequences: A384080 A384081 A384082 * A384084 A384085 A384086

Keyword

nonn,more,hard,walk

Author

Tamás Fülöp, May 18 2025

Status

approved