A375299 Number of longest winning paths in n X n Hex.

1, 3, 1, 4, 23, 51, 20, 115, 5568, 12, 3521, 40, 1058, 2104, 668, 7540, 1298, 83648, 16631833, 70630

Offset

1,2

Comments

A winning path is a set of cells connecting the top edge to the bottom edge, minimal with respect to inclusion.

Links

Table of n, a(n) for n=1..20.

Peter Selinger, Longest winning paths in Hex, arXiv:2408.05601 [math.CO], 2024.

Example

For n = 4, the longest winning path has length 8, and the a(4) = 4 winning paths of length 8 are
   ========     ========     ========     ========
    X . . .      . X . .      X . . .      . X . .
     X . X X      X . X X      X . X X      X . X X
      X X . X      X X . X      X X . X      X X . X
       . . . X      . . . X      . . X .      . . X .
       ========     ========     ========     ========

Crossrefs

Length of longest path is A375298.

Cf. A357516.

Sequence in context: A112668 A016734 A272473 * A362270 A125846 A318382

Adjacent sequences: A375296 A375297 A375298 * A375300 A375301 A375302

Keyword

nonn,more

Author

Peter Selinger, Aug 13 2024

Status

approved