A380598 Number of moves required for the first player to win Harary's generalized tic-tac-toe (or animal tic-tac-toe) for the free polyomino with binary code A246521(n+1) on a square board of side length A380597(n), or 0 if it is a draw for all board sizes.

1, 2, 3, 3, 4, 0, 4, 5, 8, 0, 0, 0, 10, 9, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,2

Comments

The only unknown value is a(45), corresponding to the "long N" hexomino. It has been suggested that a(45) = 13 and A380597(45) = 15.

Can be read as an irregular triangle, whose n-th row contains A000105(n) terms, n >= 1.

Links

Table of n, a(n) for n=1..44.

Brady Haran and Sophie Maclean, Snakey Hexomino, Numberphile video, 2025.

Wikipedia, Harary's generalized tic-tac-toe.

James Yolkowski, Tic-tac-toe.

Index entries for sequences related to polyominoes.

Index entries for sequences related to tic-tac-toe.

Formula

a(n) = 0 for all n >= 46.

Example

As an irregular triangle:
  1;
  2;
  3, 3;
  4, 0, 4,  5, 8;
  0, 0, 0, 10, 9, 6, 0, 0, 0, 0, 0, 0;
  ...
For n = 9, the polyomino with binary code A246521(9+1) = 75 is the straight tetromino. Generalized tic-tac-toe for this polyomino (i.e., 4 cells in a row, horizontally or vertically, are needed to win) is a draw for square boards of side length less than 7, but on a 7 X 7 board the first player can force a win in at most 8 moves, so a(9) = 8.

Crossrefs

Cf. A000105, A246521, A380597.

Sequence in context: A012887 A177876 A079633 * A285891 A060573 A279086

Adjacent sequences: A380595 A380596 A380597 * A380599 A380600 A380601

Keyword

nonn,tabf,more

Author

Pontus von Brömssen, Jan 27 2025

Status

approved