cp's OEIS Frontend

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.

%I A380598 #8 Jan 29 2025 12:47:17
%S A380598 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,
%T A380598 0,0,0,0,0,0,0,0,0,0
%N 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.
%C A380598 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.
%C A380598 Can be read as an irregular triangle, whose n-th row contains A000105(n) terms, n >= 1.
%H A380598 Brady Haran and Sophie Maclean, <a href="https://www.numberphile.com/videos/snakey-hexomino">Snakey Hexomino</a>, Numberphile video, 2025.
%H A380598 Wikipedia, <a href="https://en.wikipedia.org/wiki/Harary&#39;s_generalized_tic-tac-toe">Harary's generalized tic-tac-toe</a>.
%H A380598 James Yolkowski, <a href="https://mathlair.allfunandgames.ca/tictactoe.php">Tic-tac-toe</a>.
%H A380598 <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>.
%H A380598 <a href="/index/Th#TTT">Index entries for sequences related to tic-tac-toe</a>.
%F A380598 a(n) = 0 for all n >= 46.
%e A380598 As an irregular triangle:
%e A380598   1;
%e A380598   2;
%e A380598   3, 3;
%e A380598   4, 0, 4,  5, 8;
%e A380598   0, 0, 0, 10, 9, 6, 0, 0, 0, 0, 0, 0;
%e A380598   ...
%e A380598 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.
%Y A380598 Cf. A000105, A246521, A380597.
%K A380598 nonn,tabf,more
%O A380598 1,2
%A A380598 _Pontus von Brömssen_, Jan 27 2025