cp's OEIS Frontend

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

%I A380597 #7 Jan 29 2025 12:47:06
%S A380597 1,2,3,4,4,0,5,3,7,0,0,0,7,7,6,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A380597 0,0,0,0,0,0,0,0,0,0
%N A380597 Smallest side length of a square board on which Harary's generalized tic-tac-toe (or animal tic-tac-toe) for the free polyomino with binary code A246521(n+1) is a first-player win, or 0 if it is a draw for all board sizes.
%C A380597 The only unknown value is a(45), corresponding to the "long N" hexomino. It has been suggested that a(45) = 15 and A380598(45) = 13.
%C A380597 Can be read as an irregular triangle, whose n-th row contains A000105(n) terms, n >= 1.
%C A380597 The number of free polyominoes of size k = 1, 2, ... for which the game is a first-player win is 1, 1, 2, 4, 3, x, 0, 0, ..., where x is 0 or 1 and all terms after x are 0.
%H A380597 Brady Haran and Sophie Maclean, <a href="https://www.numberphile.com/videos/snakey-hexomino">Snakey Hexomino</a>, Numberphile video, 2025.
%H A380597 Wikipedia, <a href="https://en.wikipedia.org/wiki/Harary&#39;s_generalized_tic-tac-toe">Harary's generalized tic-tac-toe</a>.
%H A380597 James Yolkowski, <a href="https://mathlair.allfunandgames.ca/tictactoe.php">Tic-tac-toe</a>.
%H A380597 <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>.
%H A380597 <a href="/index/Th#TTT">Index entries for sequences related to tic-tac-toe</a>.
%F A380597 a(n) = 0 for all n >= 46.
%e A380597 As an irregular triangle:
%e A380597   1;
%e A380597   2;
%e A380597   3, 4;
%e A380597   4, 0, 5, 3, 7;
%e A380597   0, 0, 0, 7, 7, 6, 0, 0, 0, 0, 0, 0;
%e A380597   ...
%e A380597 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) = 7.
%Y A380597 Cf. A000105, A246521, A380598.
%K A380597 nonn,tabf,more
%O A380597 1,2
%A A380597 _Pontus von Brömssen_, Jan 27 2025