A317573 Irregular triangle read by rows: T(n,k) is the number of n X n tic-tac-toe positions (up to rotation and reflection) with k tokens (i.e., after k plays) which allow a winning strategy for X (n > 0, 0 <= k <= n^2).

1, 1, 1, 1, 2, 2, 0, 0, 0, 7, 9, 85, 67, 139, 70, 23, 12, 0, 0, 0, 0, 0, 0, 1100, 280, 26771, 11535, 91567, 36362, 78138, 26146, 12900, 3774, 0

Offset

1,5

Comments

Only positions occurring in a game are counted. This excludes, for instance, those with two complete lines.

Positions where X has already won are included.

The number of positions headed for a draw (provided that both players play their best moves from there on) is A317575(n,k) - T(n,k) - A317574(n,k).

Links

Table of n, a(n) for n=1..34.

Index entries for sequences related to tic-tac-toe

Formula

For even n, T(n,n^2) = 0.

Example

Triangle begins:
  n\k |  0   1   2   3   4   5   6   7   8   9
  ----+---------------------------------------
   1  |  1   1
   2  |  1   1   2   2   0
   3  |  0   0   7   9  85  67 139  70  23  12

Crossrefs

Cf. A317574, A317575, A317401 (3rd row).

Sequence in context: A285244 A263148 A230819 * A032337 A058190 A055736

Adjacent sequences: A317570 A317571 A317572 * A317574 A317575 A317576

Keyword

nonn,tabf,more

Author

Álvar Ibeas, Jul 31 2018

Status

approved