A317574 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 O (n > 0, 0 <= k <= n^2).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 5, 72, 38, 56, 23, 0, 0, 0, 0, 0, 0, 0, 0, 2476, 642, 31841, 11251, 66364, 21718, 29258, 8496, 1335, 371

Offset

1,11

Comments

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

Positions where O 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) - A317573(n,k) - T(n,k).

Links

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

Index entries for sequences related to tic-tac-toe

Formula

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

Example

Triangle begins:
  n\k |  0   1   2   3   4   5   6   7   8   9
  ----+---------------------------------------
   1  |  0   0
   2  |  0   0   0   0   0
   3  |  0   0   0   8   5  72  38  56  23   0

Crossrefs

Cf. A317573, A317575, A317402 (3rd row).

Sequence in context: A296437 A038283 A317402 * A195532 A106287 A361711

Adjacent sequences: A317571 A317572 A317573 * A317575 A317576 A317577

Keyword

nonn,tabf,more

Author

Álvar Ibeas, Jul 31 2018

Status

approved