A317576 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 end a game (n > 0, 0 <= k <= n^2).

0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 21, 21, 58, 23, 15, 0, 0, 0, 0, 0, 0, 0, 280, 642, 4942, 6770, 20286, 16042, 20998, 7970, 3774, 1059, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,6

Comments

If k < n^2, T(n,k) is the number of positions where X (odd k) or O (even k) has won after k plays. T(n,n^2) = A317575(n,n^2) counts draws as well.

The number of draw positions is T(n,n^2) - A317573(n,n^2) for odd n and T(n,n^2) - A317574(n,n^2) for even n.

Links

Table of n, a(n) for n=1..43.

Index entries for sequences related to tic-tac-toe

Formula

For 0 <= k < 2n-1, T(n,k) = 0; T(n,2n-1) > 0.

Example

Triangle begins:
  n\k |  0   1   2   3   4   5   6   7   8   9
  ----+---------------------------------------
   1  |  0   1
   2  |  0   0   0   2   0
   3  |  0   0   0   0   0  21  21  58  23  15

Crossrefs

Cf. A317573-A317575, A048245 (3rd row).

Sequence in context: A053201 A028605 A319532 * A070205 A138363 A080225

Adjacent sequences: A317573 A317574 A317575 * A317577 A317578 A317579

Keyword

nonn,tabf,more

Author

Álvar Ibeas, Jul 31 2018

Status

approved