

A317574


Irregular triangle read by rows: T(n,k) is the number of n X n tictactoe 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).


3



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
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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 tictactoe


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 A239862
Adjacent sequences: A317571 A317572 A317573 * A317575 A317576 A317577


KEYWORD

nonn,tabf,more


AUTHOR

Álvar Ibeas, Jul 31 2018


STATUS

approved



