

A317576


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


0



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
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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 tictactoe


FORMULA

For 0 <= k < 2n1, T(n,k) = 0; T(n,2n1) > 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. A317573A317575, 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



