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A317573
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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).
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3
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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
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OFFSET
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1,5
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COMMENTS
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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).
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LINKS
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FORMULA
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For even n, T(n,n^2) = 0.
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EXAMPLE
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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
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CROSSREFS
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KEYWORD
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nonn,tabf,more
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AUTHOR
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STATUS
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approved
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