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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).
3

%I #13 Aug 23 2018 17:07:37

%S 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,

%T 11535,91567,36362,78138,26146,12900,3774,0

%N 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).

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

%C Positions where X has already won are included.

%C 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).

%H <a href="/index/Th#TTT">Index entries for sequences related to tic-tac-toe</a>

%F For even n, T(n,n^2) = 0.

%e Triangle begins:

%e n\k | 0 1 2 3 4 5 6 7 8 9

%e ----+---------------------------------------

%e 1 | 1 1

%e 2 | 1 1 2 2 0

%e 3 | 0 0 7 9 85 67 139 70 23 12

%Y Cf. A317574, A317575, A317401 (3rd row).

%K nonn,tabf,more

%O 1,5

%A _Álvar Ibeas_, Jul 31 2018