%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