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%I #12 Aug 23 2018 17:08:32
%S 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,
%T 6770,20286,16042,20998,7970,3774,1059,0,0,0,0,0,0,0,0,0
%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 end a game (n > 0, 0 <= k <= n^2).
%C 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.
%C 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.
%H <a href="/index/Th#TTT">Index entries for sequences related to tic-tac-toe</a>
%F For 0 <= k < 2n-1, T(n,k) = 0; T(n,2n-1) > 0.
%e Triangle begins:
%e n\k | 0 1 2 3 4 5 6 7 8 9
%e ----+---------------------------------------
%e 1 | 0 1
%e 2 | 0 0 0 2 0
%e 3 | 0 0 0 0 0 21 21 58 23 15
%Y Cf. A317573-A317575, A048245 (3rd row).
%K nonn,tabf,more
%O 1,6
%A _Álvar Ibeas_, Jul 31 2018
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