A317574 - OEIS

A317574

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 O (n > 0, 0 <= k <= n^2).

%I #12 Aug 23 2018 17:08:05

%S 0,0,0,0,0,0,0,0,0,0,8,5,72,38,56,23,0,0,0,0,0,0,0,0,2476,642,31841,

%T 11251,66364,21718,29258,8496,1335,371

%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 O (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 O 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) - A317573(n,k) - T(n,k).

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

%F For odd 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 | 0 0

%e 2 | 0 0 0 0 0

%e 3 | 0 0 0 8 5 72 38 56 23 0

%Y Cf. A317573, A317575, A317402 (3rd row).

%K nonn,tabf,more

%O 1,11

%A _Álvar Ibeas_, Jul 31 2018