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%I #20 Jul 11 2021 03:41:26
%S 2,3,8,4,52,126,5,184,8460,10016,6,480,143028,14394092,3648810,7,1040,
%T 1217196,1960824272,231197740500,5616280768,8,1988,6835050,
%U 82673548892,443471777729100
%N Table read by downward antidiagonals: T(n,k) is the number of n X n 0..k arrays with no row or column sum equal to the previous one.
%C Table starts
%C 2. 3, 4, 5, 6, 7, 8, ...
%C 8, 52, 184, 480, 1040, 1988, ...
%C 126, 8460, 143028, 1217196, 6835050, ...
%C 10016, 14394092, 1960824272, 82673548892, ...
%C 3648810, 231197740500, 443471777729100, ...
%C 5616280768, ...
%e Some solutions for n=3, k=3:
%e 2 0 3 2 0 1 0 0 3 0 1 3 0 0 3 1 2 1 2 0 3
%e 1 0 0 0 1 3 3 0 2 1 2 3 0 3 2 0 2 3 2 0 0
%e 3 1 0 2 0 0 0 0 1 0 1 3 2 1 0 0 2 1 0 1 3
%Y Rows n=2..4: A035288, A202652, A202653.
%Y Column 3 is A202631.
%K nonn,tabl,more
%O 1,1
%A _R. H. Hardin_, Dec 22 2011