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A377063 Array read by antidiagonals: T(n,k) is the number of {-1,0,1} n X k matrices with all rows and columns summing to zero up to permutations of rows.

%I A377063 #9 Oct 15 2024 15:42:54
%S A377063 1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,4,2,1,1,1,1,10,6,3,1,1,1,1,26,30,
%T A377063 12,3,1,1,1,1,71,166,117,18,4,1,1,1,1,197,981,1421,345,30,4,1,1,1,1,
%U A377063 554,5937,20326,9691,1042,42,5,1,1,1,1,1570,36646,307063,336596,63076,2746,63,5,1,1
%N A377063 Array read by antidiagonals: T(n,k) is the number of {-1,0,1} n X k matrices with all rows and columns summing to zero up to permutations of rows.
%C A377063 Columns are not permutable.
%C A377063 Equivalently, the number of n X k 0..2 arrays with row sums k and column sums n up to permutations of rows.
%H A377063 Andrew Howroyd, <a href="/A377063/b377063.txt">Table of n, a(n) for n = 0..434</a> (first 29 antidiagonals)
%e A377063 Array begins:
%e A377063 ===================================================
%e A377063 n\k | 0 1 2  3    4      5        6           7 ...
%e A377063 ----+----------------------------------------------
%e A377063   0 | 1 1 1  1    1      1        1           1 ...
%e A377063   1 | 1 1 1  1    1      1        1           1 ...
%e A377063   2 | 1 1 2  4   10     26       71         197 ...
%e A377063   3 | 1 1 2  6   30    166      981        5937 ...
%e A377063   4 | 1 1 3 12  117   1421    20326      307063 ...
%e A377063   5 | 1 1 3 18  345   9691   336596    12650093 ...
%e A377063   6 | 1 1 4 30 1042  63076  5328136   506525279 ...
%e A377063   7 | 1 1 4 42 2746 369036 76292516 18490880339 ...
%e A377063   ...
%Y A377063 Main diagonal is A377064.
%Y A377063 Rows n=0..4 are A000012, A000012, A257520, A377065, A377066.
%Y A377063 Columns k=0..4 are A000012, A000012, A008619, A377067, A377068.
%Y A377063 Cf. A334549.
%K A377063 nonn,tabl
%O A377063 0,13
%A A377063 _Andrew Howroyd_, Oct 14 2024