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 A334549 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. 10
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 7, 7, 1, 1, 1, 1, 19, 31, 19, 1, 1, 1, 1, 51, 175, 175, 51, 1, 1, 1, 1, 141, 991, 2371, 991, 141, 1, 1, 1, 1, 393, 5881, 32611, 32611, 5881, 393, 1, 1, 1, 1, 1107, 35617, 481381, 1084851, 481381, 35617, 1107, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS Equivalently, the number of n X k 0..2 arrays with row sums k and column sums n. LINKS FORMULA T(n,k) = T(k,n). EXAMPLE Array begins: ==================================================================== n\k | 0 1   2     3       4          5            6            7 ----|---------------------------------------------------------------   0 | 1 1   1     1       1          1            1            1 ...   1 | 1 1   1     1       1          1            1            1 ...   2 | 1 1   3     7      19         51          141          393 ...   3 | 1 1   7    31     175        991         5881        35617 ...   4 | 1 1  19   175    2371      32611       481381      7343449 ...   5 | 1 1  51   991   32611    1084851     39612501   1509893001 ...   6 | 1 1 141  5881  481381   39612501   3680774301 360255871641 ...   7 | 1 1 393 35617 7343449 1509893001 360255871641 ...      ... The T(3,2) = 7 matrices are:   [0 0]  [ 0  0]  [ 0  0]  [ 1 -1]  [-1  1]  [ 1 -1]  [-1  1]   [0 0]  [ 1 -1]  [-1  1]  [ 0  0]  [ 0  0]  [-1  1]  [ 1 -1]   [0 0]  [-1  1]  [ 1 -1]  [-1  1]  [ 1 -1]  [ 0  0]  [ 0  0] CROSSREFS Columns k=0..14 are A000012, A000012, A002426, A172634, A172642, A172639, A172633, A172636, A172638, A172641, A172637, A172644, A172640, A172643, A172635. Main diagonal is A172645. Cf. A008300, A333901. Sequence in context: A124371 A147989 A119329 * A333901 A054724 A061494 Adjacent sequences:  A334546 A334547 A334548 * A334550 A334551 A334552 KEYWORD nonn,tabl AUTHOR Andrew Howroyd, May 09 2020 STATUS approved

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Last modified April 16 09:40 EDT 2021. Contains 343030 sequences. (Running on oeis4.)