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A334549
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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.
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10
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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
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OFFSET
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0,13
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COMMENTS
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Equivalently, the number of n X k 0..2 arrays with row sums k and column sums n.
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LINKS
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FORMULA
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T(n,k) = T(k,n).
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EXAMPLE
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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]
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CROSSREFS
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Columns k=0..14 are A000012, A000012, A002426, A172634, A172642, A172639, A172633, A172636, A172638, A172641, A172637, A172644, A172640, A172643, A172635.
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KEYWORD
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AUTHOR
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STATUS
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approved
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