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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
Main diagonal is A172645.
Sequence in context: A124371 A147989 A119329 * A333901 A054724 A360440
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, May 09 2020
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)