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A178990
T(n,k)=Number of nXk arrays of nonnegative integers with rows and columns in lexicographically increasing order and some row sum or column sum equalling each of the values 1..n+k
0
0, 1, 1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1924, 1924, 0, 0, 0, 0, 19799, 68302, 19799, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3219407612, 25797991623, 25797991623, 3219407612, 0, 0, 0, 0, 0, 0
OFFSET
1,5
COMMENTS
Table starts
.0.1.....0.....0.....0...........0..........0.0.0.0
.1.4.....0.....0.....0...........0..........0.0.0
.0.0.....0..1924.19799...........0..........0.0
.0.0..1924.68302.....0...........0.3219407612
.0.0.19799.....0.....0.25797991623
.0.0.....0.....0
.0.0.....0
.0.0
.0
A solution is possible only if (n+k)*(n+k+1)/2 is even and (n)*(n+1) <= (n+k)*(n+k+1)/2 >= (k)*(k+1)
EXAMPLE
Various solutions
..1......0..1....0..0..1....0..0..0..1....0..0..1....0..0..0..0..1
..2......2..2....0..0..2....0..0..0..2....0..0..2....0..0..0..0..2
.................0..1..3....0..0..4..3....0..0..3....0..0..0..0..3
.................3..4..0....3..4..1..0....0..3..1....0..0..0..3..3
..........................................5..3..0....0..0..5..5..0
.....................................................4..5..2..0..0
...
..0..0..0..1......0..0..0..0..0..1....0..0..0..0..1....0..0..0..1
..0..0..0..2......0..0..0..0..0..2....0..0..0..0..2....0..0..0..2
..0..0..0..3......0..0..0..0..0..3....0..0..0..0..3....0..0..0..3
..0..0..0..4......0..0..0..0..7..3....0..0..0..0..4....0..0..0..4
..0..0..4..1......0..0..3..7..1..0....0..0..0..6..0....0..0..3..2
..0..3..5..0......4..5..3..0..0..0....0..0..8..3..0....0..0..6..0
..6..4..0..0..........................5..7..0..0..0....0..6..1..0
.......................................................8..3..0..0
...
..0..0..0..0..0..0..1......0..0..0..0..0..1....0..0..0..0..1
..0..0..0..0..0..0..2......0..0..0..0..0..2....0..0..0..0..2
..0..0..0..0..0..0..3......0..0..0..0..0..3....0..0..0..0..3
..0..0..0..0..0..0..4......0..0..0..0..0..4....0..0..0..0..4
..0..0..0..0..0..6..2......0..0..0..0..0..5....0..0..0..0..5
..0..0..0..0..8..5..0......0..0..0..0..6..0....0..0..0..6..0
..0..0..3..9..2..0..0......0..0..0..7..5..0....0..0..0..7..0
..5..6..4..0..0..0..0......0..1..9..3..0..0....0..0..7..1..0
...........................7..7..0..0..0..0....0..6..5..0..0
...............................................9..4..0..0..0
CROSSREFS
Sequence in context: A005873 A217511 A307380 * A276570 A360543 A236378
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Jan 03 2011
STATUS
approved