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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 (list; table; graph; refs; listen; history; text; internal format)
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)

LINKS

Table of n, a(n) for n=1..58.

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 A236378 A341880

Adjacent sequences:  A178987 A178988 A178989 * A178991 A178992 A178993

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Jan 03 2011

STATUS

approved

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Last modified September 26 05:00 EDT 2022. Contains 356986 sequences. (Running on oeis4.)