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A183652 T(n,k)=Number of (n+1)X(k+1) 0..4 arrays with every 2X2 subblock summing to 8 10
85, 325, 325, 1333, 1001, 1333, 5725, 3445, 3445, 5725, 25405, 12785, 10213, 12785, 25405, 115525, 50125, 33325, 33325, 50125, 115525, 535333, 205001, 116653, 97145, 116653, 205001, 535333, 2517805, 867205, 431125, 307525, 307525, 431125, 867205 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Table starts
.......85......325......1333.....5725....25405...115525...535333..2517805
......325.....1001......3445....12785....50125...205001...867205..3771425
.....1333.....3445.....10213....33325...116653...431125..1664533..6663805
.....5725....12785.....33325....97145...307525..1037585..3684925.13653545
....25405....50125....116653...307525...889525..2764525..9103453.31446805
...115525...205001....431125..1037585..2764525..7969001.24478885.79273025
...535333...867205...1664533..3684925..9103453.24478885
..2517805..3771425...6663805.13653545.31446805
.11982925.16784125..27510973.52436725
.57575125.76156601.116631205
LINKS
FORMULA
Empirical, for every row and column: a(n)=15*a(n-1)-85*a(n-2)+225*a(n-3)-274*a(n-4)+120*a(n-5)
The coefficient of a(n-i) is -s(6,6-i), s() being the Stirling number of the first kind, via D. S. McNeil and M. F. Hasler in the Sequence Fans Mailing List.
For a 0..z array with 2X2 blocks summing to 2z, the coefficients are -s(z+2,z+2-i)
EXAMPLE
Some solutions for 4X3
..1..1..2....2..2..3....3..3..1....2..3..2....0..2..2....2..1..3....2..3..2
..3..3..2....4..0..3....0..2..2....1..2..1....4..2..2....3..2..2....0..3..0
..2..0..3....2..2..3....2..4..0....1..4..1....2..0..4....1..2..2....1..4..1
..3..3..2....2..2..1....2..0..4....1..2..1....3..3..1....4..1..3....3..0..3
CROSSREFS
Sequence in context: A038472 A020200 A020298 * A183644 A068559 A045017
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Jan 06 2011
STATUS
approved

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Last modified June 14 23:20 EDT 2024. Contains 373401 sequences. (Running on oeis4.)