A183652 T(n,k)=Number of (n+1)X(k+1) 0..4 arrays with every 2X2 subblock summing to 8

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

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

R. H. Hardin, Table of n, a(n) for n = 1..84

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

Adjacent sequences: A183649 A183650 A183651 * A183653 A183654 A183655

Keyword

nonn,tabl

Author

R. H. Hardin Jan 06 2011

Status

approved