A183652 T(n,k) = number of (n+1) X (k+1) 0..4 arrays with every 2 X 2 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, 2517805

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

Cf. A183643, A183644, A183645, A183646, A183647, A183648, A183649, A183650, A183651.

Cf. A008275, A048994.

Sequence in context: A038472 A020200 A020298 * A183644 A068559 A045017

Adjacent sequences: A183649 A183650 A183651 * A183653 A183654 A183655

Keyword

nonn,tabl,changed

Author

R. H. Hardin, Jan 06 2011

Status

approved