A185435 T(n,k)=Number of (n+2)X(k+2) 0..7 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order

6842284, 284037544, 284037544, 8653394212, 21536560306, 8653394212, 212298419684, 1090205284029, 1090205284029, 212298419684, 4370405405266, 41910604337378, 84722449466168, 41910604337378, 4370405405266

Offset

1,1

Comments

Table starts

.............6842284..............284037544................8653394212

...........284037544............21536560306.............1090205284029

..........8653394212..........1090205284029............84722449466168

........212298419684.........41910604337378..........4772160687307074

.......4370405405266.......1297535366114472........209290512833668811

......77657199293322......33575010264022917.......7468756070356586903

....1216284173329482.....745543958045415621.....223694029250999654095

...17062128865116751...14492443009379677098....5755145891541173071730

..217083576402029968..250496452202647761530..129520045203909930078682

.2530473438240068012.3898612401674733619729.2587203198419699686906895

Links

R. H. Hardin, Table of n, a(n) for n = 1..83

R. H. Hardin, Polynomials for columns 1-3

Formula

Empirical: T(n,k) is a polynomial of degree 7k+112, for fixed k

Let T(n,k,z) be the number of (n+2)X(k+2) 0..z arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order

Then empirically T(n,k,z) is a polynomial of degree z*k + z*(z+1)*(z+5)/6 in n, for fixed k.

Example

Some solutions for 5X4
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..0..4....0..0..0..0....0..0..0..0....0..0..0..4
..0..1..1..2....0..0..2..3....0..1..4..5....0..0..5..6....0..0..6..7
..0..3..7..3....0..7..0..5....0..2..1..6....2..2..6..4....0..4..3..0

Crossrefs

Sequence in context: A088238 A079015 A372085 * A185427 A185426 A250457

Adjacent sequences: A185432 A185433 A185434 * A185436 A185437 A185438

Keyword

nonn,tabl

Author

R. H. Hardin, General degree formula intuited by D. S. McNeil in the Sequence Fans Mailing List, Jan 27 2011

Status

approved