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

Author

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

Keywords

• nonn
• tabl

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

Examples

			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
		

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.