A184548 T(n,k)=Number of (n+2)X(k+2) binary arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

45, 89, 89, 147, 193, 147, 220, 340, 340, 220, 309, 537, 631, 537, 309, 415, 792, 1048, 1048, 792, 415, 539, 1114, 1627, 1837, 1627, 1114, 539, 682, 1513, 2413, 3024, 3024, 2413, 1513, 682, 845, 2000, 3461, 4774, 5313, 4774, 3461, 2000, 845, 1029, 2587, 4837

Offset: 1

Author

R. H. Hardin, general degree formula intuited by D. S. McNeil in the Sequence Fans Mailing List, Jan 16 2011

Keywords

• nonn
• tabl

Comments

Table starts

...45...89..147...220...309....415....539....682.....845....1029....1235

...89..193..340...537...792...1114...1513...2000....2587....3287....4114

..147..340..631..1048..1627...2413...3461...4837....6619....8898...11779

..220..537.1048..1837..3024...4774...7307..10909...15944...22867...32238

..309..792.1627..3024..5313...8989..14767..23648...36997...56634...84939

..415.1114.2413..4774..8989..16345..28844..49489...82648..134509..213640

..539.1513.3461..7307.14767..28844..54543..99872..177207..305112..510719

..682.2000.4837.10909.23648..49489..99872.194245..364432..660821.1160932

..845.2587.6619.15944.36997..82648.177207.364432..719905.1369596.2516995

.1029.3287.8898.22867.56634.134509.305112.660821.1369596.2725367.5225554

Examples

			Some solutions for 5X4
..0..0..0..1....0..0..0..1....0..0..0..0....0..0..0..1....0..0..0..0
..0..0..1..1....0..0..0..1....0..0..0..0....0..0..1..1....0..0..0..0
..0..0..1..1....0..0..1..1....0..0..0..0....0..0..1..1....0..0..0..0
..0..1..0..0....0..1..0..1....0..0..0..1....0..1..1..1....0..0..1..1
..1..1..0..0....1..1..0..1....1..1..1..0....0..1..1..1....1..1..0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..9378
• R. H. Hardin, Polynomials for columns 1-8

Formula

Empirical: T(n,k) is a polynomial of degree k+2 in n, 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.