A227263 T(n,k)=Number of nXk 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(k+1) binary array having a sum of two or less, with rows and columns of the latter in lexicographically nondecreasing order.

2, 3, 3, 4, 9, 4, 5, 23, 23, 5, 6, 50, 98, 50, 6, 7, 96, 353, 353, 96, 7, 8, 168, 1111, 2201, 1111, 168, 8, 9, 274, 3136, 11932, 11932, 3136, 274, 9, 10, 423, 8065, 57146, 112349, 57146, 8065, 423, 10, 11, 625, 19146, 244818, 937865, 937865, 244818, 19146, 625, 11

Offset: 1

Author

R. H. Hardin Jul 04 2013

Keywords

• nonn
• tabl

Comments

Table starts

..2...3.....4.......5.........6...........7...........8...........9

..3...9....23......50........96.........168.........274.........423

..4..23....98.....353......1111........3136........8065.......19146

..5..50...353....2201.....11932.......57146......244818......951917

..6..96..1111...11932....112349......937865.....6961606....46364258

..7.168..3136...57146....937865....13855163...182525275..2147322451

..8.274..8065..244818...6961606...182525275..4307345460.90839025368

..9.423.19146..951917..46364258..2147322451.90839025368

.10.625.42385.3403038.280471755.22777463128

Examples

			Some solutions for n=4 k=4
..1..1..0..0....1..1..1..1....1..1..1..1....1..1..1..0....1..1..1..1
..1..0..0..0....1..0..0..1....1..0..0..1....1..0..0..1....1..1..0..1
..1..1..1..0....1..0..0..1....1..1..0..1....0..0..1..1....1..0..1..1
..1..1..1..0....1..1..0..0....1..1..0..0....0..0..1..1....0..0..1..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..112

Formula

Empirical for column k:

k=1: a(n) = n + 1

k=2: a(n) = (1/24)*n^4 + (5/12)*n^3 + (11/24)*n^2 + (13/12)*n + 1

k=3: [polynomial of degree 9] for n>5

k=4: [polynomial of degree 19] for n>9

k=5: [polynomial of degree 39] for n>20