A227385 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 one, with rows and columns of the latter in lexicographically nondecreasing order.

2, 3, 3, 4, 7, 4, 5, 15, 15, 5, 6, 30, 54, 30, 6, 7, 56, 185, 185, 56, 7, 8, 98, 587, 1104, 587, 98, 8, 9, 162, 1704, 6160, 6160, 1704, 162, 9, 10, 255, 4532, 31073, 61127, 31073, 4532, 255, 10, 11, 385, 11126, 141192, 550010, 550010, 141192, 11126, 385, 11, 12, 561

Offset: 1

Author

R. H. Hardin Jul 09 2013

Keywords

• nonn
• tabl

Comments

Table starts

..2...3.....4.......5.........6...........7...........8...........9..........10

..3...7....15......30........56..........98.........162.........255.........385

..4..15....54.....185.......587........1704........4532.......11126.......25430

..5..30...185....1104......6160.......31073......141192......581706.....2192737

..6..56...587....6160.....61127......550010.....4450124....32473856...215116595

..7..98..1704...31073....550010.....8988949...133142369..1779353333.21501389691

..8.162..4532..141192...4450124...133142369..3657501287.91016881301

..9.255.11126..581706..32473856..1779353333.91016881301

.10.385.25430.2192737.215116595.21501389691

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..111

Crossrefs

Column 2 is A055795(n+2)

Formula

Empirical for column k:

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

k=2: a(n) = (1/24)*n^4 + (1/12)*n^3 + (11/24)*n^2 + (17/12)*n + 1

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

k=4: [polynomial of degree 19] for n>7

k=5: [polynomial of degree 39] for n>22