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

1,1

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

Links

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

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

Example

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

Crossrefs

Column 2 is A055795(n+2)

Sequence in context: A267245 A266428 A180985 * A049790 A222188 A368307

Adjacent sequences: A227382 A227383 A227384 * A227386 A227387 A227388

Keyword

nonn,tabl

Author

R. H. Hardin Jul 09 2013

Status

approved